# A Study of the Spatial Effects of Financial Support and Economic Growth under Optimal Control of Nonlinear Generalized Complex Systems

Authors: Xuexue Tang
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

This paper provides an in-depth analysis and study of the spatial effects of financial support and economic growth with the help of nonlinear generalized complex systems. Taking the industrial sector as the research object and combining the relevant contents of neoclassical investment theory, information economics, and institutional economics, this paper clearly defines and argues that the main feature of current financial policy is financial constraint rather than financial inhibition based on an in-depth understanding of the theoretical connotation and policy rationality of financial constraint and, as a premise, further analyzes the financial constraint policy causing excessive investment and capital mismatch in the corporate sector. It further analyzes the mechanism of the role of financial constraint policies in causing overinvestment and capital mismatch in the corporate sector and conducts empirical tests from three research perspectives of measuring investment efficiency, output efficiency of investment, allocation efficiency of industry capital, and investment behavior of microenterprises, and finally puts forward relevant policy recommendations in conjunction with the evaluation of the efficiency of financial constraint policies. This paper selects three dimensions of the financial system, namely, financial structure, financial efficiency, and financial scale, and studies the adaptability between these three dimensions and the development of the real economy, respectively, and then uses different empirical methods to analyze the dynamic adaptability effects between the development of the real economy and these three dimensions of the financial system and finally explores the way of adaptability between the financial system and the development of the real economy. This paper provides a medium and micro theoretical basis and new empirical evidence for understanding the importance of financial system reform on economic growth and also opens up a space for exploring the exit path of financial constraints and using interest rate marketization as a general grip to reasonably guide financial resources to achieve economic transformation and upgrading and sustainable and healthy development through supporting high-quality investment, using more interprovincial level data in the analysis, so it is more comprehensive and detailed than previous scholars’ studies. The examination is more comprehensive and detailed than previous scholars’ studies.


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## Body

## 1. Introduction

As the fastest engine to jump-start the economy and an important policy tool for macroeconomic regulation, investment has played a leading role in maintaining high economic growth [1]. However, with the economy entering a new normal, structural contradictions such as overcapacity have become increasingly prominent, and the continued low efficiency of investment, mainly manifested by excessive investment and declining efficiency of capital allocation, has become an important constraint on sustainable economic growth. The traditional economic growth model of high investment for high growth is unsustainable, and the shift from focusing on the scale of investment to improving the quality and efficiency of investment, improving investment efficiency, cultivating, and strengthening new drivers of economic growth will become an important focus of economic development in the next phase [2]. The key to effectively enhance investment efficiency lies in identifying the causes of investment inefficiency. However, as the economy has entered a new normal, structural contradictions such as overcapacity have become increasingly prominent. The continuous decline in investment efficiency, which is mainly manifested by excessive investment and the decline in the efficiency of capital allocation, has become an important incentive to restrict sustainable economic growth. In recent years, there was a time when the overcapacity industry had deteriorating profitability and high leverage, as well as the phenomenon of high nonperforming loan ratio and its increase. The immediate motivation for enterprises’ overinvestment and overindebtedness closely related to their behavior is the relatively low external financing cost, which is generally attributed by the theoretical community to unreasonable government intervention. Excessive or unreasonable government intervention can distort the price of funds, resulting in an inefficient allocation of capital, making the financial market unable to exert a positive regulatory effect on the real economy through the price mechanism, which in turn greatly increases the probability of inefficient corporate investment. Therefore, the financial system or financial policy becomes a key breakthrough in studying and improving the efficiency of investment. In recent years, industries with overcapacity have experienced deteriorating profitability, high leverage, high nonperforming loan ratios, and high growth rates. The direct cause of corporate overinvestment and overindebtedness is the relatively low cost of external financing. Theorists generally attribute it to the unreasonable government intervention.The global financial crisis of 2008 led to financial market turmoil in major developed economies, stagnant market liquidity, and a credit crunch, which in turn led to a deep economic recession. Before that, few would have anticipated the onset of the crisis or some of the aftermath, including interest rates near liquidity trap levels in many advanced economies, inflation running below target levels, and, in many economies, weak economic growth [3]. In the context of financial instability as we now understand it, where interest rate floors and cyclical recessions have been threatening the world today, strong stabilization policies are key; and monetary policy, as an important stabilization policy, is bound to be the key of keys. Central banks in many countries have seen the need to adopt new stabilization policies to influence the financial system to stabilize prices and output [4]. This has spawned a discussion of the complex linkages between macroeconomics, the financial system, and monetary policy. The relationship between monetary policy, systemic risk in the financial system, and macroeconomics has become a major topic in the postcrisis era, receiving unprecedented attention.If the economy is the muscle, then finance is the bloodline. Only when the blood vessels are open can the organism of the national economy continue to grow and develop healthily and stably [5]. Finance is also a double-edged sword that has both positive and negative effects on the growth of the real economy. If finance serves the real economy with a variety of functions, it will promote the growth and development of the real economy; on the contrary, if financial development and the growth and development of the real economy are disconnected, not synchronized, not coordinated, or even there is financial “strutting,” as well as “self-indulgence,” then eventually the results of economic growth and development will certainly be reversed. At present, with the financial disengagement, economic overcapacity, and capital market irregularities, the Government proposed to carry out financial supply-side reform to achieve financial services to the real economy; in this context, the study of the endogenous role of financial development on the economy and the study of the mechanism of financial development on economic growth and efficiency issues, both theoretically and practically, have greater significance.


## 2. Related Works

The scope of theoretical research on financial development has been extended from developing countries to developed countries, and the content of research has been expanded from how developing countries promote economic growth through financial deepening to how they promote capital accumulation and technological progress through financial development and further expanded from a specific view of financial institutions to a general view of financial functions [6]. The relationship between the financial system and economic development is inextricably linked, and scholars have studied both in greater depth and more literature. Since the general trend of the real economy and economic development is consistent, the previous studies on the relationship between the financial system and economic development also have a greater reference value [7]. The proposed financial structure theory has been widely recognized in developed countries and is more compatible with the economic conditions of developed countries, and the financial structure theory has also laid the theoretical foundation for the empirical analysis of financial development and economic growth. Excessive government intervention suppresses the free development of financial markets [8]. In the context of financial instability as we now understand, the lower bound of interest rates and cyclical recessions are threatening the world today. Therefore, a strong stabilization policy is the key. As an important stabilization policy, monetary policy will inevitably become the key. Based on various characteristics of financial markets in developing countries, they put forward the financial suppression theory and the financial deepening theory, respectively. The financial suppression theory encourages the promotion of financial liberalization, which greatly contributes to financial efficiency in developing countries, thus increasing the efficiency of converting savings into an investment [9]. By examining the development of the US financial system, it is argued that while the real sector of the economy has shown a more important role in the growth of the modern US economy, the financial system is the real source of economic growth. An empirical study of stock markets and economic growth in developed countries uses the control variables approach, ignoring irrelevant factors and maintaining stock market fallibility, ultimately concluding through empirical analysis that stock markets are conducive to economic growth [10]. After studying the relationship between the financial sector and the real economy after the financial crisis, it is argued that the link between the two is very complex and the models adopted by researchers can lead to opposing conclusions. Policymakers must use a series of complementary models in their research to compensate for the shortcomings of individual models [11].In turn, the credit expansion in the derivative process is achieved by money sinking or withdrawing from circulation. Second, the mismatch between short-term liabilities and long-term assets is a way of leveraging. The main reference here is to commercial banks, which use the funds incorporated on the short-term liability side for unwinding funds on the long-term asset side. For commercial banks, their liabilities and assets are mismatched in terms of maturity structure, realizing the process of leverage. Third, structural differences in financial institutions are another way of leveraging [12]. Consider banks of different sizes, such as large-scale and small-scale banks, with large-scale banks having easier access to funds from the central bank and the household sector and small-scale banks having relatively more difficulty. Economic growth or economic development is, of course, an extremely complex concept [13]. A simple quantitative increase does not mean that economic development is optimal for society, nor can it even be called “progress.” As resource-consuming growth is increasingly revealing its shortcomings and environmental pollution is becoming increasingly serious, how to seek sustainable development has become a worldwide concern [14]. It is believed that developed countries in Europe and the United States are under pressure to deleverage financial products, financial institutions, investors, and consumers in four areas, and, even along with deleveraging, developed countries in the European Union are also trying to deglobalize [15]. This will have a huge impact and influence on the recovery of the world economy.From the macrofinancial structure, the imbalance in the financial structure will lead to geographical differences in financial development, but, at this stage, the imbalance in the supply of financial assets makes China’s corporate financing needs more satisfied through indirect financing, and the imbalance in the open knot leads to the restricted inflow of foreign capital into the country, and the function of optimizing resource allocation in the financial market has not yet fully functioned [16]. From the perspective of the structure of the financial industry, financial institutions must play the role of the main force in the process of serving the real economy. At present, China’s financial system still has the problem of “derealization to deficiency,” with funds flowing within the financial system or to the real estate market, and the funds required by the real economy cannot be met, which has led to high financing costs for the real economy and difficulties in financing and expensive financing for enterprises. Through studying the development process of the American financial system, it is believed that, in the process of modern American economic growth, although the real economic sector has shown a more important role, the financial system is the real source of economic growth. When conducting empirical research on the stock market and economic growth of developed countries, the controlled variable method is used, irrelevant factors are ignored, the stock market is volatile, and the stock market is finally conducive to economic growth through empirical analysis. Then solving the problem of imbalance in financial structure will help to enhance the ability of financial services to the real economy. The financial system plays the function of optimizing resource allocation and is an important driving force for supply-side structural reform. The real economy is the root of finance, and financial efficiency that is detached from the real economy is of no practical significance. Financial efficiency should be closely focused on the main line of serving the real economy, but the flow of financial resources within the financial system and inadequate information will all reduce financial efficiency, so it is necessary to look for factors that inhibit financial efficiency at the source and address the problem of low financial efficiency at its root.


## 3. Analysis of the Spatial Effects of Optimal Control Financial Support and Economic Growth for Nonlinear Generalized Complex Systems

### 3.1. Design of Nonlinear Generalized Complex Systems with Optimal Control

At the early stage of the development of generalized systems, the fundamental theory of generalized systems was discussed more systematically, thus marking a new stage of development in the research on the fundamental theory of generalized systems. In the following years, the research work on generalized systems received increased attention from experts and scholars in different fields of control and achieved an impressive and vigorous development [17]. A generalized system is a powerful tool for portraying and describing real systems, and the generalized system model is proposed with a profound background of practical applications and exists in many fields of social production. Based on the above fundamental research on generalized systems and the complexity of practical engineering problems, important results have been achieved in various aspects of generalized systems research, from linear to nonlinear, from deterministic to uncertain, from time-invariant to time-varying, from continuous to discrete, from time-lagless to time-lagged, from interference-free to interference, and from deterministic to uncertain.The cointegration relationship is one of the important correlations that may exist between long memory processes, which have typical statistical features and rich economic significance. In the process of studying cointegration relations, econometric scholars have formed an increasingly comprehensive theoretical understanding of the modeling methods of cointegration relations and the corresponding economic explanations, and relatively mature modeling and analysis tools have been formed. A simple increase in quantity does not mean that the economic development of the entire society has reached the best state, nor can it even be called “progress.” As the growth of resource consumption has increasingly exposed its drawbacks and environmental pollution has become increasingly serious, how to seek sustainable development has become an issue of concern to the world. Firstly, the connotations of some important concepts in cointegration theory are introduced. These concepts are the basis on which the whole text can be developed. Then, an introduction to the unit root test tool is given. A unit root test is a fundamental tool for analyzing the long memory characteristics of a sequence, and the long memory of the variables is a prerequisite for the cointegration relationship to hold. Next, the model settings used in the analysis of cointegrating relationships, the test methods for cointegrating relationships, and the parameter estimation methods in the analysis of cointegrating relationships are introduced. In time series analysis, nonlinear relationships and variable structure phenomena are sometimes encountered. The form of the nonlinear parametric model is more complicated, but its modeling idea is like that of the linear model, which is to analyze and predict the series by studying the recurrence relationship of the series group. However, the variable structure phenomenon interrupts the recurrence relationship of sequence groups. To analyze and study time series with variable structure phenomenon, some new research tools are needed. Therefore, this chapter provides a separate introduction to modeling tools for variable structure phenomena in time series analysis. The research tools discussed above are mainly based on parametric econometric models and parametric statistical methods. Nonparametric kernel regression methods are presented next. Finally, based on the above tools, this chapter investigates the application of kernel regression methods in cointegration modeling, as shown in Figure1.Figure 1
Nonlinear generalized complex system.The monetary policy stabilization mechanism of action refers to the mechanism of action of how the implementation of monetary policy affects various aspects of the stabilization objective. The elaboration of this mechanism of action is an important objective of monetary theory and is closely related to whether monetary policy is effective enough to play the role of regulating the real economy. This means that monetary policy either needs to be changed more sharply to achieve the original objective or is excluded from stabilization policy [18]. The real economy is the foundation of finance, and financial efficiency without real economy is meaningless. Financial efficiency must focus on the main line of serving the real economy, but the circulation of financial resources within the financial system and insufficient information will reduce financial efficiency. Therefore, it is necessary to find the factors that inhibit financial efficiency from the source and solve the problem of financial inefficiency from the root. Therefore, to effectively achieve the stabilization objective, monetary policymakers must have an accurate understanding of the stabilization mechanism of monetary policy. In the theoretical evolution of the stabilization mechanism of monetary policy, different schools of thought have developed different theories depending on their theoretical assumptions and so forth.(1)Ext=Axt−But2,•yt2=Cxt2.The control and stability analysis of generalized systems is an important part of the research, and there have been many well-formed research results on the control analysis and solution of generalized systems, such as the design problems of state observers and dynamic compensators, the design of parametric controllers, the sedimentation problem, linear quadratic optimal control, robust control, and optimal control. The iterative learning control problem applies to the controlled system with repetitive operation characteristics, and the main contents of the research include the construction of the iterative learning control algorithm, the convergence and stability of the learning algorithm, the tracking performance and convergence speed of the system, the initial learning and the initial value problem, the robustness of the learning process, and the application of the iterative learning control problem. The study of iterative learning control does not require the exact dynamics of the system and the controller design is simple in structure and computationally small, making it very far-reaching for more practical application problems.(2)x•kt=fxkt2,ukt,t,ykt=gCxt.x•kt, xkt2, and ukt are the state variables, control variables, and output variables of the system at the kth operation, respectively. The proposal of iterative learning control theory itself has a strong engineering background, and the establishment development and refinement of this theory will inevitably lead to the fast performance of complex dynamical systems for repetitive operational tasks. The study of iterative learning control problems will play an increasingly important role as other application areas continue to develop. Changes in the state of a system are caused by events such as the creation or disappearance of certain conditions, certain operations, or manipulations. Discrete-time generalized systems are a class of systems in which all or key component variables have discrete signal forms and the state of the system changes at discrete points in time, and its analysis of motion generally boils down to the solution of the differential state equation. The theory of discrete-time generalized systems is widely used in social, economic, and engineering systems, such as automata, impulse control, sampling regulation, and digital control.(3)Ext=Axt−But,yt=−Cxt.Discrete-time generalized systems have promoted the development of intelligent control and gradually become a hot spot in modern control theory research, but the research on iterative learning control algorithms for discrete-time generalized systems is still in its early stages. The application of iterative learning control algorithms to discrete-time generalized systems is to achieve complete tracking of the system infinite time intervals, and this method does not rely on the exact mathematical model of the controlled discrete generalized system and only requires system inputs and error signals, and the algorithm structure is simple with a small computational burden, which will be a popular research topic shortly. In this paper, based on the dynamics of discrete-time generalized systems, we apply the restricted equivalence transformation of generalized systems to reduce the relatively complex generalized system to a special form with a simple structure and then analyze and study it. The PD-type iterative learning control law is applied to the system, which enables the system output to effectively track the desired trajectory in a finite time interval.(4)I0tαft=∫0tft2dgtτ.For complex systems, each subsystem has its degree of freedom and relative independence, and the inputs and outputs of each subsystem cannot be perfectly coordinated; there must be redundant and insufficient inputs and outputs [19]. These redundant and insufficient inputs and outputs become system disturbances, which are random, sudden, and unpredictable. With the increase of modern control requirements, uncertainties and disturbances need to be fully considered, so the study of generalized fractional-order systems with disturbances has important theoretical and practical significance and is also in urgent demand.(5)EDtαxkt=Axkt−Bxkt,ykt=−Cxkt.Nonlinearity is common in practical production life; if the system contains one or more elements with nonlinear characteristics, it is called a nonlinear system. The nonlinear theory is an important subdiscipline in automatic control theory; with the economic development and scientific and technological progress, the nonlinear problems of controlled systems have attracted a lot of attention from scholars, and nonlinear analysis and its applications have become one of the important branches in the field of mathematics, which has received the attention of experts at home and abroad. A new method is to obtain the threshold of the pulsed nonlinear stochastic constant zero models with saturated growth rate in a polluted environment. According to the theory of pulsed differential equation and stochastic differential equation, the conditions for extinction and maintenance of persistence of microorganisms in deterministic constant zero model and stochastic constant zero are obtained, as shown in Figure2.Figure 2
Nonlinear optimal control principle.Interference is system-independent; in the process of signal input, transmission, and output of some unwanted various uncertainties, interference is always present and inevitable. For complex systems, each subsystem has its degree of freedom and relative independence, the input and output of each subsystem cannot be perfect, and there must be redundant and insufficient input and output. These redundant and insufficient inputs and outputs become system disturbances. Based on the basic research of singular systems and the complexity of practical engineering problems, the research content of singular systems has achieved important results. These results include the nonlinearity, uncertainty, time variation, and discreteness of the system. With the increase in modern control requirements, uncertainties and disturbances need to be fully considered. This also poses a serious challenge to study the control problems of the system. Traditional control theories and methods are difficult to solve the state tracking problems of such uncertain complex systems, and iterative learning control provides new ideas and ways to solve the control problems of such systems. For nonlinear generalized fractional-order systems, iterative learning control techniques belong to model-free control system synthesis methods, which are also essentially applicable to such nonlinear generalized fractional-order systems. Therefore, in this section, the main object of study is a class of nonlinear generalized fractional-order complex systems and their iterative learning control problems are considered. By making control attempts on the controlled system, a suitable iterative learning control law is used to achieve the task of complete tracking of the system over a finite time interval.


### 3.2. Analysis of the Spatial Effects of Financial Support and Economic Growth

The direct financing sector helps the surplus fund units to buy financial products directly from the production units, and the direct transfer of funds to the production units can facilitate R&D and production in the production units, and investors voting with their feet can motivate producers to improve the quality of their products. For the demanders of funds, the pricing of loans, to whom funds are lent or not, is not determined by the initial suppliers of funds but to a large extent or even essentially by the banks, thus giving rise to the rationality of bank credit facilities. Rationality in bank credit funding implies that banks will decide on the flow of credit funds based on their economic efficiency drive. This may exacerbate interregional imbalances in economic growth [20]. If the monetary policy stabilization mechanism is blocked, then the monetary policy cannot effectively achieve the ultimate goal, which means that the monetary policy either will need to make more substantial changes to achieve the original goal or will be excluded from the stabilization policy. Therefore, in order to effectively achieve the goal of stabilization, monetary policymakers must accurately grasp the mechanism of monetary policy stabilization. The higher the level of economic development of a region is, the more bank loan funds it receives, which is conducive to the growth of the local economy, hence a virtuous circle; conversely, the lower the level of economic development of a region is, the less bank loan funds it receives, which is detrimental to the growth of the local economy, hence a vicious circle. Similarly, the rationing of bank credit funds can lead to a virtuous or vicious cycle for different enterprises.The indirect financing quantity-based mechanism of action refers mainly to the promotion of economic growth by banks through the channel of capital accumulation. As pointed out in the previous model, this mechanism mainly involves the conversion of savings into an investment using banks increasing the size of their loans, so that material inputs can be expanded to drive economic growth. The process of converting incoming savings deposits into loan investments by banks is subject to a variety of factors and does not convert all savings into investments. What proportion of savings is then converted into investment is influenced not only by bank interest rates but also by the efficiency of bank staff in an increasingly market-oriented financial world. Banks must take the savings deposits they receive and eventually disburse them to form loans. Banks need to be particularly careful in granting loans and to screen and examine the qualifications of the loan recipients, which requires the efforts of bank staff; otherwise, the loans granted will easily form bad and doubtful debts. Of course, the efficiency of bank staff is in turn significantly affected by the bank’s business management system, as shown in Table1.Table 1
Comparison table of fixed-effects corrections.
Classification(1)(2)(3)(4)Previous model0.3470.7330.1830.332Mechanism0.1380.2690.3180.64Size of their loans0.4460.5520.6420.694Economic growth0.7360.1740.4720.442Converting investments0.7020.5980.3240.207The liquidity risk of microeconomic agents is the extent to which they can liquidate their assets quickly without suffering losses. It is then easy to understand the reason why the real property is less liquid than securities. A considerable part of the reason why assets cannot be liquidated quickly comes from the uncertainty and information asymmetry in the asset conversion process. The development of direct financing markets eliminates the need for the time and cost of finding a counterparty to a transaction, simply by selling the stocks and bonds held for cash in the secondary or liquid market. In this chapter, the main research object is a class of nonlinear generalized fractional-order complex systems, and its iterative learning control problem is considered. By trying to control the controlled system and adopting a suitable iterative learning control law, the complete tracking task of the system in a limited time interval is realized. Business operational risk refers to the process of production and operation of enterprises, as well as the supply, production, and sales of their goods in all aspects of the uncertainty factors, resulting in a delay in the movement of corporate funds, which leads to changes in the value of the enterprise. As competition between firms increases, the operational risk faced by firms also increases. In the context of direct financing, corporate managers can successfully spread the operational risk of the firm through stock market financing and pass it on to each investor in the stock.(6)limδuk−1λ≥1.The theory is that appropriate financial constraints can promote economic development to a certain extent; for example, in less developed countries, where the financial system is also relatively backward, the government should adopt a series of financial constraints, including the legalization of financial management, elimination of credit rationing, marketization of financial asset prices, and liberalization of competition among financial institutions, under the premise of macroeconomic stability, especially low inflation to provide financial sector and the productive sector to create opportunities for excess returns to alleviate the incentive problems of financial institutions and the corporate sector due to information asymmetries, thereby promoting financial deepening and economic growth. For those in need of funds, the price of loans is not determined by the initial supplier of funds but by the bank to a large extent, and this has resulted in bank credit funds. The rationing of bank credit funds means that banks will determine the flow of credit funds based on their own economic benefits. This may exacerbate the imbalance in economic growth between regions.At the same time, however, selective government intervention should be dynamically adjusted in line with the degree of financial deepening. As financial development proceeds, the government should gradually ease financial constraints to facilitate the economy’s transition to a free market.The use of a fixed-effect model or random-effect model directly affects the accuracy of the regression, and the Hausman test is a common treatment to test whether the panel data is the fixed or random effect when dealing with panel data. With the spatial Durbin model identified, the Hausman test will be conducted in this paper and the results are shown in Figure3; the Hausman test statistic is positive with a p value of 0.0004, significant at the 1% level, so the original hypothesis is rejected and the alternative hypothesis that there is a fixed effect is accepted.Figure 3
Hausman test.From the results of the spatial Durbin model test with two-way fixed effects in time and space in the third column, only the coefficients of financial industry scale structure, financial market structure, and financial openness structure pass the significance test, among which the coefficients of financial industry scale structure and financial market structure are positive; that is, financial industry scale structure and financial market structure can promote the level of development of the real economy, but the coefficient of financial openness structure coefficient is negative, indicating that the greater the degree of financial openness is, on the contrary, the more detrimental it is to the development of the real economy. The coefficients of the other explanatory variables financing structure, banking industry structure, securities industry structure, and insurance industry structure and the level of development of the real economy are all positive, but none of them pass the significance test. Banks need to be particularly cautious when issuing loans. They need to screen and examine the qualifications of the loan recipients. This requires the efforts of bank staff. Otherwise, the loans issued will easily lead to bad debts. Of course, the working efficiency of bank staff is greatly affected by the bank’s management system.First, the size of financial leverage did not move significantly in line with economic growth rates. The size of financial leverage in emerging economies is largely on an upward trend, but economic growth rates in emerging economies are mixed; the size of financial leverage in developed economies and all countries in the sample is marginally on the rise, but economic growth rates are also mixed. Second, there is no homogeneous trend between the size of financial leverage and economic growth rate; that is, it is not the case that the higher the size of financial leverage, the higher the economic growth rate. Emerging economies have lower financial leverage than developed economies, yet their economic growth rates are consistently higher than those of developed economies.


## 3.1. Design of Nonlinear Generalized Complex Systems with Optimal Control

At the early stage of the development of generalized systems, the fundamental theory of generalized systems was discussed more systematically, thus marking a new stage of development in the research on the fundamental theory of generalized systems. In the following years, the research work on generalized systems received increased attention from experts and scholars in different fields of control and achieved an impressive and vigorous development [17]. A generalized system is a powerful tool for portraying and describing real systems, and the generalized system model is proposed with a profound background of practical applications and exists in many fields of social production. Based on the above fundamental research on generalized systems and the complexity of practical engineering problems, important results have been achieved in various aspects of generalized systems research, from linear to nonlinear, from deterministic to uncertain, from time-invariant to time-varying, from continuous to discrete, from time-lagless to time-lagged, from interference-free to interference, and from deterministic to uncertain.The cointegration relationship is one of the important correlations that may exist between long memory processes, which have typical statistical features and rich economic significance. In the process of studying cointegration relations, econometric scholars have formed an increasingly comprehensive theoretical understanding of the modeling methods of cointegration relations and the corresponding economic explanations, and relatively mature modeling and analysis tools have been formed. A simple increase in quantity does not mean that the economic development of the entire society has reached the best state, nor can it even be called “progress.” As the growth of resource consumption has increasingly exposed its drawbacks and environmental pollution has become increasingly serious, how to seek sustainable development has become an issue of concern to the world. Firstly, the connotations of some important concepts in cointegration theory are introduced. These concepts are the basis on which the whole text can be developed. Then, an introduction to the unit root test tool is given. A unit root test is a fundamental tool for analyzing the long memory characteristics of a sequence, and the long memory of the variables is a prerequisite for the cointegration relationship to hold. Next, the model settings used in the analysis of cointegrating relationships, the test methods for cointegrating relationships, and the parameter estimation methods in the analysis of cointegrating relationships are introduced. In time series analysis, nonlinear relationships and variable structure phenomena are sometimes encountered. The form of the nonlinear parametric model is more complicated, but its modeling idea is like that of the linear model, which is to analyze and predict the series by studying the recurrence relationship of the series group. However, the variable structure phenomenon interrupts the recurrence relationship of sequence groups. To analyze and study time series with variable structure phenomenon, some new research tools are needed. Therefore, this chapter provides a separate introduction to modeling tools for variable structure phenomena in time series analysis. The research tools discussed above are mainly based on parametric econometric models and parametric statistical methods. Nonparametric kernel regression methods are presented next. Finally, based on the above tools, this chapter investigates the application of kernel regression methods in cointegration modeling, as shown in Figure1.Figure 1
Nonlinear generalized complex system.The monetary policy stabilization mechanism of action refers to the mechanism of action of how the implementation of monetary policy affects various aspects of the stabilization objective. The elaboration of this mechanism of action is an important objective of monetary theory and is closely related to whether monetary policy is effective enough to play the role of regulating the real economy. This means that monetary policy either needs to be changed more sharply to achieve the original objective or is excluded from stabilization policy [18]. The real economy is the foundation of finance, and financial efficiency without real economy is meaningless. Financial efficiency must focus on the main line of serving the real economy, but the circulation of financial resources within the financial system and insufficient information will reduce financial efficiency. Therefore, it is necessary to find the factors that inhibit financial efficiency from the source and solve the problem of financial inefficiency from the root. Therefore, to effectively achieve the stabilization objective, monetary policymakers must have an accurate understanding of the stabilization mechanism of monetary policy. In the theoretical evolution of the stabilization mechanism of monetary policy, different schools of thought have developed different theories depending on their theoretical assumptions and so forth.(1)Ext=Axt−But2,•yt2=Cxt2.The control and stability analysis of generalized systems is an important part of the research, and there have been many well-formed research results on the control analysis and solution of generalized systems, such as the design problems of state observers and dynamic compensators, the design of parametric controllers, the sedimentation problem, linear quadratic optimal control, robust control, and optimal control. The iterative learning control problem applies to the controlled system with repetitive operation characteristics, and the main contents of the research include the construction of the iterative learning control algorithm, the convergence and stability of the learning algorithm, the tracking performance and convergence speed of the system, the initial learning and the initial value problem, the robustness of the learning process, and the application of the iterative learning control problem. The study of iterative learning control does not require the exact dynamics of the system and the controller design is simple in structure and computationally small, making it very far-reaching for more practical application problems.(2)x•kt=fxkt2,ukt,t,ykt=gCxt.x•kt, xkt2, and ukt are the state variables, control variables, and output variables of the system at the kth operation, respectively. The proposal of iterative learning control theory itself has a strong engineering background, and the establishment development and refinement of this theory will inevitably lead to the fast performance of complex dynamical systems for repetitive operational tasks. The study of iterative learning control problems will play an increasingly important role as other application areas continue to develop. Changes in the state of a system are caused by events such as the creation or disappearance of certain conditions, certain operations, or manipulations. Discrete-time generalized systems are a class of systems in which all or key component variables have discrete signal forms and the state of the system changes at discrete points in time, and its analysis of motion generally boils down to the solution of the differential state equation. The theory of discrete-time generalized systems is widely used in social, economic, and engineering systems, such as automata, impulse control, sampling regulation, and digital control.(3)Ext=Axt−But,yt=−Cxt.Discrete-time generalized systems have promoted the development of intelligent control and gradually become a hot spot in modern control theory research, but the research on iterative learning control algorithms for discrete-time generalized systems is still in its early stages. The application of iterative learning control algorithms to discrete-time generalized systems is to achieve complete tracking of the system infinite time intervals, and this method does not rely on the exact mathematical model of the controlled discrete generalized system and only requires system inputs and error signals, and the algorithm structure is simple with a small computational burden, which will be a popular research topic shortly. In this paper, based on the dynamics of discrete-time generalized systems, we apply the restricted equivalence transformation of generalized systems to reduce the relatively complex generalized system to a special form with a simple structure and then analyze and study it. The PD-type iterative learning control law is applied to the system, which enables the system output to effectively track the desired trajectory in a finite time interval.(4)I0tαft=∫0tft2dgtτ.For complex systems, each subsystem has its degree of freedom and relative independence, and the inputs and outputs of each subsystem cannot be perfectly coordinated; there must be redundant and insufficient inputs and outputs [19]. These redundant and insufficient inputs and outputs become system disturbances, which are random, sudden, and unpredictable. With the increase of modern control requirements, uncertainties and disturbances need to be fully considered, so the study of generalized fractional-order systems with disturbances has important theoretical and practical significance and is also in urgent demand.(5)EDtαxkt=Axkt−Bxkt,ykt=−Cxkt.Nonlinearity is common in practical production life; if the system contains one or more elements with nonlinear characteristics, it is called a nonlinear system. The nonlinear theory is an important subdiscipline in automatic control theory; with the economic development and scientific and technological progress, the nonlinear problems of controlled systems have attracted a lot of attention from scholars, and nonlinear analysis and its applications have become one of the important branches in the field of mathematics, which has received the attention of experts at home and abroad. A new method is to obtain the threshold of the pulsed nonlinear stochastic constant zero models with saturated growth rate in a polluted environment. According to the theory of pulsed differential equation and stochastic differential equation, the conditions for extinction and maintenance of persistence of microorganisms in deterministic constant zero model and stochastic constant zero are obtained, as shown in Figure2.Figure 2
Nonlinear optimal control principle.Interference is system-independent; in the process of signal input, transmission, and output of some unwanted various uncertainties, interference is always present and inevitable. For complex systems, each subsystem has its degree of freedom and relative independence, the input and output of each subsystem cannot be perfect, and there must be redundant and insufficient input and output. These redundant and insufficient inputs and outputs become system disturbances. Based on the basic research of singular systems and the complexity of practical engineering problems, the research content of singular systems has achieved important results. These results include the nonlinearity, uncertainty, time variation, and discreteness of the system. With the increase in modern control requirements, uncertainties and disturbances need to be fully considered. This also poses a serious challenge to study the control problems of the system. Traditional control theories and methods are difficult to solve the state tracking problems of such uncertain complex systems, and iterative learning control provides new ideas and ways to solve the control problems of such systems. For nonlinear generalized fractional-order systems, iterative learning control techniques belong to model-free control system synthesis methods, which are also essentially applicable to such nonlinear generalized fractional-order systems. Therefore, in this section, the main object of study is a class of nonlinear generalized fractional-order complex systems and their iterative learning control problems are considered. By making control attempts on the controlled system, a suitable iterative learning control law is used to achieve the task of complete tracking of the system over a finite time interval.


## 3.2. Analysis of the Spatial Effects of Financial Support and Economic Growth

The direct financing sector helps the surplus fund units to buy financial products directly from the production units, and the direct transfer of funds to the production units can facilitate R&D and production in the production units, and investors voting with their feet can motivate producers to improve the quality of their products. For the demanders of funds, the pricing of loans, to whom funds are lent or not, is not determined by the initial suppliers of funds but to a large extent or even essentially by the banks, thus giving rise to the rationality of bank credit facilities. Rationality in bank credit funding implies that banks will decide on the flow of credit funds based on their economic efficiency drive. This may exacerbate interregional imbalances in economic growth [20]. If the monetary policy stabilization mechanism is blocked, then the monetary policy cannot effectively achieve the ultimate goal, which means that the monetary policy either will need to make more substantial changes to achieve the original goal or will be excluded from the stabilization policy. Therefore, in order to effectively achieve the goal of stabilization, monetary policymakers must accurately grasp the mechanism of monetary policy stabilization. The higher the level of economic development of a region is, the more bank loan funds it receives, which is conducive to the growth of the local economy, hence a virtuous circle; conversely, the lower the level of economic development of a region is, the less bank loan funds it receives, which is detrimental to the growth of the local economy, hence a vicious circle. Similarly, the rationing of bank credit funds can lead to a virtuous or vicious cycle for different enterprises.The indirect financing quantity-based mechanism of action refers mainly to the promotion of economic growth by banks through the channel of capital accumulation. As pointed out in the previous model, this mechanism mainly involves the conversion of savings into an investment using banks increasing the size of their loans, so that material inputs can be expanded to drive economic growth. The process of converting incoming savings deposits into loan investments by banks is subject to a variety of factors and does not convert all savings into investments. What proportion of savings is then converted into investment is influenced not only by bank interest rates but also by the efficiency of bank staff in an increasingly market-oriented financial world. Banks must take the savings deposits they receive and eventually disburse them to form loans. Banks need to be particularly careful in granting loans and to screen and examine the qualifications of the loan recipients, which requires the efforts of bank staff; otherwise, the loans granted will easily form bad and doubtful debts. Of course, the efficiency of bank staff is in turn significantly affected by the bank’s business management system, as shown in Table1.Table 1
Comparison table of fixed-effects corrections.
Classification(1)(2)(3)(4)Previous model0.3470.7330.1830.332Mechanism0.1380.2690.3180.64Size of their loans0.4460.5520.6420.694Economic growth0.7360.1740.4720.442Converting investments0.7020.5980.3240.207The liquidity risk of microeconomic agents is the extent to which they can liquidate their assets quickly without suffering losses. It is then easy to understand the reason why the real property is less liquid than securities. A considerable part of the reason why assets cannot be liquidated quickly comes from the uncertainty and information asymmetry in the asset conversion process. The development of direct financing markets eliminates the need for the time and cost of finding a counterparty to a transaction, simply by selling the stocks and bonds held for cash in the secondary or liquid market. In this chapter, the main research object is a class of nonlinear generalized fractional-order complex systems, and its iterative learning control problem is considered. By trying to control the controlled system and adopting a suitable iterative learning control law, the complete tracking task of the system in a limited time interval is realized. Business operational risk refers to the process of production and operation of enterprises, as well as the supply, production, and sales of their goods in all aspects of the uncertainty factors, resulting in a delay in the movement of corporate funds, which leads to changes in the value of the enterprise. As competition between firms increases, the operational risk faced by firms also increases. In the context of direct financing, corporate managers can successfully spread the operational risk of the firm through stock market financing and pass it on to each investor in the stock.(6)limδuk−1λ≥1.The theory is that appropriate financial constraints can promote economic development to a certain extent; for example, in less developed countries, where the financial system is also relatively backward, the government should adopt a series of financial constraints, including the legalization of financial management, elimination of credit rationing, marketization of financial asset prices, and liberalization of competition among financial institutions, under the premise of macroeconomic stability, especially low inflation to provide financial sector and the productive sector to create opportunities for excess returns to alleviate the incentive problems of financial institutions and the corporate sector due to information asymmetries, thereby promoting financial deepening and economic growth. For those in need of funds, the price of loans is not determined by the initial supplier of funds but by the bank to a large extent, and this has resulted in bank credit funds. The rationing of bank credit funds means that banks will determine the flow of credit funds based on their own economic benefits. This may exacerbate the imbalance in economic growth between regions.At the same time, however, selective government intervention should be dynamically adjusted in line with the degree of financial deepening. As financial development proceeds, the government should gradually ease financial constraints to facilitate the economy’s transition to a free market.The use of a fixed-effect model or random-effect model directly affects the accuracy of the regression, and the Hausman test is a common treatment to test whether the panel data is the fixed or random effect when dealing with panel data. With the spatial Durbin model identified, the Hausman test will be conducted in this paper and the results are shown in Figure3; the Hausman test statistic is positive with a p value of 0.0004, significant at the 1% level, so the original hypothesis is rejected and the alternative hypothesis that there is a fixed effect is accepted.Figure 3
Hausman test.From the results of the spatial Durbin model test with two-way fixed effects in time and space in the third column, only the coefficients of financial industry scale structure, financial market structure, and financial openness structure pass the significance test, among which the coefficients of financial industry scale structure and financial market structure are positive; that is, financial industry scale structure and financial market structure can promote the level of development of the real economy, but the coefficient of financial openness structure coefficient is negative, indicating that the greater the degree of financial openness is, on the contrary, the more detrimental it is to the development of the real economy. The coefficients of the other explanatory variables financing structure, banking industry structure, securities industry structure, and insurance industry structure and the level of development of the real economy are all positive, but none of them pass the significance test. Banks need to be particularly cautious when issuing loans. They need to screen and examine the qualifications of the loan recipients. This requires the efforts of bank staff. Otherwise, the loans issued will easily lead to bad debts. Of course, the working efficiency of bank staff is greatly affected by the bank’s management system.First, the size of financial leverage did not move significantly in line with economic growth rates. The size of financial leverage in emerging economies is largely on an upward trend, but economic growth rates in emerging economies are mixed; the size of financial leverage in developed economies and all countries in the sample is marginally on the rise, but economic growth rates are also mixed. Second, there is no homogeneous trend between the size of financial leverage and economic growth rate; that is, it is not the case that the higher the size of financial leverage, the higher the economic growth rate. Emerging economies have lower financial leverage than developed economies, yet their economic growth rates are consistently higher than those of developed economies.


## 4. Analysis of Results

### 4.1. Optimal Control of Nonlinear Generalized Complex System Performance

The maximum tracking trajectory error curve of the system is given in Figure4. Based on the trajectory shown in the figure, for a known desired trajectory, the output error of the system gradually converges to zero as the number of iterations increases, and full tracking can be achieved using the proposed iterative learning algorithm.Figure 4
Tracking trajectory of the system for the system’s desired output trajectory as a tracking curve graph.For complex systems, each subsystem has its degree of freedom and relative independence, and the inputs and outputs of each subsystem cannot be perfectly coordinated; there must be redundant and insufficient inputs and outputs, and these redundant and insufficient inputs and outputs become the system interference. Interference always exists in real-life and industrial production applications, especially state interference. For fractional-order systems, the learning of state disturbances is crucial. The state of the system may be affected by noise and disturbances due to various uncertainties in the real system. With the development of science and technology and the improvement of modern control requirements, uncertainties and disturbance phenomena need to be fully considered, so there is an important theoretical and practical significance and an urgent need to study generalized fractional-order systems with disturbances. The financial system is also relatively backward. The government should adopt a series of financial restraint measures under the preconditions of macroeconomic stability, especially low inflation rate, including the legalization of financial management, the abolition of credit rationing, the marketization of financial asset prices, and financial institutions. The liberalization of competition creates opportunities for the financial sector and the production sector to obtain excess returns, so as to alleviate the incentive problems of financial institutions and corporate sectors due to information asymmetry, thereby promoting financial deepening and economic growth. However, traditional control theories and methods are difficult to solve the state tracking problems of such uncertain complex systems, and iterative learning control provides new ideas and approaches to solve the control problems of such systems. This includes generalized nonlinear fractional-order systems, generalized nonlinear time-lag fractional-order systems, and generalized nonlinear fractional-order systems with state disturbances. To accomplish the tracking objective on a finite time interval, a suitable iterative learning control algorithm is applied to the system according to the dynamics of the system itself, the sufficiency condition for the convergence of the system output to the desired output is given, and the validity and correctness of the system convergence results are verified by arithmetic simulation, which extends the results of the existing references and greatly enriches the study of iterative learning control theory for generalized systems. Comparing the two types of models, it can be found that, in the credit constraint relaxation model and the benchmark model, the impulse responses of macroeconomic variables to housing preference shocks are consistent. However, as the proportion of loan value increases, the credit-constrained financial friction mechanism has enabled the real estate sector to obtain more credit resources; on the contrary, the credit scale of the real economy sector has fallen more.Comparing the two types of models, it can be observed that the impulse responses of macroeconomic variables to housing preference shocks are consistent in the credit constraint relaxation model and the benchmark model. However, as the loan-to-value ratio becomes larger, the credit constraint financial friction mechanism allows the real estate sector to access more credit resources; conversely, the real economy sector experiences a greater decline in the size of the credit. In addition, the financial friction mechanism in the banking sector allows more credit resources to be allocated to the real estate sector and a larger increase in net assets in the banking sector as the easing of credit markets makes banks more willing to lend. The increase in real estate investment is greater under the housing preference shock compared to the benchmark model; residential land and real estate capital prices increase more significantly; meanwhile, investment, employment, and output in the real sector of the economy fall more, as shown in Figure5.Figure 5
Comparison of the baseline model with the credit constraint relaxation model.
(a)(b)Based on the basics of the state space of generalized systems, the restricted equivalence transformations are applied, and the relatively complex generalized systems are reduced to a special form with a simple structure based on the characteristics of the restricted equivalence changes of generalized systems to maintain the qualitative nature of the system, and then they are studied analytically. For the second type of equation, iterative learning control problems for linear and nonlinear generalized impulsive systems are discussed based on the iterative learning control theory of impulsive differential equations. With the help of the linearization of nonlinear factors, some new results are obtained by applying the proposed iterative learning control law. For the third class of systems, the iterative learning control algorithm for fractional-order systems is applied to generalized fractional-order systems based on the research basis of fractional-order differential equations. The iterative learning control problems for generalized fractional-order time-lag systems and generalized fractional-order systems with state disturbances are discussed. Through the study of the above problems and iterative learning control algorithms, the basic theoretical framework of iterative learning control for generalized systems is established, and the application scope of modern control theory methods is enriched and developed.


### 4.2. Analysis of the Results of the Spatial Effects of Financial Support and Economic Growth

As for the control variables, the degree of industrialization hurts economic volatility; that is, the degree of industrialization increases, and the degree of economic volatility decreases, which means that the more the economy relies on developed and mature industrialization, the more likely it is to remain stable; the fitted results for both developed and emerging economies fail the significance test, but both pass the 1% significance test in the overall sample. The capital formation rate has a significant positive effect on economic volatility; in the model, both pass the 1% significance test, which indicates that the capital formation rate, which represents an investment, has a greater impact on economic stimulus and exacerbates economic volatility; in the model, for example, for every 1% increase in the capital formation rate, economic volatility will increase by 0.63%. The inflation rate has a positive effect on economic volatility, inflation affects the economy from all aspects of consumption and production, directly or indirectly exacerbating economic volatility, and this effect is relatively insignificant in emerging economies, as shown in Figure6.Figure 6
Systematic estimates of money growth rate on economic volatility.As for the core explanatory variables, the growth rate of total financial leverage has a significant positive effect on economic volatility; that is, the higher the growth rate of total financial leverage, the higher the economic volatility. The growth rate of total financial leverage has an extremely significant positive correlation with the growth rate of the economy, which has been verified, and the higher the growth rate of total financial leverage, the higher the growth rate of the economy, which itself implies greater economic volatility, except that the direction of economic volatility is consistent with the direction of change in the size of total financial leverage. The squared term of the growth rate of total financial leverage hurts economic volatility, which leads to the assumption that there may be a nonlinear effect of the growth rate of total financial leverage on economic volatility. The capital formation rate has a significant positive impact on the economic volatility. In the model, it can pass the 1% significance test. This shows that the capital formation rate, which represents investment, has a greater impact on economic stimulus and aggravates economic volatility. Taking the model as an example, for every 1% increase in the capital formation rate, the economic volatility rate will increase by 0.63%.Compared to time series data, the use of panel data analysis can eliminate the bias in the overall estimates due to individual differences. However, in economic growth, endogeneity is a more common and very problematic issue, and the presence of endogeneity can bias the model estimates. The role of instrumental variables in the empirical analysis is particularly prominent, and therefore the validity of instrumental variables needs to be tested statistically first to find valid instrumental variables that can be used to test the endogeneity of the explanatory variables. Therefore, before doing the empirical analysis, a unit root test is performed on the panel data to determine whether the sample data is a smooth panel, which is an important reference for subsequent empirical modeling. Several commonly used panel unit root tests have been described in detail and will not be repeated in this chapter. According to the analysis of previous scholars, based on the principle of “minority follows majority,” if most of the method test is smooth, the indicator is judged to be smooth, as shown in Figure7.Figure 7
Spatial series smoothness test results.Looking at the two-zone systems divided by the threshold effect, the coefficient is positive and significant at the 1% level for both zone systems. When the stock of financial size is less than the threshold, the coefficient is 1.1217, and when the level of financial development increases by 1%, it will make the level of real economic development increase by 1.12%, but when the stock of financial size is greater than 13.2371, the coefficient decreases to 1.085, which means that when the stock of financial size exceeds a certain amount, with the further increase of financial size, the level of financial development on the real economy still has a driving effect on the growth rate of the real economy as the financial size increases further, but the marginal effect will be slightly reduced, and when the level of financial development increases by 1%, the level of real economic development will increase by 1.09%. Although the coefficient of financial development level does not change much after exceeding the threshold value of financial scale stock, from the actual situation of the financial market, the role of promoting the development of real economy should not be underestimated because of the large value of financial development level indicator.It is worth noting, however, that the level of financial development within the threshold interval is higher than its average level in terms of its contribution to the real economy. Therefore, it also shows that there is a limit to the growth of the total financial stock in the country and that, within a certain interval, financial development has a strong contribution to the real economy, and once this interval is exceeded, financial development can still contribute to the development of the real economy, but its marginal effect is reduced, which has important practical implications for the development of the financial system and the real economy.


## 4.1. Optimal Control of Nonlinear Generalized Complex System Performance

The maximum tracking trajectory error curve of the system is given in Figure4. Based on the trajectory shown in the figure, for a known desired trajectory, the output error of the system gradually converges to zero as the number of iterations increases, and full tracking can be achieved using the proposed iterative learning algorithm.Figure 4
Tracking trajectory of the system for the system’s desired output trajectory as a tracking curve graph.For complex systems, each subsystem has its degree of freedom and relative independence, and the inputs and outputs of each subsystem cannot be perfectly coordinated; there must be redundant and insufficient inputs and outputs, and these redundant and insufficient inputs and outputs become the system interference. Interference always exists in real-life and industrial production applications, especially state interference. For fractional-order systems, the learning of state disturbances is crucial. The state of the system may be affected by noise and disturbances due to various uncertainties in the real system. With the development of science and technology and the improvement of modern control requirements, uncertainties and disturbance phenomena need to be fully considered, so there is an important theoretical and practical significance and an urgent need to study generalized fractional-order systems with disturbances. The financial system is also relatively backward. The government should adopt a series of financial restraint measures under the preconditions of macroeconomic stability, especially low inflation rate, including the legalization of financial management, the abolition of credit rationing, the marketization of financial asset prices, and financial institutions. The liberalization of competition creates opportunities for the financial sector and the production sector to obtain excess returns, so as to alleviate the incentive problems of financial institutions and corporate sectors due to information asymmetry, thereby promoting financial deepening and economic growth. However, traditional control theories and methods are difficult to solve the state tracking problems of such uncertain complex systems, and iterative learning control provides new ideas and approaches to solve the control problems of such systems. This includes generalized nonlinear fractional-order systems, generalized nonlinear time-lag fractional-order systems, and generalized nonlinear fractional-order systems with state disturbances. To accomplish the tracking objective on a finite time interval, a suitable iterative learning control algorithm is applied to the system according to the dynamics of the system itself, the sufficiency condition for the convergence of the system output to the desired output is given, and the validity and correctness of the system convergence results are verified by arithmetic simulation, which extends the results of the existing references and greatly enriches the study of iterative learning control theory for generalized systems. Comparing the two types of models, it can be found that, in the credit constraint relaxation model and the benchmark model, the impulse responses of macroeconomic variables to housing preference shocks are consistent. However, as the proportion of loan value increases, the credit-constrained financial friction mechanism has enabled the real estate sector to obtain more credit resources; on the contrary, the credit scale of the real economy sector has fallen more.Comparing the two types of models, it can be observed that the impulse responses of macroeconomic variables to housing preference shocks are consistent in the credit constraint relaxation model and the benchmark model. However, as the loan-to-value ratio becomes larger, the credit constraint financial friction mechanism allows the real estate sector to access more credit resources; conversely, the real economy sector experiences a greater decline in the size of the credit. In addition, the financial friction mechanism in the banking sector allows more credit resources to be allocated to the real estate sector and a larger increase in net assets in the banking sector as the easing of credit markets makes banks more willing to lend. The increase in real estate investment is greater under the housing preference shock compared to the benchmark model; residential land and real estate capital prices increase more significantly; meanwhile, investment, employment, and output in the real sector of the economy fall more, as shown in Figure5.Figure 5
Comparison of the baseline model with the credit constraint relaxation model.
(a)(b)Based on the basics of the state space of generalized systems, the restricted equivalence transformations are applied, and the relatively complex generalized systems are reduced to a special form with a simple structure based on the characteristics of the restricted equivalence changes of generalized systems to maintain the qualitative nature of the system, and then they are studied analytically. For the second type of equation, iterative learning control problems for linear and nonlinear generalized impulsive systems are discussed based on the iterative learning control theory of impulsive differential equations. With the help of the linearization of nonlinear factors, some new results are obtained by applying the proposed iterative learning control law. For the third class of systems, the iterative learning control algorithm for fractional-order systems is applied to generalized fractional-order systems based on the research basis of fractional-order differential equations. The iterative learning control problems for generalized fractional-order time-lag systems and generalized fractional-order systems with state disturbances are discussed. Through the study of the above problems and iterative learning control algorithms, the basic theoretical framework of iterative learning control for generalized systems is established, and the application scope of modern control theory methods is enriched and developed.


## 4.2. Analysis of the Results of the Spatial Effects of Financial Support and Economic Growth

As for the control variables, the degree of industrialization hurts economic volatility; that is, the degree of industrialization increases, and the degree of economic volatility decreases, which means that the more the economy relies on developed and mature industrialization, the more likely it is to remain stable; the fitted results for both developed and emerging economies fail the significance test, but both pass the 1% significance test in the overall sample. The capital formation rate has a significant positive effect on economic volatility; in the model, both pass the 1% significance test, which indicates that the capital formation rate, which represents an investment, has a greater impact on economic stimulus and exacerbates economic volatility; in the model, for example, for every 1% increase in the capital formation rate, economic volatility will increase by 0.63%. The inflation rate has a positive effect on economic volatility, inflation affects the economy from all aspects of consumption and production, directly or indirectly exacerbating economic volatility, and this effect is relatively insignificant in emerging economies, as shown in Figure6.Figure 6
Systematic estimates of money growth rate on economic volatility.As for the core explanatory variables, the growth rate of total financial leverage has a significant positive effect on economic volatility; that is, the higher the growth rate of total financial leverage, the higher the economic volatility. The growth rate of total financial leverage has an extremely significant positive correlation with the growth rate of the economy, which has been verified, and the higher the growth rate of total financial leverage, the higher the growth rate of the economy, which itself implies greater economic volatility, except that the direction of economic volatility is consistent with the direction of change in the size of total financial leverage. The squared term of the growth rate of total financial leverage hurts economic volatility, which leads to the assumption that there may be a nonlinear effect of the growth rate of total financial leverage on economic volatility. The capital formation rate has a significant positive impact on the economic volatility. In the model, it can pass the 1% significance test. This shows that the capital formation rate, which represents investment, has a greater impact on economic stimulus and aggravates economic volatility. Taking the model as an example, for every 1% increase in the capital formation rate, the economic volatility rate will increase by 0.63%.Compared to time series data, the use of panel data analysis can eliminate the bias in the overall estimates due to individual differences. However, in economic growth, endogeneity is a more common and very problematic issue, and the presence of endogeneity can bias the model estimates. The role of instrumental variables in the empirical analysis is particularly prominent, and therefore the validity of instrumental variables needs to be tested statistically first to find valid instrumental variables that can be used to test the endogeneity of the explanatory variables. Therefore, before doing the empirical analysis, a unit root test is performed on the panel data to determine whether the sample data is a smooth panel, which is an important reference for subsequent empirical modeling. Several commonly used panel unit root tests have been described in detail and will not be repeated in this chapter. According to the analysis of previous scholars, based on the principle of “minority follows majority,” if most of the method test is smooth, the indicator is judged to be smooth, as shown in Figure7.Figure 7
Spatial series smoothness test results.Looking at the two-zone systems divided by the threshold effect, the coefficient is positive and significant at the 1% level for both zone systems. When the stock of financial size is less than the threshold, the coefficient is 1.1217, and when the level of financial development increases by 1%, it will make the level of real economic development increase by 1.12%, but when the stock of financial size is greater than 13.2371, the coefficient decreases to 1.085, which means that when the stock of financial size exceeds a certain amount, with the further increase of financial size, the level of financial development on the real economy still has a driving effect on the growth rate of the real economy as the financial size increases further, but the marginal effect will be slightly reduced, and when the level of financial development increases by 1%, the level of real economic development will increase by 1.09%. Although the coefficient of financial development level does not change much after exceeding the threshold value of financial scale stock, from the actual situation of the financial market, the role of promoting the development of real economy should not be underestimated because of the large value of financial development level indicator.It is worth noting, however, that the level of financial development within the threshold interval is higher than its average level in terms of its contribution to the real economy. Therefore, it also shows that there is a limit to the growth of the total financial stock in the country and that, within a certain interval, financial development has a strong contribution to the real economy, and once this interval is exceeded, financial development can still contribute to the development of the real economy, but its marginal effect is reduced, which has important practical implications for the development of the financial system and the real economy.


## 5. Conclusion

From the econometric analysis of the financial structure and real economic development through the spatial Durbin model, the results of the direct effect indicate that the local financial market structure, financial openness structure, and securities industry structure have a direct impact on the changes in the level of development of the real economy. The results of indirect effects show that the spillover effects of financial industry scale structure and financial market structure are larger, and through the flow of financial resources between geographically close provinces and cities, the full sharing and effective complementation of financial resources can be achieved, thus enhancing the level of development of the real economy. There is a two-way dynamic adaptation effect between the financial system and the development of the real economy, but when the financial system and the real economy produce changes, the mutual impact is asymmetrical. The financial system and the development of the real economy should be matched in terms of not only the total amount but, more importantly, structural suitability. The development of the financial structure is unbalanced with the development of the real economy; it is highly correlated with the real economy in terms of the financing structure, but the development of the open structure and the instrument structure is lagging. The unreasonable open structure also makes the scale of foreign currency financing small, still dominated by market financing, and the degree of market openness still needs to be improved. In addition, the supply of funds in the financial system is misaligned with the demand of the real economy, and sectors in the real economy cannot obtain services from corresponding financial channels promptly, such as the dominance of state-owned banks in the banking sector, the relatively large share of total stocks and bonds issued by state-owned enterprises, and the unreasonable allocation of the instrument structure, which leads to the high efficiency of financial services to enterprises.



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*Source: 2834009-2022-01-04.xml*