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

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

on the periodic solutions of periodic multi species kolmogorov type competitive system with delays and feedback controls abstract in this paper we consider a periodic multi species kolmogorov type competitive system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive periodic solution of the system are obtained as application the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed

constructing narmax models using armax models this paper outlines how it is possible to decompose a complex non linear modelling problem into a set of simpler linear modelling problems local armax models valid within certain operating regimes are interpolated to construct a global narmax non linear narmax model knowledge of the system behaviour in terms of operating regimes is the primary basis for building such models hence it should not be considered as a pure black box approach but as an approach that utilizes a limited amount of a priori system knowledge it is shown that a large class of non linear systems can be modelled in this way and indicated how to decompose the systems range of operation into operating regimes standard system identification algorithms can be used to identify the narmax model and several aspects of the system identification problem are discussed and illustrated by a simulation example

strongly order preserving semiflows generated by functional differential equations the aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems due to the authors 12 13 j to certain systems of functional differential equations fde s which do not enjoy the quasimonotone property considered by one of us in 9 the present work extends our previous results in this direction for scalar equations in 111 to systems in the fundamental paper s m w hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space x tend to the set e of equilibria employing ideas of hirsch and of h matano 7 the authors have extended the theory to obtain some improvements in the results of hirsch and matano under matano s weaker assumption that the semiflow is strongly order preserving recently in 13 we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium these conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium p policik s has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties in this paper wc apply the convergence results developed in 131 to nonquasimonotone fde s in this introduction wc briefly review the application of monotone dynamical systems theory to fde s enjoying the quasimonotone property this research appeared in 9 133 then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property m holds some simple examples are given which

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

fuzzy adaptive control of a certain class of siso discrete time processes in this manuscript we address the problem of the stability of a certain class of siso discrete time processes controlled by an adaptive fuzzy controller by using lyapunov stability theory these results were recently obtained for adaptive neural controllers and are extended here to adaptive fuzzy controllers of sugeno s type in order to achieve tracking of a reference signal with this kind of fuzzy system we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law we first present the gradient based steepest descent adaptation law and we argue that this gradient based adaptation law can be simplified dramatically thereafter we show the asymptotic stability of the overall system the convergence of the tracking error to zero when using this simplified parameters adjustment law unfortunately this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking that is when the parameters are initialized not too far from their optimal values local stability however when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules i e the membership functions of the premises are not modified and when the reference signal is the delayed desired output the stability result is strictly valid the parameters do not have to be initialized around the perfectly tuned values in this case the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented

fuzzy network model based fuzzy state controller design the performance of model based controller design relies heavily on the quality and suitability of the utilized process model this contribution proposes a fuzzy network based nonlinear controller design methodology fuzzy networks are a model approach combining high approximation quality with high interpretability the input output i o models commonly used for identification are transformed to fuzzy state space models transferring and adjusting methods from linear state space theory a control concept consisting of a fuzzy state controller and an adaptive set point filter for nonlinear dynamic processes is deduced the capability of the method is demonstrated for a hydraulic drive

approximation accuracy of some neuro fuzzy approaches many methods have been proposed in the literature for designing fuzzy systems from input output data the so called neuro fuzzy methods but very little was done to analyze the performance of the methods from a rigorous mathematical point of view in this paper we establish approximation bounds for two of these methods the table lookup scheme proposed by wang et al 1992 and the clustering method studied by wang 1993 1997 we derive detailed formulas of the error bounds between the nonlinear function to be approximated and the fuzzy systems designed using the methods based on input output data these error bounds show explicitly how the parameters in the two methods influence their approximation capability we also propose modified versions for the two methods such that the designed fuzzy systems are well defined over the whole input domain

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

approximation and convergence rate of nonlinear eigenvalues lipschitz perturbations of a bounded self adjoint operator abstract we consider nonlinear eigenvalue problems of the form t x b x x where t is a self adjoint bounded linear operator acting in a real hilbert space h and b h h is a possibly nonlinear continuous perturbation term assuming that 0 is an isolated eigenvalue of finite multiplicity of t we ask if for 0 and small there are eigenvalues of near 0 that is numbers for which is satisfied by some normalized eigenvector x of t b in this paper we recall some recent results giving an affirmative answer to this question and for these cases we prove assuming in addition lipschitz continuity on b upper and lower bounds for the perturbed eigenvalues which are determined by those for the nonlinear rayleigh quotient b v v v v with v in the eigenspace ker t 0 i this yields in particular information on the rate of convergence of to 0 as 0 applications are given in the sequence space l 2 and in the sobolev space h 0 1 to deal with some nonlinearly perturbed ordinary or partial differential equations

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

experimental studies in nonlinear discrete time adaptive prediction and control this paper presents implementation results using recently introduced discrete time adaptive prediction and control techniques using online function approximators we consider a process control experiment as our test bed and develop a discrete time adaptive predictor for liquid volume and a discrete time adaptive controller for reference volume tracking we use takagi sugeno ts fuzzy systems as our function approximators and for both prediction and control we investigate the use of a least squares update of the fuzzy system s parameters

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

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

adaptive linear control of nonlinear systems the theory of stable parameter adaptive control has advanced to allow linear time varying plants however a more honest view of such systems is that they are often derived from inexact linearization about a trajectory of a nonlinear system standard adaptive control based on a linear model can then be interpreted as one way to realize a nonlinear controller for a nonlinear plant the implications of this view are studied analytically the stability problem is seen to be equivalent to showing robustness to time varying parameters and a locally bounded model uncertainty it is shown that if the trajectory is known to be within a bound a parameter estimator with projection can ensure boundedness of departures from the trajectory

fuzzy systems and controllers lyapunov tools for a regionwise approach this paper reviews a class of tools which can help to check the stability of fuzzy linguistic controllers which is a difficult task due to their regionwise structure the application of conventional methods when considering a fuzzy controller as a global nonlinear controller often leads to conservative stability results the use of appropriate continuous or piecewise continuous lyapunov functions allows to address the stability of nonlinear systems under fuzzy control while taking into account the local structure of the fuzzy controllers some methods are presented which enforce the global lyapunov function to decrease when leaving one subspace for another closer to the equilibrium using concentric domains and providing less conservative conditions

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples

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

optimal tracking design for stochastic fuzzy systems in general fuzzy control design for stochastic nonlinear systems is still difficult since the fuzzy bases are stochastic so as to increase the difficulty and complexity of the fuzzy tracking control design in this study a fuzzy stochastic moving average model with control input fuzzy armax model is introduced to describe nonlinear stochastic systems from the fuzzy armax model a fuzzy one step ahead prediction model is developed based on a fuzzy one step ahead prediction stochastic model optimal design algorithms are proposed to achieve the optimal tracking of nonlinear stochastic systems in this study the minimum variance tracking control generalized minimum variance tracking control and the optimal model reference tracking control are developed for stochastic fuzzy systems we construct some basic stability conditions for general stochastic fuzzy systems and use these conditions to verify the stability of the fuzzy tracking control systems finally two simulation examples are given to indicate the performance of the proposed methods

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

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

stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic abstract this paper deals with the design of stable rule based fuzzy control systems interval analysis is applied to design a stable fuzzy takagi sugeno kang controller using a robust condition to ensure the stability the presented methodology starts with a state model of the plant finds a candidate fuzzy controller and uses an interval arithmetic algorithm to verify the stability of closed loop fuzzy model it is important to emphasize the generality of the presented methodology for fuzzy controller synthesis since there are no constraints in the state vector nor in the control vector this methodology can also be used with nonlinear plant models in previous works we showed the applicability of the interval analysis to design a controller that ensures the stability of first order nonlinear system in this paper we extend the analysis and the synthesis of stable fuzzy control system to the multivariable case an example with a fuzzy controller for a nonlinear system is presented to illustrate the design procedure

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

variable selection algorithm for the construction of mimo operating point dependent neurofuzzy networks an input variable selection procedure is introduced for the identification and construction of multi input multi output mimo neurofuzzy operating point dependent models the algorithm is an extension of a forward modified gram schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting the proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice based modeling algorithms such as radial basis function neurofuzzy networks enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm

construction of fuzzy models through clustering techniques abstract in this note we will discuss fuzzy models designed with the aid of fuzzy clustering the clustering method utilizes a generalized objective function involving a collection of linear varieties in this way the model is distributed and consists of a series of local linear type models based on the revealed clusters in comparison to the algorithms existing in the literature and producing function like models the proposed one is of a relational character allowing for multidirectional accessibility a detailed identification algorithm is given and illustrated with the aid of numerical examples

on the periodic solutions of periodic multi species competitive systems with delays the paper considers general n species periodic kolmogorov competitive systems of functional differential equations with finite or infinite delays applying schauder s fixed point theorem a criterion on the existence of the positive periodic solutions is established as applications the existence and global asymptotic stability of the single species logistic periodic model and n species lotka volterra type periodic model with delays are discussed