a new approach to the design of a fuzzy sliding mode controller by defining a new generalized error transformation as a complement to the conventional sliding variable we derived a novel stable sliding mode control scheme on which the design of a new two input one output fuzzy sliding mode controller is based a significant advantage of this control scheme is its distinct capability of improving the transient behavior of the system during the reaching phase as well as the guaranteed steady state tracking precision while in the boundary layer the design procedure was illustrated by a force adaptive robot effector acting on various profiles of surfaces as demonstrated from simulations it appears that a comparatively good performance can be reached by the proposed fuzzy controller

two step stability analysis for general polynomial fuzzy model based control systems this paper investigates the stability of a polynomial fuzzy model based pfmb control system formed by a nonlinear plant represented by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop three cases of polynomial fuzzy controllers are proposed for the control process with the consideration of a matched mismatched number of rules and or premise membership functions which demonstrate different levels of controller complexity design flexibility and stability analysis results a general polynomial lyapunov function candidate is proposed to investigate the system stability unlike the published work there is no constraint on the polynomial lyapunov function candidate which is independent of the form of the polynomial fuzzy model thus it can be applied to a wider class of pfmb control systems and potentially produces more relaxed stability analysis results two step stability conditions in terms of sum of squares sos are obtained to numerically find a feasible solution to facilitate the stability analysis and relax the stability analysis result the boundary information of membership functions is taken into account in the stability analysis and incorporated into the sos based stability conditions simulation examples are given to illustrate the effectiveness of the proposed approach

adaptive fuzzy control of mimo nonlinear systems this paper presents a novel fuzzy basis function approach for adaptive control of multi input and multi output mimo systems in the method the nonlinear plant is first linearised and the fuzzy basis function vector is introduced to adaptively learn the upper bound of the system uncertainty vector while its output is used as the parameter of the compensator in the sense that both the robustness and the asymptotic error convergence can be obtained for the closed loop nonlinear control system

control design for fuzzy systems based on relaxed nonquadratic stability and h_ infty performance conditions in this paper new approaches to hinfin controller design for a class of discrete time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis dependent lyapunov functions are used first two relaxed conditions of nonquadratic stability with h infin norm bound are presented for this class of systems the two relaxed conditions are shown to be useful in designing fuzzy control systems by introducing some additional instrumental matrix variables the two relaxed conditions are used to develop hinfin controllers in the control design the first relaxed condition has fewer inequality constraints but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables finally two examples are given to demonstrate the applicability of the proposed approach

lmi based stability analysis for fuzzy model based control systems using artificial t s fuzzy model this paper investigates the stability of fuzzy model based fmb control systems an alternative stability analysis approach using an artificial fuzzy system based on the lyapunov stability theory is proposed to facilitate the stability analysis the continuous membership functions of the takagi sugeno t s fuzzy model are represented by the staircase ones with the nice property of the staircase membership functions it turns the set of infinite number of linear matrix inequality lmi based stability conditions into a finite one furthermore the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions the stability of the original fmb control systems is guaranteed by the satisfaction of the lmi based stability conditions the proposed stability analysis is applied to the fmb control systems of which the t s fuzzy model and fuzzy controller do not share the same premise membership functions and thus is able to enhance the design flexibility of the fuzzy controller a simulation example is given to illustrate the merits of the proposed approach

fuzzy rule based combination of linear and switching state feedback controllers this paper presents a fuzzy rule base combined controller which is a fuzzy rule based combination of linear and switching state feedback controllers for nonlinear systems subject to parameter uncertainties the switching state feedback controller is employed to drive the system states toward the origin when the system state approaches the origin the linear state feedback controller will gradually replace the switching state feedback controller the smooth transition between the linear and switching state feedback controllers is governed by the fuzzy rules by using the fuzzy rule based combination technique the proposed fuzzy rule base combined controller integrates the advantages of both the linear and switching state feedback controllers but eliminates their disadvantages as a result the proposed fuzzy controller provides good performance during the transient period and the chattering effect is removed when the system state approaches the origin stability conditions will be derived to guarantee the system stability furthermore a saturation function is employed to replace the switching component to alleviate the chattering during the transient period by using the proposed fuzzy rule based combination technique the steady state error introduced by the saturation function can be eliminated application examples will be given to show the merits of the proposed approach

output regulation of polynomial fuzzy model based control systems this paper investigates the output regulation problem of polynomial fuzzy model based pfmb control systems with the consideration of system stability and control synthesis using the sum of squares sos based approach a pfmb control system is formed by a polynomial fuzzy model and a polynomial fuzzy controller with integral action connected in a closed loop three cases of pfmb control systems regarding the premise membership functions and number of fuzzy rules which have their own properties and advantages are considered the stability of the pfmb control systems is investigated based on the lyapunov stability theory with consideration of the information of membership functions sos based stability conditions corresponding to each case are obtained to guarantee system stability and to realize output regulation simulation examples are given to compare the three cases and illustrate the effectiveness of the proposed approach

distributed continuous time convex optimization on weight balanced digraphs this technical note studies the continuous time distributed optimization of a sum of convex functions over directed graphs contrary to what is known in the consensus literature where the same dynamics works for both undirected and directed scenarios we show that the consensus based dynamics that solves the continuous time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting this study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge on any strongly connected weight balanced digraph to the set of minimizers of a sum of convex differentiable functions with globally lipschitz gradients our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results

variable structure adaptive fuzzy control for a class of nonlinear time delay systems abstract in this paper the problem of variable structure adaptive fuzzy control for a class of nonlinear time delay systems is investigated sliding surface dependent of the time delay is constructed based on the lyapunov krasovskii method two adaptive fuzzy logic systems are proposed to approximate two unknown continuous nonlinear functions containing the current state and the delayed state respectively the corresponding reaching law is designed which can drive the state trajectory of the closed system onto the sliding surface within limited time simulation investigation verifies the effect of the main results of the paper

stability analysis and performance design for fuzzy model based control system under imperfect premise matching this paper investigates the stability analysis and performance design of nonlinear systems to facilitate the stability analysis the takagi sugeno t s fuzzy model is employed to represent the nonlinear plant under the imperfect premise matching in which t s fuzzy model and fuzzy controller do not share the same membership functions a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant however the nice characteristic given by the perfect premise matching leading to conservative stability conditions vanishes in this paper under the imperfect premise matching information of membership functions of the fuzzy model and controller are considered in stability analysis with the introduction of slack matrices relaxed linear matrix inequality lmi based stability conditions are derived using lyapunov based approach furthermore lmi based performance conditions are provided to guarantee system performance simulation examples are given to illustrate the effectiveness of the proposed approach

quadratic stability analysis of fuzzy model based control systems using staircase membership functions this paper presents the stability analysis of fuzzy model based fmb control systems staircase membership functions are introduced to facilitate the stability analysis through the staircase membership functions approximating those of the fuzzy model and fuzzy controller the information of the membership functions can be brought into the stability analysis based on the lyapunov stability theory stability conditions in terms of linear matrix inequalities lmis are derived in a simple and easy to understand manner to guarantee the system stability the proposed stability analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the lmi based stability conditions for a dedicated fmb control system furthermore the proposed stability analysis approach can be applied to the fmb control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers by employing membership functions with simple structure it is possible to lower the structural complexity and the implementation cost simulation examples are given to illustrate the merits of the proposed approach

adaptive fuzzy output tracking control of mimo nonlinear uncertain systems in this paper the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple input multiple output mimo nonlinear systems with the block triangular structure the fuzzy logic systems are used to approximate the unknown nonlinear functions by using the backstepping technique the adaptive fuzzy tracking control design scheme is developed which has minimal learning parameterizations the adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed loop system are semiglobally uniformly ultimately bounded two examples are used to show the effectiveness of the approach

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

stability analysis of polynomial fuzzy model based control systems with mismatched premise membership functions this paper investigates the stability of polynomial fuzzy model based pfmb control system which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop to enhance the design flexibility the number of rules and the shape of premise membership functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model however which make the stability analysis more difficult and potentially lead to conservative stability analysis result a sum of squares sos based stability analysis approach using the lyapunov stability theory is proposed to investigate the stability of the pfmb control systems and synthesize the polynomial fuzzy controller to facilitate the stability analysis and relax the stability analysis result the property of the membership functions and the boundary information of the membership grades and premise variables are taken into account in the stability analysis and incorporated into the sos based stability conditions a simulation example is given to illustrate the effectiveness of the proposed approach

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

polynomial fuzzy models for nonlinear control a taylor series approach classical takagi sugeno t s fuzzy models are formed by convex combinations of linear consequent local models such fuzzy models can be obtained from nonlinear first principle equations by the well known sector nonlinearity modeling technique this paper extends the sector nonlinearity approach to the polynomial case this way generalized polynomial fuzzy models are obtained the new class of models is polynomial both in the membership functions and in the consequent models importantly t s models become a particular case of the proposed technique recent possibilities for stability analysis and controller synthesis are also discussed a set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard t s approaches as the degrees of the involved polynomials increase

polynomial fuzzy model based control systems stability analysis via piecewise linear membership functions this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems using the sum of squares sos approach the pfmb control system under consideration requires that the polynomial fuzzy model and polynomial fuzzy controller share neither the same premise membership functions nor the same number of fuzzy rules this class of pfmb control systems offers a greater design flexibility to the polynomial fuzzy controller however due to the imperfectly matched membership functions it usually produces more conservative stability conditions by following the traditional stability analysis approach for the fmb control systems to facilitate the stability analysis piecewise linear membership functions plmfs are proposed which offer a nice property that the grades of membership are governed by a finite number of sample points thus it allows the plmfs to be brought to the sos based stability conditions which are applied to the pfmb control systems with the specified plmfs rather than any shapes the system stability can be examined by checking only the pfmb control system at the sample points it is worth mentioning that the plmfs which are not necessarily implemented physically are a mathematical tool to carry out the stability analysis to verify the stability analysis result a simulation example is given to demonstrate the effectiveness of the proposed approach

robust fuzzy design for nonlinear uncertain stochastic systems via sliding mode control this paper deals with the sliding mode control smc problem for nonlinear stochastic time delay systems by means of fuzzy approach the takagi sugeno t s fuzzy stochastic time delay model with parametric uncertainties and unknown nonlinearities is presented a sufficient condition for the exponential stability in mean square of the sliding motion is also derived moreover it is shown that when the linear matrix inequalities lmis with equality constraint are feasible the designs of both sliding surface and sliding mode controller can be easily obtained via convex optimization a simulation example illustrating the proposed method is given

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

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

stabilization of uncertain fuzzy time delay systems via variable structure control approach in view of a recent new application of variable structure control vsc to the stabilization problem for takagi sugeno t s fuzzy models this paper aims to study the stabilization of uncertain fuzzy time delay systems in t s fuzzy model via vsc approach there are mainly two features in this paper one lies in the incorporation of time delays both smooth and nonsmooth delays in which case lyapunov functionals and razumikhin theorem are required to solve the stabilization problem the other feature is that not only matched uncertainties but also mismatched uncertainties in the state variables are considered as a sequence the contribution of this paper consists of various control schemes proposed for the vsc design and the present results are in terms of linear matrix inequalities lmis an illustrative example is given to show the effectiveness of our various results

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

a novel takagi sugeno based robust adaptive fuzzy sliding mode controller in this paper a nonlinear dynamic system is first approximated by n fuzzy based linear state space subsystems to track a trajectory dominant by a specific frequency the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule similarly the same fuzzy sets of the system rule are employed to design robust fuzzy sliding mode control rfsmc and adaptive fuzzy sliding mode control afsmc the difference between rfsmc and afsmc is that afsmc contains an updating law to learn system uncertainties and then an extra compensation is designed it is different from the most previous papers to learn the whole nonlinear functions as the norm of the sliding surface is inside of a defined set the updating law starts simultaneously as it is outside of the other set the updating law stops for the purpose of smoothing the possibility of discontinuous control input a transition between rfsmc and afsmc is also assigned under the circumstances the proposed control robust adaptive fuzzy sliding mode control rafsmc can automatically tune as a rfsmc or an afsmc then the advantages coming from the rfsmc and afsmc are obtained finally the stabilities of the overall system of rfsmc afsmc and rafsmc are verified by lyapunov stability theory the compared simulations among rfsmc afsmc and rafsmc are also carried out to confirm the usefulness of the proposed control scheme

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller

sos based stability analysis of polynomial fuzzy model based control systems via polynomial membership functions this paper presents stability analysis of polynomial fuzzy model based fmb control systems using the sum of squares sos approach recently stability analysis of the polynomial fuzzy control systems which is a generalized form of the well known takagi sugeno t s fmb control systems has been reported in the form of sos based stability conditions lack of information on the relations between membership functions and premise variables in the existing stability analysis approaches causes conservatism of their results in this paper to derive relaxed stability conditions for polynomial fmb control systems membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis considering a polynomial fmb control system and based on the lyapunov stability theory stability conditions in the form of fuzzy summations are derived where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller each product term is approximated by a polynomial in order to obtain better approximation the operating domain of membership functions is partitioned to subregions then sos based stability conditions for all subregions are derived unlike some published stability analysis approaches the proposed one can be employed for stability analysis of polynomial fuzzy control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions the solution of the sos based stability conditions can be found numerically using sostools which is a free third party matlab toolbox numerical examples are given to illustrate the effectiveness of the proposed stability conditions