on discrete algebraic riccati equations a rank characterization of solutions abstract we give a rank characterization of the solution set of discrete algebraic riccati equations dares involving real matrices our characterization involves the use of invariant subspaces of the system matrix we observe that a dare can be considered as a specific type of a non symmetric continuous time algebraic riccati equation we show how to extract the low rank solutions from the full rank solution of a homogeneous dare we also study the eigen structure of various feedback closed loop matrices associated with solutions of a dare we show as a consequence of our observations that a solution x of a dare for controllable systems and certain specific types of uncontrollable systems satisfies the inequality x m i n x x m a x we characterize conditions under which the solution set of dare is bounded unbounded we use the method of invariant subspaces to identify some invariant sets of a difference riccati equation

on the generalization of single input rule modules connected type fuzzy reasoning method yubazaki have proposed a ldquosingle input rule modules connected type fuzzy reasoning method sirms method rdquo in which its final output is obtained by summarizing the product of importance degree and inference result from single input fuzzy rule modules this paper proposes a ldquofunctional type sirms method rdquo which is an extended version of the sirms method and clarifies the relationship between the takagi sugeno t s reasoning method and the functional type sirms method the functional type sirms method can be shown to be transformed to the t s reasoning method but generally the conversion to functional type sirms method from the t s reasoning method is impossible it is shown however that the t s reasoning method can be transformed to the functional type sirms method when the t s reasoning method fills some conditions for this reason it is shown that the functional type sirms method is the subset of the t s reasoning method

sirms connected fuzzy inference method adopting emphasis and suppression the single input rule modules connected fuzzy inference method sirms method can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods however the inference results obtained by the sirms method is generally simple compared with those of the conventional fuzzy inference methods for example the sirms method may be not equivalent to the product sum gravity method and fuzzy singleton type inference method if the fuzzy sets of the antecedent parts are limited to normal fuzzy sets in this paper we propose a fuzzy singleton type sirms method which weights the rules of the sirms method in order to solve the above problem this paper also clarifies the property of the fuzzy singleton type sirms method from the view point of equivalence and monotonicity moreover the fuzzy singleton type sirms method is shown to be superior to the conventional sirms method by applying to a medical diagnosis system

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

all optimal hankel norm approximations and their error bounds in discrete time this paper investigates a parallel problem to glover 1984 approximate a multivariable transfer function g z of mcmillan degree n by of mcmillan degree smaller than k in discrete time a state space solution is derived to the optimal hankel norm approximation problem together with characterization to all optimal hankel norm approximations it is shown that the error bound derived in glover 1984 holds for discrete time systems as well

representation and factorization of discrete time rational all pass functions in this paper we obtain a general characterization of discrete time all pass rational matrix functions from state space representations we establish a general characterization of the solutions of lmi s and riccati equations finally we derive a complete factorization theory of all pass functions our results are obtained in the most general setting without introducing any ad hoc assumption and can be applied to a variety of problems such as the discrete time counterpart of the h infty model reduction problems solved by glover in continuous time

a learning process for fuzzy control rules using genetic algorithms abstract the purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples it is developed in three stages the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach the second one combines two kinds of rules experts rules if there are and the previously generated fuzzy control rules removing the redundant fuzzy rules and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules the three components of the learning process are developed formulating suitable genetic algorithms

a parameterized fuzzy processor and its applications abstract in this paper a parameterized fuzzy processor pfp is presented based on a designed fuzzy instruction set of the parameterized fuzzy number pfn this pfn is presented by some parameters of the universe of the discourse instead of a series of the membership grades the algorithms of these instructions are based on the parameter operations to implement the fuzzy arithmetics and the fuzzy reasoning methods the instruction set supports the versatility of the fuzzy information e g fuzzy arithmetic operations inference operations fuzzy logic operations data translations and data exchangements based upon these the characteristics of the pfn are discussed and the architecture of the pfp outlined is constructed in this paper and its processing time is saved due to the adaptation of the parameterized fuzzy number pfn to evaluate the performance of pfn instructions and pfp structure two experiments are presented one is the speed performance evaluated for the pfn to compare with the discrete fuzzy number dfn the other is the confirmation of the feasibility and the capability of the instructions which is demonstrated by three examples relateld to human inference intuitive control and decision making

fuzzy hierarchical swing up and sliding position controller for the inverted pendulum cart system in this paper a fuzzy hierarchical swing up and sliding position controller is proposed for the swing up and position controls of an inverted pendulum cart system the proposed fuzzy hierarchical swing up and sliding position controller includes a fuzzy switching controller a fuzzy swing up controller and a twin fuzzy sliding position controller the fuzzy switching controller is designed to smoothly switch between the swing up and position controls with the inverted pendulum cart system decomposed into a pendulum subsystem and a cart subsystem fuzzy sliding position controllers are presented to robustly balance the pendulum and cart at the desired positions the sliding mode and stability of the fuzzy sliding position control systems are guaranteed moreover an adaptive mechanism is provided to on line adjust the parameters in the fuzzy sliding position controllers simulation results are included to illustrate the effectiveness of the proposed fuzzy hierarchical swing up and sliding position controller

a proposal of sirms dynamically connected fuzzy inference model for plural input fuzzy control single input rule modules sirms dynamically connected fuzzy inference model is proposed for plural input fuzzy control for each input item a sirm is constructed and a dynamic importance degree is defined the dynamic importance degree consists of a base value insuring the role of the input item through a control process and a dynamic value changing with control situations to adjust the dynamic importance degree each dynamic value can be easily tuned based on the local information of current state the model output is obtained by summarizing the products of the dynamic importance degree and the fuzzy inference result of each sirm the controller constructing method for constant value control systems is given and constant value controls of typical first and second order lag plants are tested the simulation results show that by using the proposed mode the reaching time can be reduced by more than 15 without any steady state error overshoot or vibration compared with the sirms fixed importance degree connected fuzzy inference model the proposed model is further successfully applied to stabilization control of an inverted pendulum system including the position control of the cart

on the equivalence conditions of fuzzy inference methods part 1 basic concept and definition this paper addresses equivalence of fuzzy inference methods it first presents several well known fuzzy inference methods the product sum gravity method the simplified fuzzy inference method the fuzzy singleton type inference method the single input rule modules connected type fuzzy inference method sirms method and the single input connected fuzzy inference method sic method second three fuzzy inference methods of the product sum gravity method simplified fuzzy inference method and fuzzy singleton type inference method which are all widely used as fuzzy control methods are shown to be equivalent to each other third the equivalence conditions between the sirms method and the sic method known as single input type fuzzy inference method are shown finally it also gives the equivalence conditions between the single input type fuzzy inference methods and the previous three fuzzy inference methods investigating the equivalence among various fuzzy inference methods would help to understand the relationship of those fuzzy inference methods

causality and model abstraction abstract much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time in formal descriptions of processes in terms of parameters and equations the notion of causality is rarely made explicit formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables nevertheless the notion of causality plays an important role in our understanding of phenomena even when we describe the behavior of a system formally in terms of acausal mathematical relations we often give an informal intuitive explanation of why the system behaves the way it does in terms of cause effect relations in this paper we will present an operational definition of causal ordering the definition allows us to extract causal dependency relations among variables implicit in a model of a system when a model is represented as a set of acausal mathematical relations our approach is based on the theory of causal ordering first presented by simon 22 the paper shows how to use the theory and its extension in reasoning about physical systems further the paper studies the relation of the theory to the problems of model aggregation

the generalised discrete algebraic riccati equation in linear quadratic optimal control this paper investigates the properties of the solutions of the generalised discrete algebraic riccati equation arising from the classic infinite horizon linear quadratic lq control problem in particular a geometric analysis is used to study the relationship existing between the solutions of the generalised riccati equation and the output nulling subspaces of the underlying system and the corresponding reachability subspaces this analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil in establishing the main results of this paper several ancillary problems on the discrete lyapunov equation and spectral factorisation are also addressed and solved

analysis and design of functionally weighted single input rule modules connected fuzzy inference systems the single input rule modules sirms connected fuzzy inference method can efficiently solve the fuzzy rule explosion phenomenon which usually occurs in the multivariable modeling and or control applications however the performance of the sirms connected fuzzy inference system sirm fis is limited due to its simple input output mapping in this paper to further enhance the performance of sirm fis a functionally weighted sirm fis fwsirm fis which adopts multivariable functional weights to measure the important degrees of the sirms is presented then in order to show the fundamental differences of the sirms methods properties of the traditional sirm fis the type 2 sirm fis t2sirm fis the functional sirm fis fsirm fis the sirms model with single variable functional weights sirm fw and fwsirm fis are explored these properties demonstrate that the proposed fwsirm fis has more general and complex input output mapping than the existing sirms methods such properties theoretically guarantee that better performance can be achieved by fwsirm fis furthermore based on the least squares method a novel data driven optimization method is presented for the parameter learning of fwsirm fis it can also be used to optimize the parameters of sirm fis t2sirm fis fsirm fis and sirm fw due to the properties of the least squares method the proposed parameter learning algorithm can overcome the drawbacks of the gradients based parameter learning methods and obtain both smallest training errors and smallest parameters finally to show the effectiveness and superiority of fwsirm fis and the proposed optimization method six examples and detailed comparisons are given simulation results show that fwsirm fis can obtain better performance than the other sirms methods and compared with some well known methods fwsirm fis can achieve similar or better performance but has much less parameters and faster training speed

application of limit fuzzy controllers to stability analysis abstract we propose a method to examine the stability of fuzzy control systems it is based on the limit law of fuzzy controllers constructed from regular fuzzy rules the main idea is to use lyapunov functions for the system with limit laws to examine the stability of the system with fuzzy controllers this method is particularly useful when the system and the limit law are both linear it is applied to an inverted pendulum system two cases with and without friction are considered simulation results and the analysis confirm certain experimental and theoretical results already reported

stablization of an inverted pendulum by a high speed fuzzy logic controller hardware system abstract a high speed fuzzy controller hardware system employing min max operations is presented it has fifteen control rule boards and one defuzzifier grades of membership are represented with 0 v 5 v corresponding to 0 0 1 0 this fuzzy controller facilitates approximate reasoning at 1 000 000 fips fuzzy inferences per second and is able to be used for various purposes by programming on each control rule board it handles fuzzy linguistic information of the form nl negative large nm negative medium ns negative small zr approximately zero ps positive small pm positive medium pl positive large and ng negation this fuzzy controller hardware system makes an inverted pendulum stand on a vehicle by using seven control rules two pendulums 5 mm diameter 15 cm length 3 5 g weight respectively 10 mm 50 cm and 50 g can be stabilized by the same rule set it is much easier to produce control rules than to solve the nonlinear differential equations representing the dynamics of an inverted pendulum this fuzzy controller hardware system can be applied to attitude control of a space booster rocket and satellite an automatic aircraft landing system pattern recognition stabilization of nuclear fuel rods in a reactor an intelligent sensor and many other applications which need swift approximate reasoning

a new fuzzy controller for stabilization of parallel type double inverted pendulum system a new fuzzy controller with 6 input items and 1 output item for stabilizing a parallel type double inverted pendulum system is presented based on the single input rule modules sirms dynamically connected fuzzy inference model each input item is assigned with a sirm and a dynamic importance degree the sirms and the dynamic importance degrees are designed such that the angular control of the longer pendulum takes the highest priority over the angular control of the shorter pendulum and the position control of the cart when the angle of the longer pendulum is big by using the sirms and the dynamic importance degrees the priority orders of the three controls are automatically adjusted according to control situations the proposed fuzzy controller has a simple and intuitively understandable structure and executes the three controls entirely in parallel simulation results show that the proposed fuzzy controller can stabilize completely a parallel type double inverted pendulum system within 10 0 s for a wide range of the initial angles of the two pendulums this is the first result for a fuzzy controller to achieve successfully complete stabilization control of a parallel type double inverted pendulum system

implementation of the fati hierarchical fuzzy inference system using the immutability decomposition method abstract most practical implementations of fuzzy inference systems chiefly encompass rule based systems fita due to their lower implementation cost classic fuzzy relational inference systems fati are rarely used in practice this paper presents a hierarchical architecture of the fati system which allows one to reduce the resources necessary for its software or hardware implementation the system consists of single input single output siso subsystems which have the same architecture but differ from each other in the contents of their knowledge in the form of fuzzy subrelations these subrelations are created using decomposition of a global fuzzy relation of the primary classic multiple input single output miso fuzzy inference system calculation of the global fuzzy relation based on the knowledge base of the fita system is time consuming and requires much memory to store it therefore decomposition has been moved to the linguistic level decomposition is a lossy operation thus the fuzzy inference result of the hierarchical system is fuzzier than the classic one to avoid inference error we present novel methods based on derivative linguistic values and partitioning of the primary knowledge base with immutability of its contents during the decomposition step which can be used for any fuzzy inference system an example of a fati system proves the suitability of the developed methods in a real practical application

families of solutions of algebraic riccati equations abstract we consider homogeneous algebraic riccati equations in the general situation when the matrix of the dynamics can be mixed we show that in this case the equation may have infinitely many families of solutions an analysis of these families is carried over and an explicit formula is derived when the matrix of the dynamics is unmixed this formula provides an explicit parametrization of the whole set of the solutions we finally show that there are situations in which the equation has spurious solutions that do not belong to any of the families and derive sufficient conditions under which on the contrary the union of the families covers the whole set of solutions

a methodology to model fuzzy systems using fuzzy clustering in a rapid prototyping approach in this paper we present different approaches to the problem of fuzzy rules extraction by using fuzzy clustering they try to investigate the use of fuzzy clustering as a technique that let us obtain a first approximation of the fuzzy model in a rapid prototyping approach the key ideas here are to generate in a first step a collection of fuzzy rules from numerical data pairs subsequently these rules can be converted either in a collection of linguistic rules in order to obtain a descriptive approach or in an inference machine so that we obtain an approximative approach this can be considered as a quasi descriptive approach because it assigns a weight to the fuzzy rules like in the descriptive approaches but also it generates the fuzzy sets directly in the product space of the input variables like in approximative approaches both by using the information disclosed by means of a fuzzy clustering process

adaptive fuzzy controller application to the control of the temperature of a dynamic room in real time this paper presents a direct adaptive fuzzy controller for unknown monotonic nonlinear systems thus not requiring the system model but only a little information about it the plant monotonicity and its delay without any off line pre training the algorithm achieves very high control performance through a three stage algorithm 1 output scale factor 2 adaptation of the fuzzy rule consequents and 3 optimization of the position of the membership functions the design is simple in the sense that both the membership functions and the rule base can be initialized from arbitrary values it can be applied to a large class of monotonic dynamic or static plants due the fact that the system is able to modify its behaviour in real time i e during the control process

impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions abstract a data determined method for testing structural models of the errors in vector autoregressions is discussed the method can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification in one dimension it turns out that standard t statistics can be used to test the various overidentifying restrictions that are implied by a model in another dimension the method compares a priori knowledge of a structural model for the errors with the properties exhibited by the data thus this method may help to ensure that orderings of the errors for impulse response and forecast error variance decomposition analyses are sensible given the data two economic examples are used to illustrate the method

silverman algorithm and the structure of discrete time stochastic systems abstract it is a well known yet poorly understood fact that contrary to the continuous time case the same discrete time process y can be represented by minimal linear models see 1 1a 1 1b below which may either have a non singular or a singular d matrix in fact models with d 0 have been commonly used in the statistical literature on the other hand for models with a singular d matrix the riccati difference equation of kalman filtering involves in general the pseudo inversion of a singular matrix this cheap filtering problem dual to the better known cheap control problem has been studied for several decades in connection with the so called invariant directions of the riccati equation for a singular d a reduction of the order of the riccati equation is in general possible the reasons for such a reduction do not seem to be completely clear either in this paper we provide an explanation of this phenomenon from the classical point of view of zero flipping among minimal spectral factors changing d s occurs whenever zeros are flipped from z to their reciprocals at z 0 it is well known that for finite zeros the zero flipping process takes place by multiplication of the underlying spectral factor by a suitable rational all pass matrix function for infinite zeros zero flipping is implemented by a dual version of the silverman structure algorithm using this interpretation we derive a new algorithm for filtering of non regular processes based on a reduced order riccati equation we also obtain a precise characterization of the reduction of the order of the riccati equation which is afforded by zeros either at z or at the origin this order reduction has traditionally been associated with the study of invariant directions a point of view which as we show does not capture the essence of the phenomenon

prediction of nasopharyngeal carcinoma recurrence by neuro fuzzy techniques neuro fuzzy techniques for prediction of nasopharyngeal carcinoma recurrence are mainly focused in this paper a technique named generalized neural network type single input rule modules connected fuzzy inference method is proposed in the study clinical data of patients with nasopharyngeal carcinoma were collected from ramathibodi hospital thailand in total 495 records were taken into account relevant factors were extracted and employed in developing predictive models the results showed that the proposed technique was superior to the other neuro fuzzy techniques stand alone neural network logistic regression and cox proportional hazard model accuracy and auc above 80 and 0 8 could be achieved to show validity of the proposed technique two nonlinear problems i e function approximation and the xor classification problems are studied simulation results showed that the proposed technique could simplify the problem by converting the original nonlinear input into the lower complexity one in addition it can solve the xor problem whereas the traditional approach cannot tackle this problem

causal ordering comparative statics and near decomposability abstract the notion of causal ordering has been explicated for systems in the form of sets of linear algebraic equations and also for dynamic models consisting of linear differential equations since we often wish to aggregate or disaggregate models of systems or to consider the static equilibrium of a dynamic model the question arises as to how these transformations from one model of a system to another affect the causal ordering of variables the present paper provides some answers to this question

unmixed solutions of the discrete time algebraic riccati equation the algebraic riccati equation of the optimal control problem associated with the discrete time system x k 1 fx k gu k is studied it is shown that in the case of a controllable system there exist solutions with prescribed unmixed characteristic polynomial of the corresponding closed loop matrix existence of solutions will also be proved under the weaker condition of modulus controllability maximal solutions are discussed

on the monotonicity of fuzzy inference methods related to t s inference method yubazaki et al have proposed a single input rule modules connected type fuzzy inference method sirms method whose final output is obtained by combining the products of the importance degrees and the inference results from single input fuzzy rule modules moreover seki et al have proposed a functional type sirms method whose consequent parts are generalized to functions from real numbers it is expected that inference results from the functional type sirms method are monotone if the antecedent parts and the consequent parts of fuzzy rules in the functional type sirms rule modules are monotone however this paper points out that even if consequent parts in the functional type sirms rule modules are monotone the inference results are not necessarily monotone when the antecedent parts are noncomparable fuzzy sets and it clarifies the conditions for the monotonicity of inference results from the functional type sirms method moreover for the takagi sugeno t s inference method the monotonicity condition is clarified in the case of two inputs by using the equivalence relation of fuzzy inference

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

a parametrization of solutions of the discrete time algebraic riccati equation based on pairs of opposite unmixed solutions the paper describes the set of solutions of the discrete time algebraic riccati equation it is shown that each solution is a combination of a pair of opposite unmixed solutions there is a one to one correspondence between solutions and invariant subspaces of the closed loop matrix of an unmixed solution the results of the paper provide an extended counterpart of the parametrization theory of continuous time algebraic riccati equations by willems coppel and shayman

upswing and stabilization control of inverted pendulum system based on the sirms dynamically connected fuzzy inference model abstract a new fuzzy controller is presented based on the single input rule modules sirms dynamically connected fuzzy inference model for upswing and stabilization control of inverted pendulum system the fuzzy controller takes the angle and angular velocity of the pendulum and the position and velocity of the cart as its input items and the driving force as its output item each input item is assigned with a sirm and a dynamic importance degree when the pendulum locates at the pending domain the fuzzy controller becomes an upswing controller by using the saturation feature of the membership functions of the pendulum angle when the pendulum locates at the upright domain the fuzzy controller then becomes a stabilization controller and realizes smoothly the pendulum angular control and the cart position control in parallel by using the sirms and the dynamic importance degrees the fuzzy controller has a simple structure and is easily understandable compared with the other approaches simulation results show that the fuzzy controller can swing up the pendulum from the pending position and then stabilize the whole system in about 3 0 s

handling the nonlinearity of a fuzzy logic controller at the transition between rules abstract a fuzzy logic controller approximates a desired control surface by using the outputs of its fuzzy control rules the shape of this control surface is mainly influenced by the linguistic variables of the rule base the basic operators of the fuzzy sets the implication the inference and the defuzzification method the linearity nonlinearity of this control surface is discussed in many studies however none of those studies has explicitly considered the linearity nonlinearity at the transition between fuzzy logic rules in this paper a simple approach to control the linearity nonlinearity at this transition by a modified center of gravity defuzzification method is proposed namely by introducing the so called defuzzification weights to the overlapping areas of the consequent those defuzzification weights can be determined heuristically or automatically both cases will be demonstrated for the latter a feedforward neural network is employed