# Organization Learning Oriented Approach with Application to Discrete Flight Control

Authors: Lin Yu; Shixing Wang; Yongan Zheng
Journal: Discrete Dynamics in Nature and Society
 (2016)

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## Abstract

In nature and society, there exist many learning modes; thus, in this paper the goal is to incorporate features from the social organizations to improve the learning of intelligent systems. Inspired by future prediction, in the high level, the discrete dynamics is further written into the equivalent prediction model which can provide the bridge from now to the future. In the low level, the efficiency could be improved in way of group learning. The philosophy is integrated into discrete neural flight control where the cascade dynamics is written into the prediction form and the minimal-learning-parameter technique is designed for parameter learning. The effectiveness of the proposed method is verified with simulation.


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## Body

## 1. Introduction

Optimization and control exist everywhere in nature and society. Human beings are trying all their best to learn from the nature to see how the optimization is going by observing the process of biology. Genetic algorithm [1] is proposed in use of techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. By mimicking ants’ behavior to find food with pheromone trail, ant colony optimization [2] is widely studied. Similarly, there exist many other evolutionary algorithms, such as particle swarm optimization [3] and estimation of distribution algorithm [4].During the controller design, different systems are analyzed such as strict-feedback system [5], pure-feedback system [6], networked system [7], and multiagent system [8]. One main topic is to deal with the uncertainty. For example, unknown parameters widely exist in many industrial processes and therefore intelligent control is an important area in several decades. Towards the unknown dynamics, fuzzy logic system (FLS) [9, 10] and neural networks (NNs) [11–14] are widely employed as function approximation. In view of approximation role, in the indirect design [9, 15], the functions are approximated separately and then the controller is constructed. In the direct design, the desired control input is approximated by the NN [16–18]. While many papers are with backstepping scheme [19] to deal with complex dynamics, the interesting design [20–22] is developed without backstepping by transforming the dynamics into the new form. Also adaptive dynamic programming [23–26] or reinforcement learning [27–29] is gaining more and more attention since the optimal performance is expected.In nature and society, discrete signals are everywhere. For example, the population statistics and migration are all in discrete-time domain. With the new development of hardware, applications are required with digital computer or microprocessor. As a result, the controller design in discrete case is widely studied [30–33]. In particular, for flight vehicle and robotic systems [34, 35], the online algorithm should be produced by the digital computer and one concern is the computation burden. How to define the efficient learning algorithm is crucial for online application.For social organization, it is very complex system. In this system, agents are learning by themselves or learning from other agents to improve the capability to adapt to different situations. For the learning process, the goal should be clear while the rule should be specific. Furthermore, there should be such kind of mechanism to motivate different agents to learn from each other and share the knowledge or experience to others. Also for social organization, the vision should be far enough to lead the group to be more intelligent.In this paper, we try to construct new learning scheme from the analysis of social organization. To make the idea more intuitive, the flight dynamics [36] is considered as example. First, the discrete dynamics is obtained with Euler approximation. Then, with the idea of future prediction, the equivalent prediction model is obtained and, in this way, the control input is designed according to future output. During the backstepping design, in each step, the learning algorithm is with group learning and the computation burden is greatly reduced.This paper is organized as follows. The social organization is briefly discussed in Section2. Section 3 describes the longitudinal dynamics of the flight vehicle. Section 4 presents the dynamics transformation and adaptive neural controller design. The simulation result is included in Section 5. Section 6 presents several comments and final remarks.


## 2. Organization Learning

With the dramatic changes in the external environment and the continuous development of information technology, there exist optimization problems in both nature and human society organizational learning. However, most of our organizational structure is pyramid-hierarchical structure with overstaffed organization, which seriously affects the efficiency of the organization.In tense global competition, the complexity and uncertainty of the index explosion of technology and the growing market are increasing, the needs of modern organizations in the turbulent business environment, constantly seeking new sources of competitive advantage. Theorists and leaders of both organizations increasingly consider learning as the most critical factor in achieving sustainable development and competitiveness of excellent organizational performance, which means a continuous generation, dissemination, and integration of new knowledge. And thus, terms such as “organizational learning” and “learning organization” have raised concerns to both academics and organizational practitioners. A reasonable explanation for this note is that organizational learning is often regarded as a solution to problems caused by the hierarchy and bureaucracy of the organizations.The advent of information age and knowledge economy society requires a more flexible organization with a flat organizational structure in order to prompt a faster way to meet market demand and improve the efficiency of the organization. In the current volatile environment, the importance of organizational learning and learning organization has been increasingly recognized, and the research of these issues has obtained a corresponding result. One very important issue is how to establish a link of intrinsic logic model which can well explain and predict changes in the fluctuant environment and under this environment the organization also has the ability to survive and maintain sustainable development; how to establish a set of learning methods that impact and promote organizational learning, so as to continuously improve organizational performance; how to build the mechanism between individual self-learning, learning from others, and team learning and the transformation between these three levels of learning.The concept of organizations as learning system has undergone continuous development and evolution process. Learning organization refers to the organization which has the ability to consciously, systematically, and consistently create, accumulate, and use the knowledge resources, to change or redesign itself in order to adapt to the changing external environment, so as to maintain a sustainable competitive advantage of the organization. Organizational learning refers to members of the organization who continue to gain knowledge, to improve their behavior, and to optimize the organization of the system as well as to maintain a sustainable, healthy, and harmonious development process of the organization under the changing external environment.Organizational learning capacity refers to the members of the organization to make the organization as a whole have the ability to maintain a sustainable and healthy organizational development. These learning abilities can be summed up from the existing law of experience or history through self-innovation and they can also be summarized from the experience of others by self-integration. Because of these ways of thinking, the birth of some new ideas can be made possible.In organization learning, two important features should be considered. As demonstrated in Figure1, the learning should be with future vision which means, according to experience, it should be able to predict what will happen in the future. Accordingly, with future prediction, one has to decide how they should act now. For learning, usually there exist too many things and the burden is huge. As a result, group learning is an efficient way since the number of parameters is greatly reduced. For example, for a large matrix, it is complicated to compute its inverse. However, if the matrix could be divided into several small parts, each of which is easy to calculate, then it is much easier to get the inverse. Similar idea exists in organization learning.Figure 1
Organization learning.


## 3. Problem Formulation

Hypersonic flight is one key technology gaining increasing attention recently [37–39]. Different from traditional flight vehicles, the flight condition of high mach numbers and high altitude makes the control system extremely sensitive to changes in atmospheric conditions as well as physical and aerodynamic parameters. Controller design on this topic is widely studied such as system uncertainty [40, 41], actuator constraint [42], fault tolerant control [43, 44], and non-minimum phase system [45]. Accordingly, robust control and adaptive control are designed for the dynamics. In [46], the detail of recent progress in hypersonic flight is reviewed.To make the procedure clear, the paper considers only the altitude subsystem while the velocity is not considered in this paper. The altitude dynamics is as follows:(1)h˙=Vsin⁡γ,γ˙=L+Tsin⁡αmV-μ-V2rcos⁡γVr2,α˙=q-γ˙,q˙=MyyIyy.More details of the dynamics could be found in [41].Following the design [36], define x1=h, x2=γ, x3=θp, x4=q, θp=α+γ, x¯i=[x1,…,xi]T, and uA=δe.The strict-feedback form is obtained as(2)x˙1=f1x1+g1x1x2,x˙2=f2x¯2+g2x¯2x3,x˙3=f3x¯3+g3x¯3x4,x˙4=f4x¯4+g4x¯4uA,uA=δe,yA=x1,where f1=0, g1=V, f2=-μ-V2rcos⁡γ/(Vr2)-q¯S×0.6203/(mV)×γ, g2=q¯S×0.6203/(mV), f3=0, g3=1, f4=q¯Sc¯[CM(α)+CM(q)-0.0292α]/Iyy, and g4=0.0292q¯Sc¯/Iyy.


## 4. Backstepping Design for the Altitude Subsystem

Lemma 1.
Given the functionU∗, there exists an ideal weight vector ω∗ such that the smooth function can be approximated by an ideal NN on a compact set:(3)U∗=ω∗TSθ+ξθ,ξθ<ξM,where θ⊂Rm is the input to NN, N is the nodes number, ξ(θ) is the bounded NN approximation error, and ξM is the supreme of ξ(θ).


### 4.1. Equivalent Prediction Model

In Section2, the prediction function is mentioned. For the flight dynamics, it is with cascade structure. In this part, we will see how to get the prediction model. From (2), it is observed that xi is dependant on xi+1, i=1,2,3, while x4 is governed by UA. To clearly find out the relationship of the system states, by Euler approximation with sample time Ts, systems (2) can be approximated by a discrete-time model as (4)xik+1=Fix¯ik+Gix¯ikxi+1k,x4k+1=F4cx¯4k+G4cx¯4kuAk,yk=x1k,i=1,2,3,where x¯ik=x1k,x2k,…,xikT are the state variables, Ts is sample period, Fjx¯jk=xjk+Tsfjk, Gjx¯jk=Tsgjk, j=1,2,3,4, F4cx¯4k=F4x¯4k, and G4cx¯4k=G4x¯4k.Remark 2.
In the one-step ahead model (4), xi(k+1) is controlled by xi+1(k) while x4(k+1) is controlled by uA(k). It is difficult to see the future dynamics since xi(k+1), i=1,2,3, is not directly connected to uA(k). Thus, additional efforts should be made to transform the dynamics into another prediction form.Ignoring the analysis detail, the original system can be expressed as the following equivalent prediction model [36]:(5)x1k+4=F1cx¯4k+G1cx¯4kx2k+3,x2k+3=F2cx¯4k+G2cx¯4kx3k+2,x3k+2=F3cx¯4k+G3cx¯4kx4k+1,x4k+1=F4cx¯4k+G4cx¯4kuAk.Remark 3.
The philology behind (5) is important since it observes the transfer of the dynamics where actually u(k) is governing x1(k+4) instead of x1(k+1). Since in this paper we try to use new idea from social organization to construct novel NN approximation and learning, more detail is not presented here.Remark 4.
With the equivalent prediction model in (5), there is mapping between u(k) and x1(k+4). It can be observed that the future output could be deduced from current control input. Vice versa, it is expected to determine the current control input based on future reference.


### 4.2. Discrete Control Design

From Figure1, it is important to construct the new learning scheme to reduce online computation burden. This is especially true for the hypersonic flight control since the system is changing fast and requires timely learning. Now the focus is on how to develop more efficient learning approach.For neural approximation,ω∗ is bounded and unknown. Let (6)ω∗=ηsgn⁡η,(7)sgn⁡η=1ifη≥00ifη<0,where η is unknown constant.With (6), inspired by the social organization, we try to update the system signal in batch instead of one by one.Define signals with the following form:(8)z1k=x1k-x1dk,z2k=x2k-x2dk,z3k=x2k-x3dk,z4k=x4k-x4dk,where x2d, x3d, and x4d are signals to be constructed.For the first equation, the virtual controlx2d is proposed as (9)x2dk+3=1-C1z1kG1ck+η^1kS1θ1k,where 0<C1<1 is the design parameter.Remark 5.
One itemη^1kS1θ1k is included in the controller to approximate the system uncertainty. It is interesting to find that η^1 is scalar and the item is easy to calculate.To updateη^1, we have (10)η^1k+1=η^1k1-λ1z1k+1S1θ1k1-δ1η^1k1,where k1=k-3, λ1>0, and 0<δ1<1.Remark 6.
It is noted that the update ofη^1 is simple since the online parameter is reduced to be only one. In this way, the computation burden could be greatly decreased. The main idea from social organization is that to improve efficiency updating should be group by group instead of one by one.Remark 7.
The subscript in (10) is k1 instead of k since the dynamics used for controller design is the equivalent prediction model.For the second equation, the virtual controlx3d is designed as (11)x3dk+2=-x2k+x2dk+3+C2z2kG2Nck+η^2kS2θ2k,where 0<C2<1 is the design parameter and θ2k=x¯4T(k),x2d(k+3)T.To updateη^2, we have (12)η^2k+1=η^2k2-λ2z2k+1S2θ2k2-δ2η^2k2,where k2=k-2, λ2>0, and 0<δ2<1.For the third equation, the virtual controlx4d is designed as (13)x4dk+1=-x3k+x3dk+2+C3z3kG3ck+η^3kS3θ3k,where 0<C3<1 is the design parameter and θ3k=x¯4(k).To updateη^3, we have (14)η^3k+1=η^3k3-λ3z3k+1S3θ3k3-δ3η^3k3,where k3=k-1, λ3>0, and 0<δ3<1.For the fourth equation, the control input is designed as(15)uAk=-x4k+x4dk+1+C4z4kG4Nck+η^4TkS4θ4k,where 0<C4<1 is the design parameter and θ4k=x¯4T(k),x4d(k+1)T.The robust updating law for NN weights is proposed as(16)η^4k+1=η^4k4-λ4z4k+1S4θ4k4-δ4η^4k4,where k4=k, λ4>0, and 0<δ4<1.Remark 8.
In (16), it shows k4=k because actually there is no change of this equation compared with the one-step ahead equation.The following theorem is achieved.Theorem 9.
For system (4), if the signals (9), (11), (13), and (15) and the update laws (10), (12), (14), and (16) are designed, all the tracking errors are uniformly ultimately bounded.The proof is similar to the procedure in [36]; thus, it is omitted here.


## 4.1. Equivalent Prediction Model

In Section2, the prediction function is mentioned. For the flight dynamics, it is with cascade structure. In this part, we will see how to get the prediction model. From (2), it is observed that xi is dependant on xi+1, i=1,2,3, while x4 is governed by UA. To clearly find out the relationship of the system states, by Euler approximation with sample time Ts, systems (2) can be approximated by a discrete-time model as (4)xik+1=Fix¯ik+Gix¯ikxi+1k,x4k+1=F4cx¯4k+G4cx¯4kuAk,yk=x1k,i=1,2,3,where x¯ik=x1k,x2k,…,xikT are the state variables, Ts is sample period, Fjx¯jk=xjk+Tsfjk, Gjx¯jk=Tsgjk, j=1,2,3,4, F4cx¯4k=F4x¯4k, and G4cx¯4k=G4x¯4k.Remark 2.
In the one-step ahead model (4), xi(k+1) is controlled by xi+1(k) while x4(k+1) is controlled by uA(k). It is difficult to see the future dynamics since xi(k+1), i=1,2,3, is not directly connected to uA(k). Thus, additional efforts should be made to transform the dynamics into another prediction form.Ignoring the analysis detail, the original system can be expressed as the following equivalent prediction model [36]:(5)x1k+4=F1cx¯4k+G1cx¯4kx2k+3,x2k+3=F2cx¯4k+G2cx¯4kx3k+2,x3k+2=F3cx¯4k+G3cx¯4kx4k+1,x4k+1=F4cx¯4k+G4cx¯4kuAk.Remark 3.
The philology behind (5) is important since it observes the transfer of the dynamics where actually u(k) is governing x1(k+4) instead of x1(k+1). Since in this paper we try to use new idea from social organization to construct novel NN approximation and learning, more detail is not presented here.Remark 4.
With the equivalent prediction model in (5), there is mapping between u(k) and x1(k+4). It can be observed that the future output could be deduced from current control input. Vice versa, it is expected to determine the current control input based on future reference.


## 4.2. Discrete Control Design

From Figure1, it is important to construct the new learning scheme to reduce online computation burden. This is especially true for the hypersonic flight control since the system is changing fast and requires timely learning. Now the focus is on how to develop more efficient learning approach.For neural approximation,ω∗ is bounded and unknown. Let (6)ω∗=ηsgn⁡η,(7)sgn⁡η=1ifη≥00ifη<0,where η is unknown constant.With (6), inspired by the social organization, we try to update the system signal in batch instead of one by one.Define signals with the following form:(8)z1k=x1k-x1dk,z2k=x2k-x2dk,z3k=x2k-x3dk,z4k=x4k-x4dk,where x2d, x3d, and x4d are signals to be constructed.For the first equation, the virtual controlx2d is proposed as (9)x2dk+3=1-C1z1kG1ck+η^1kS1θ1k,where 0<C1<1 is the design parameter.Remark 5.
One itemη^1kS1θ1k is included in the controller to approximate the system uncertainty. It is interesting to find that η^1 is scalar and the item is easy to calculate.To updateη^1, we have (10)η^1k+1=η^1k1-λ1z1k+1S1θ1k1-δ1η^1k1,where k1=k-3, λ1>0, and 0<δ1<1.Remark 6.
It is noted that the update ofη^1 is simple since the online parameter is reduced to be only one. In this way, the computation burden could be greatly decreased. The main idea from social organization is that to improve efficiency updating should be group by group instead of one by one.Remark 7.
The subscript in (10) is k1 instead of k since the dynamics used for controller design is the equivalent prediction model.For the second equation, the virtual controlx3d is designed as (11)x3dk+2=-x2k+x2dk+3+C2z2kG2Nck+η^2kS2θ2k,where 0<C2<1 is the design parameter and θ2k=x¯4T(k),x2d(k+3)T.To updateη^2, we have (12)η^2k+1=η^2k2-λ2z2k+1S2θ2k2-δ2η^2k2,where k2=k-2, λ2>0, and 0<δ2<1.For the third equation, the virtual controlx4d is designed as (13)x4dk+1=-x3k+x3dk+2+C3z3kG3ck+η^3kS3θ3k,where 0<C3<1 is the design parameter and θ3k=x¯4(k).To updateη^3, we have (14)η^3k+1=η^3k3-λ3z3k+1S3θ3k3-δ3η^3k3,where k3=k-1, λ3>0, and 0<δ3<1.For the fourth equation, the control input is designed as(15)uAk=-x4k+x4dk+1+C4z4kG4Nck+η^4TkS4θ4k,where 0<C4<1 is the design parameter and θ4k=x¯4T(k),x4d(k+1)T.The robust updating law for NN weights is proposed as(16)η^4k+1=η^4k4-λ4z4k+1S4θ4k4-δ4η^4k4,where k4=k, λ4>0, and 0<δ4<1.Remark 8.
In (16), it shows k4=k because actually there is no change of this equation compared with the one-step ahead equation.The following theorem is achieved.Theorem 9.
For system (4), if the signals (9), (11), (13), and (15) and the update laws (10), (12), (14), and (16) are designed, all the tracking errors are uniformly ultimately bounded.The proof is similar to the procedure in [36]; thus, it is omitted here.


## 5. Simulation

The simulation is with initial states atV=15060 ft/s, h=110000 ft, α=0.032 rad, β=0, and δe=0 rad.The tracking commands are given asVc=100 ft/s and hc as square signal with amplitude of 1000 ft and period 200 s. The filter ωn1ωn22/(s+ωn1)(s2+2εcωn2s+ωn22) is used to generate the reference signal where ωn1=0.5, ωn2=0.2, and εc=0.7.For the velocity subsystem, the design in [36] is borrowed. For controller, we select C1=0.9, C2=0.9, C3=0.9, C4=0.8, and CV=0.9. For the updating law, we select λi=0.01 and δi=0.01, i=1,2,3,4,V. For simulation, the time interval is selected as Ts=0.05 s.From the altitude tracking depicted in Figure2, it is observed that the controller can track the reference signal very well. The elevator deflection and throttle setting are illustrated in Figures 3 and 4. At the beginning, system is not responding from trim state and there exists certain variation. From the response of system states, under proposed controller, flight path angle in Figure 5, pitch angle in Figure 6, and the pitch rate in Figure 7 can track the virtual command very well. The adaptive estimation for group learning is shown in Figure 8. It indicates that, motivated by the learning of social organization, the system is working more efficiently since the tracking performance is retained while the online learning speed is much faster since the number of parameters is reduced to be one.Figure 2
Altitude tracking.Figure 3
Elevator deflection.Figure 4
Throttle setting.Figure 5
Flight path angle.Figure 6
Pitch angle.Figure 7
Pitch rate.Figure 8
Adaptive estimation.


## 6. Conclusions and Future Work

By analysis of the social organization, the novel learning scheme is proposed for the equivalent prediction model of hypersonic flight dynamics. In this way, the online learning is much faster and the controller is working more efficiently. With simulation, the effectiveness of the proposed method is verified.For efficiency, sometimes the system is learning too much which means even with more update the accuracy will not increase. In this case, the threshold should be included such that the system can save more computation time by keeping current parameters. In other words, the update is executed when the tracking error is out of the desired performance. Also in social organization, one agent cannot own all the capabilities and thus the agent should be combined with other agents to achieve more complex learning. This work could be further extended to multiagent systems [47, 48]. The composite learning [49] is of great interest since it can provide more accurate learning.



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*Source: 3460492-2016-04-05.xml*