analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

multi dimensional fuzzy reasoning this paper suggests a method of multi dimensional fuzzy reasoning concerned with both modus ponens and modus tollens it also discusses an example to show how the method works

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

design and analysis of a fuzzy proportional integral derivative controller abstract this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional integral pi plus a derivative d controller first the fuzzy pi d controller is derived from the conventional continuous time linear pi d controller then the fuzzification control rule base and defuzzification in the design of the fuzzy controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pi d controller which has the same linear structure in the proportional integral and derivative parts but has nonconstant gains the proportional integral and derivative gains are nonlinear functions of the input signals the new fuzzy pi d controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self tuning control capability computer simulation results have demonstrated the advantages of the fuzzy controller particularly when the process to be controlled is nonlinear after a brief stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are shown to compare with the conventional pi d controller computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance

a new adaptive fuzzy controller using the parallel structure of fuzzy controller and its application abstract the paper suggests a new fuzzy adaptive controller which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers it explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system as well as related mathematical theorems and their proofs are also given the performance of the proposed adaptive control algorithm is analyzed through a design example and an experiment on hybrid force position robot control system

fuzzy stability criterion of a class of nonlinear systems abstract a fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of lyapunov first a sufficient condition that guarantees stability of a fuzzy system is given in terms of lyapunov s direct method two concepts for stability of fuzzy systems are defined locally stable and globally table second a construction procedure for lyapunov functions is presented finally the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems

a model based fuzzy controller abstract to avoid the heuristic search for linguistic control rules a fuzzy controller which is based on a fuzzy model of the plant is introduced in a first step the plant is to be identified and described by a fuzzy relation in a second step this relation is used to find trajectories from any point of the discrete state space to the origin the resulting fuzzy control system predicts the point in state space to be reached next and selects the corresponding actuating variable from the fuzzy relation

a multirule base controller using the robust property of a fuzzy controller and its design method this paper suggests a new fuzzy adaptive controller which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers it explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller the basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers this new adaptive controller uses a multirule base architecture which has several independent fuzzy controllers in parallel each with different robust stability area out of several independent fuzzy controllers the most suited one is selected by a system identifier which observes variations in the controlled system parameter here we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system related mathematical theorems and their proofs are also given the performance of the proposed adaptive control algorithm is analyzed through a design example and a dc motor control simulation

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

study on stability of fuzzy closed loop control systems abstract the problem of stability of fuzzy closed loop control systems has long been unsolved through analyzing the max min composition operator in fuzzy systems this paper presents a reasonable analytical model of fuzzy closed loop systems and then proposes a method to analyze the stability of control systems by the relational matrix of fuzzy systems an example is given to show the method available

equivalence between fuzzy logic controllers and pi controllers for single input systems abstract for a single input and single output system we prove that when a proportional integral pi controller is given one can design a fuzzy logic controller whose output is identical to that of the pi controller we also prove that if a fuzzy logic controller using specified fuzzy logic operations is given there is a pi controller whose output is identical to that of the fuzzy logic controller

analysis and design of fuzzy control systems using dynamic fuzzy global models a method for analysis and design of a fuzzy controller is developed for a class of fuzzy discrete time systems the method is based on a dynamical fuzzy state space model it is shown that the closed loop fuzzy system can be represented by a dynamical interval system and thus the methods of stability analysis in uncertain linear system theory can be used to analyse the global stability of the closed loop fuzzy system some examples are given to illustrate the application of the method

approximation accuracy analysis of fuzzy systems as function approximators this paper establishes the approximation error bounds for various classes of fuzzy systems i e fuzzy systems generated by different inferential and defuzzification methods based on these bounds the approximation accuracy of various classes of fuzzy systems is analyzed and compared it is seen that the class of fuzzy systems generated by the product inference and the center average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center average defuzzifier and the class of fuzzy systems defuzzified by the mom defuzzifier in addition it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the mom defuzzified method are given

trajectory stabilization of a model car via fuzzy control abstract this paper deals with trajectory stabilization of a computer simulated model car via fuzzy control stability conditions of fuzzy systems are given in accordance with the definition of stability in the sense of lyapunov first we approximate a computer simulated model car whose dynamics is nonlinear by t s takagi and sugeno fuzzy model fuzzy control rules which guarantee stability of the control system under a condition are derived from the approximated fuzzy model the simulation results show that the fuzzy control rules effectively realize trajectory stabilization of the model car along a given reference trajectory from all initial positions under a condition and the dynamics of the approximated fuzzy model agrees well with that of the model car

pad analysis of fuzzy control stability abstract by means of an index represented rule mapping the response g of a fuzzy controller is decomposed into two parts f the classical component and g f the nonlinear component called pad we intend to analyse the pad in order to know what the relation is between fuzzy and classical pid controllers fuzzy controllers mentioned here are defuzzified by the typical center of gravity method in the 1 input case we get that f g 0 which means that the fuzzy controller is exactly the same as the classical p controller whenever the rule mapping is simple definition 1 2 and the linguistic values are a binary family definition 4 1 in the 2 input case of error and error change for simple rule mapping and for simple linguistic values family 4 7 and perfectly for the wxyz linguistic values family definition 6 1 the fuzzy controller can be viewed as a series connection of a classical pd controller and a 1 pad element the describing function of a 1 pad element is very simple and fine and ensures that such fuzzy controller will be stable if the pd controller is the similar consequences are also obtained for the case of three inputs

a centered formulation of takagi sugeno rules for improved learning efficiency abstract we derive the gradient descent optimization equations for takagi sugeno fuzzy rule bases learning with symmetric triangular membership functions minimum operator as and operator and affine output functions standard sugeno rules a new type of affine output takagi sugeno rules called centred takagi sugeno rules is proposed as proved on a simple example it enables to avoid convergence problems which appear in precisely defined cases especially when there are many rules or when the variation domain of the inputs is not centred around zero gradient descent is tested for the approximation of a specially built one input one output analytical function including a discontinuity and a high curvature point and for the approximation of two input functions test and theoretical results are consistent and show that the proposed method is more efficient when the stated conditions are verified

invariance and stability of fuzzy systems the elaboration of a stability theory of fuzzy systems is fully justified by the use in a variety of practical situations of fuzzy controllers 11 27 28 however such a theory may be founded upon ideas that arise from a historical study of dynamical systems theory during the last quarter of the nineteenth century the study of ordinary differential equations underwent some rather radical changes prior to this period the major emphasis in the subject had been on the methods of solving equations it was during this period that peano 20 gave a rigorous proof of the existence theorem for solutions of ordinary differential equations during the same period lipschitz 151 and picard 22 showed that the method of successive approximations led to a proof of the existence and the uniqueness of solutions to the initial value problem these developments represent the dhuement of the attempts to solve differential equations as the works of peano lipschitz and picard were finishing one chapter in the book of differential equations another was being initiated with the research of liapunov 141 and poincare 23 this new chapter was based on an entirely different approach where one did not attempt to compute the solutions rather one tried to exploit their topological properties poincart in his famous m moire 23 was the first to look at an ordinary differential equation from the point of view of the geometry of the trajectories thereby creating the topological theory of ordinary differential equations almost at the same time the stability theory created by liapunov 141 although heavily quantitative in its methods stressed the importance of some topological features of ordinary differential equations during the 50 years following liapunov and poincare many important advances were made it is with the works of birkhoff 4 nemytskii and stepanov 191 and smale 26 that researchers realized that the essence of this theory was based on the notion of dynamical system based on liapunov s original works classical stability theory is concerned with the equilibrium points of the system and the dynamical

stability analysis and design for a class of continuous time fuzzy control systems this paper presents a design method for a class of fuzzy control systems the class of fuzzy systems considered can be represented by the takagi sugeno fuzzy model which is a type of dynamic fuzzy model a constructive algorithm is developed to obtain the stabilizing feedback control law for the system the main contribution of this paper is the development of an equivalent principle that is the design of a fuzzy control system is equivalent to the design of a set of linear time invariant extreme systems thus any design method in linear control system theory can be used to design a fuzzy control system an example is given to illustrate the application of the method

counter example to sufficient and necessary condition for the asymptotic stability of discrete linear interval systems abstract in this note the interval matrix result for discrete linear interval system by jiang 1988 is shown to be incorrect i e all eigenvalues of each matrix a e a 1 an interval matrix have magnitudes less than 1 if and only if all the eigenvalues of every extreme matrix of the interval matrix a 1 have magnitudes less than 1

completely positive divisibility does not mean markovianity in the classical domain it is well known that divisibility does not imply that a stochastic process is markovian however for quantum processes divisibility is often considered to be synonymous with markovianity we show that completely positive divisible quantum processes can still involve non markovian temporal correlations that we then fully classify using the recently developed process tensor formalism which generalizes the theory of stochastic processes to the quantum domain

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

a multi resolution approximation for massive spatial datasets abstractautomated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high resolution observations of spatial fields over large spatial regions if these datasets can be efficiently exploited they can provide new insights on a wide variety of issues however traditional spatial statistical techniques such as kriging are not computationally feasible for big datasets we propose a multi resolution approximation m ra of gaussian processes observed at irregular locations in space the m ra process is specified as a linear combination of basis functions at multiple levels of spatial resolution which can capture spatial structure from very fine to very large scales the basis functions are automatically chosen to approximate a given covariance function which can be nonstationary all computations involving the m ra including parameter inference and prediction are highly scalable for massive datasets crucially the inference algorithms can also be parallelize

optimal design of fuzzy sliding mode control a comparative study abstract the fuzzy logic controller is widely used in many control applications the advantages of using fuzzy logic controller are that the fuzzy logic controller can extract the control strategy from experts also the linguistic control rules of fuzzy controller are fit for human s thought however a primary drawback of the fuzzy logic controller is that the linguistic control rules are hard to generate it also requires knowledge and experience of human experts another drawback is the stability and robustness of the fuzzy control system are hard to check to achieve the stability and robustness properties of a fuzzy control system the fuzzy sliding mode control technique is proposed in the spirit of fuzzy control and sliding mode control strategy to simplify the design procedure of fuzzy sliding mode control rules two design procedures that is taguchi s method and the genetic algorithms are applied the controller design of a third order nonlinear oscillation system is illustrated as a study case comparisons between these two design procedures are also given

stability of a polytope of matrices counterexamples while there have been significant breakthroughs for the stability of a polytope of polynomials since v l kharitonov s 1978 seminal result on interval polynomials for a polytope of matrices the stability problem is considered far from completely resolved counterexamples are provided for three conjectures that are directly motivated by the results in the polynomial case these counterexamples illustrate the fundamental differences between polynomial stability and matrix stability problems and indicate that some obvious lines of attack on the matrix polytope stability problem will fail

fuzzy control theory the linear case abstract a linear fuzzy proportional integral pi controller with one input and one output is defined in terms of piecewise linear membership functions for fuzzification control rules and defuzzification algorithm it is shown that a linear fuzzy controller is not equivalent to a linear non fuzzy pi controller if the rules are evaluated using the zadeh probability or lukasiewicz fuzzy logic alone however the linear fuzzy controller is precisely equivalent to a linear non fuzzy pi controller if mixed fuzzy logic is used to evaluate the control rules when the fuzzy logics used are selected with due regard to prior associations implied by the control rule operands themselves this finding has relevance to the selection of fuzzy logics in fuzzy expert systems and for fuzzy logics in general

sufficient conditions on general fuzzy systems as function approximators abstract in a constructive way we have found sufficient conditions under which general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy more importantly we have revealed the underlying mechanism of such function approximation the fuzzy systems can uniformly approximate any polynomials which according to the weierstrass approximation theorem can uniformly approximate any continuous function on a compact domain these findings lead to the following practical results 1 explicit fuzzy rules of fuzzy systems can now be easily obtained according to functions to be approximated and 2 formulas are derived which can calculate the number of input fuzzy sets output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy the number increases as required approximation error decreases and as approximation error approaches zero the number approaches these formulas also reveal that the number is minimal when the maximum number of intersection between adjacent input fuzzy sets is one practical implications of these results will be discussed especially in the context of fuzzy control and fuzzy modeling two examples are provided to demonstrate how to design fuzzy systems to approximate given functions with required approximation accuracy

sugeno type controllers are universal controllers abstract we show that given any continuous real valued function on a compact set there is a sugeno type controller that will approximate this function to any degree of accuracy an application of this result to fuzzy control is presented which shows that this type of sugeno controller is a universal controller

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

stability analysis of control system having pd type of fuzzy controller stability of a control system having pd type of fuzzy controller a two input and single output controller is analyzed in this paper using yakubovich s method in this analysis the controller is treated as a two input and two output controller and the nonlinearity of the controller is characterized as the sector condition absolute stability conditions are derived for the control system as three conditions two are conditions for either one of control modes p or d is independently operating the third is the condition for two modes are simultaneously active the former two conditions are nothing but popov s conditions for two siso systems a new graphical method is proposed to solve the latter condition this method is explained illustratively using an example and the results obtained are compared numerically with those by other graphical methods as well as simulation results

dividing quantum channels we investigate the possibility of dividing quantum channels into concatenations of other channels thereby studying the semigroup structure of the set of completely positive trace preserving maps we show the existence of indivisible channels which can not be written as non trivial products of other channels and study the set of infinitesimal divisible channels which are elements of continuous completely positive evolutions for qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels moreover we identify those channels which are solutions of time dependent master equations for both positive and completely positive evolutions for arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and markovian approximations

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

divisibility and information flow notions of quantum markovianity for noninvertible dynamical maps we analyze the relation between completely positive cp divisibility and the lack of information backflow for an arbitrary not necessarily invertible dynamical map it is well known that cp divisibility always implies a lack of information backflow moreover these two notions are equivalent for invertible maps in this letter it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which however needs not be trace preserving interestingly for a wide class of image nonincreasing dynamical maps this propagator becomes trace preserving as well and hence the lack of information backflow implies cp divisibility this result sheds new light into the structure of the time local generators giving rise to cp divisible evolutions we show that if the map is not invertible then positivity of dissipation decoherence rates is no longer necessary for cp divisibility

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

stability analysis and stabilization of fuzzy state space models abstract a new stability test method for linguistic fuzzy state space models is proposed in this paper this method allows the determination of stability of fuzzy models by applying the lyapunov function to each rule a gradient based algorithm is suggested to simplify the stability tests using this algorithm the lyapunov equation can be updated towards the direction where the stability can be determined more correctly an additional gradient based stabilizing algorithm is also derived which allows a systematic approach to find stabilizing controls by updating the lyapunov equations towards the direction where unstable eigenvalues are decreased examples demonstrate the convenience of the stability test and the two suggested gradient based algorithms

an approach to the analysis of fuzzy systems this paper deals with a formal description of ill defined processes fuzzy systems by the use of fuzzy relational equations it is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory some equivalence between these two kinds of description is presented basic problems of fuzzy systems e g identification prediction sensitivity and stability are shown and numerical algorithms are given indices of each method are introduced especially the degree of fuzziness the sensitivity index which makes it possible to express the quality of each of them

piecewise linear identification of non linear systems methods of identifying a series of piecewise linear models which approximate to a non linear system over some operating range are investigated spatial linear models and models with signal dependent parameters are considered

structure and control of piecewise linear systems elementary algebraic topology is used in the study of the structure and optimal control of piecewise linear and non linear systems

stability analysis of fuzzy control systems in this paper we present a general review of the stability issue as related to fuzzy control systems the concept of stability and the general criterion used for fuzzy control systems are discussed the intuitive and nonlinear system stability analysis of fuzzy control systems are given popov s technique is proposed to test the stability of fuzzy systems

robust stability analysis of fuzzy control systems abstract robust stability of fuzzy control systems is studied through the popov lyapunov approach first we transform a fuzzy control system into a lur e system with uncertainties or nonlinearities second the lyapunov s direct method is used to guarantee the stability of the perturbed lur e system and then a robustness measurement which gives the bound on allowable uncertainties or nonlinearities is derived also if the bound of the uncertainties nonlinearities of the system is known we can find an estimated region of asymptotic stability in phase space a nonlinear numerical example and a magnetic bearing experiment demonstrating the feasibility of the method are illustrated

constructive method for detecting the information backflow of non markovian dynamics we investigate the relation between two approaches to the characterization of quantum markovianity divisibility and lack of information backflow we show that a bijective dynamical map is completely positive divisible if and only if a monotonic nonincrease of distinguishability is observed for two equiprobable states of the evolving system and an ancilla moreover our proof is constructive given any such map that is not completely positive divisible we give an explicit construction of two states that when taken with the same a priori probability exhibit information backflow finally while an ancilla is necessary for the equivalence to hold in general we show that it is always possible to witness the non markovianity of bijective maps without using any entanglement between the system and ancilla

design of a fuzzy logic controller as a suction controller abstract a fuzzy logic controller flc designed as a suction controller is proposed firstly we prove that there exists a switching line in the flc and the slope of the switching line is determined by scaling factors secondly a lyapunov function is selected and sufficient conditions for the fuzzy control system fcs to be globally asymptotically stable is determined based on the sufficient conditions a design procedure is suggested to guarantee that the fcs is globally asymptotically stable both a nonlinear oscillator and a cart pole system are simulated to demonstrate the proposed flc we show that not only is the flc similar to sliding mode control smc but also a realizable method for a suction controller is described in addition a lemma is introduced to interpret that the rise time of the fcs can be adjusted by the scaling factors

realization of pid controls by fuzzy control methods abstract this paper shows that pid controllers can be realized by fuzzy control methods of product sum gravity method and simplified fuzzy reasoning method pid controllers however cannot be constructed by min max gravity method known as mamdani s fuzzy reasoning method furthermore extrapolative reasoning can be executed by the product sum gravity method and simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules

robust control by fuzzy sliding mode abstract most fuzzy controllers fcs for nonlinear second order systems are designed with a two dimensional phase plane in mind we show that the performance and the robustness of this kind of fc stems from their property of driving the system into the sliding mode sm in which the controlled system is invariant to parameter fluctuations and disturbances additionally the continuous distribution of the control values in the phase plane causes a behavior similar to that of a sliding mode controller smc with a boundary layer bl near the switching line this gives assured tracking quality even in the presence of high model uncertainties tracing the fc back to the principle of an smc one obtains evidence about the stability of the closed loop system the choice of the scaling factors for the crisp inputs and outputs can be guided by the comparison of the fc with the smc and with the modified smc respectively at the end of the paper an fc for a higher order system is proposed simulation results show the practicability of the method

constructive theory for fuzzy systems abstract in this paper a constructive theory is developed to establish the fact that we can build a fuzzy system to approximate any continuous function on a compact set within a prescribed error bound based on the theory an algorithm is described that can actually construct a near minimum fuzzy system for a given function to a desired accuracy

operational characterization of divisibility of dynamical maps in this work we show the operational characterization to the divisibility of dynamical maps in terms of the distinguishability of quantum channels it is proven that the distinguishability of any pair of quantum channels does not increase under divisible maps in which the full hierarchy of divisibility is isomorphic to the structure of entanglement between system and environment this shows that i channel distinguishability is the operational quantity signifying detecting divisibility indivisibility of dynamical maps and ii the decision problem for the divisibility of maps is as hard as the separability problem in entanglement theory we also provide the information theoretic characterization to the divisibility of maps with conditional min entropy

a fuzzy variable structure approach to feedback regulation of uncertain dynamical systems with application to robotics this paper develops a fuzzy logic based control design methodology for a large class of nonlinear uncertain dynamical systems the proposed control design approach combines the powerful tools of fuzzy logic and approximate reasoning with the advanced mathematical synthesis techniques used in variable structure control systems theory the rationale for the proposed control design approach is motivated by the results of a recent study that has rigorously established some connections between fuzzy logic and variable structure control systems the results of this paper represent a step in the right direction for systematic design of a less expert dependent fuzzy logic control to illustrate the merits of the new control approach the latter is applied to a 2 degree of freedom robot manipulator preliminary simulation results suggest that the proposed control design deals effectively with the chattering problem encountered when the classical variable structure control is used alone

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm

linguistic stability analysis of fuzzy closed loop control systems abstract a linguistic analysis method for fuzzy closed loop control systems where both fuzzy controller and controlled processes are described by linguistic rules is proposed in this paper first a linguistic relation model of a fuzzy closed loop control system is deduced from the linguistic rule models of the fuzzy controller and the controlled process then the linguistic stability of the fuzzy closed loop system is discussed by a linguistic relation matrix finally an example is given to illustrate the proposed method