generalized symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear generalized symmetric dual variational problems involving vector valued functions which unify the wolfe and mond weir models for a special case our problems become the symmetric dual pair of d s kim and w j lee 1998 j math anal appl 218 34 48 under invexity assumptions we establish weak strong and converse duality theorems for our variational problems by using the concept of efficiency also we give the static case of our multiobjective generalized symmetric duality results several known results are obtained as special cases

pi fuzzy controllers for integral plants to ensure robust stability new pi fuzzy controllers comprising takagi sugeno and mamdani fuzzy systems to control a class of integral plants specific to servo systems are proposed in this paper linear pi controllers are designed in the first phase they are tuned using the extended symmetrical optimum method to ensure the desired overshoot and settling time with respect to step setpoint modifications and three types of load disturbance inputs this type of pi controller design guarantees robust stability of the closed loop system in response to parametric variations in a controlled plant following this based on the results from the linear case and the modal equivalence principle an original development method for pi fuzzy controllers is proposed some experimental results are included to illustrate the effectiveness of the design process

robust quadratic optimal control of ts fuzzy model based dynamic systems with both elemental parametric uncertainties and norm bounded approximation error this paper considers the design problem of the robust quadratic optimal parallel distributed compensation pdc controllers for takagi sugeno ts fuzzy model based control systems with both elemental parametric uncertainties and norm bounded approximation error by complementarily fusing the robust stabilizability condition the orthogonal functions approach ofa and the hybrid taguchi genetic algorithm htga an integrative method is presented in this paper to design the robust quadratic optimal pdc controllers such that 1 the uncertain ts fuzzy model based control systems can be robustly stabilized and 2 a quadratic integral performance index for the nominal ts fuzzy model based control systems can be minimized in this paper the robust stabilizability condition is proposed in terms of linear matrix inequalities lmis by using the ofa and the lmi based robust stabilizability condition the robust quadratic optimal pdc control problem for the uncertain ts fuzzy model based dynamic systems is transformed into a static constrained optimization problem represented by the algebraic equations with constraint of lmi based robust stabilizability condition thus greatly simplifying the robust optimal pdc control design problem then for the static constrained optimization problem the htga is employed to find the robust quadratic optimal pdc controllers of the uncertain ts fuzzy model based control systems two design examples of the robust quadratic optimal pdc controllers for an uncertain inverted pendulum system and an uncertain nonlinear mass spring damper mechanical system are given to demonstrate the applicability of the proposed integrative approach

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

h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

symmetric duality with pseudo invexity in variational problems abstract weak and strong duality results are established under pseudo invexity hypotheses for symmetric dual variational problems self dual problems and static symmetric dual programs are included as special cases

a state predictor for continuous time stochastic systems abstract this work investigates the state prediction problem for nonlinear stochastic differential systems affected by multiplicative state noise this problem is relevant in many state estimation frameworks such as filtering of continuous discrete systems i e stochastic differential systems with discrete measurements and time delay systems a very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise free system unfortunately these methods provide the exact solution only for linear systems instead here we provide the exact state prediction for nonlinear system in terms of the series expansion of the expected value of the state conditioned to the value in a previous time instant obtained according to the carleman embedding technique the truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation simulations support the effectiveness of the proposed state prediction algorithm in comparison to the aforementioned heuristic method

fuzzy functions with support vector machines a new fuzzy system modeling fsm approach that identifies the fuzzy functions using support vector machines svm is proposed this new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods it is a new alternate version of the earlier fsm with fuzzy functions approaches svm is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c means fcm clustering algorithm original input variables the membership values obtained from the fcm together with their transformations form a new augmented set of input variables the performance of the proposed system modeling approach is compared to previous fuzzy functions approaches standard svm lse methods using an artificial sparse dataset and a real life non sparse dataset the results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods

a note on higher order symmetric duality in this paper a pair of wolfe type higher order symmetric dual multiobjective programs is formulated strong and converse duality theorems are established under invexity assumptions duality relations for mond weir type dual models have also been obtained under pseudoinvexity assumptions

a chain observer for nonlinear systems with multiple time varying measurement delays this paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time varying delays a modular approach is followed where subobservers are connected in cascade to achieve a desired exponential convergence rate chain observer when the delay is small a single step observer is sufficient to carry out the goal two or more subobservers are needed in the the presence of large delays the observer employs delay dependent time varying gains to achieve the desired exponential error decay the proposed approach allows to deal with vector output measurements where each output component can be affected by a different delay relationships among the error decay rate the bound on the measurement delays the observer gains and the lipschitz constants of the system are presented the method is illustrated on the synchronization problem of continuous time hyperchaotic systems with buffered measurements

on some symmetric dual models in multiobjective programming certain omissions have been pointed out in some papers on symmetric duality in multiobjective programming corrective measures have also been discussed

p r invex sets and functions abstract notions of invexity of a function and of a set are generalized the notion of an invex function with respect to can be further extended with the aid of p invex sets slight generalization of the notion of p invex sets with respect to leads to a new class of functions a family of real functions called in general p r pre invex functions with respect to without differentiability or p r invex functions with respect to in the differentiable case is introduced some geometric properties of these classes of functions are derived sufficient optimality conditions are obtained for a nonlinear programming problem involving p r invex functions with respect to

symmetric dual nonlinear programming and matrix game equivalence abstract we present some equivalences between some symmetric dualities in nonlinear programming and some matrix games we study three pairs of dual problems wolfe mond weir and fractional types for each pair the paper presents two different zero sum games whose nash equilibria correspond to the solutions of the pair of nonlinear symmetric dual problems and certain conclusions about symmetric dual fractional programming and its special cases are also treated

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

a class of b p r invex functions and mathematical programming abstract invexity of a function is generalized the new class of nonconvex functions called b p r invex functions with respect to and b being introduced includes many well known classes of generalized invex functions as its subclasses some properties of the introduced class of b p r invex functions with respect to and b are studied further mathematical programming problems involving b p r invex functions with respect to and b are considered the equivalence between saddle points and optima and different type duality theorems are established for this type of optimization problems

equivalence of saddle points and optima and duality for a class of non smooth non convex problems abstract the equivalence between saddle points and optima and duality theorems are established for a much larger class of non smooth non convex problems in which functions are locally lipschitz and are satisfying invex type conditions of hanson and craven

symmetric duality for a class of nondifferentiable multi objective fractional variational problems abstract we introduce a symmetric dual pair for a class of nondifferentiable multi objective fractional variational problems weak strong converse and self duality relations are established under certain invexity assumptions the paper includes extensions of previous symmetric duality results for multi objective fractional variational problems obtained by kim lee and schaible d s kim w j lee s schaible symmetric duality for invex multiobjective fractional variational problems j math anal appl 289 2004 505 521 and symmetric duality results for the static case obtained by yang wang and deng x m yang s y wang x t deng symmetric duality for a class of multiobjective fractional programming problems j math anal appl 274 2002 279 295 to the dynamic case

new invexity type conditions with applications to constrained dynamic games abstract weaker invexity type properties are presented in the continuous case and are then applied to develop duality results between a pair of symmetric dual variational problems a constrained dynamic game is shown to be equivalent to this symmetric dual pair

memoryless approach to the lq and lqg problems with variable input delay this note studies the lq and lqg problems for linear time invariant systems with a single time varying input delay and instantaneous memoryless state feedback we extend the memoryless state feedback solution proposed in 1 in two directions we prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay for which we provide a sufficient and sometimes strict bound moreover we show that this memoryless control is optimal also in the case of time varying delays and that the quadratic cost functional has the same value as in the case without delay for time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous finally we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case but with a larger cost than the delay less lqg solution

stabilization for t s model based uncertain stochastic systems this paper considers the stabilization problem of a class of uncertain ito stochastic fuzzy systems driven by a multidimensional wiener process the uncertainty modeled in the systems is of the linear fractional type which includes the norm bounded uncertainty as a special case the objective is to design a state feedback fuzzy controller such that the closed loop system is robustly asymptotically stable under a stochastic setting by using a stochastic lyapunov approach sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique the derived stability conditions are then employed to design controllers which stabilize the uncertain ito stochastic fuzzy systems two simulation examples are given to illustrate the effectiveness of the approaches proposed

minimax and symmetric duality for a class of multiobjective variational mixed integer programming problems abstract in this paper we formulate a pair of multiobjective variational mixed integer programs for arbitrary cones under the separability and partial invexity assumptions on the functions involved we establish the weak strong converse and self duality theorems related to efficient solution

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

symmetric duality for multiobjective variational problems abstract a mond weir type symmetric dual for a multiobjective variational problem is formulated weak and strong duality theorems under generalized convexity assumptions are proved for properly efficient solutions under an additional condition on the kernel function that occurs in the formulation of the problems a self duality theorem is proved a close relationship between these variational problems and symmetric dual nonlinear multiobjective programming problems is also incorporated

state feedback control of continuous time t s fuzzy systems via switched fuzzy controllers this paper studies the problem of state feedback control of continuous time t s fuzzy systems switched fuzzy controllers are exploited in the control design which are switched based on the values of membership functions and the control scheme is an extension of the parallel distributed compensation pdc scheme sufficient conditions for designing switched state feedback controllers are obtained with meeting an h norm bound requirement and quadratic d stability constraints it is shown that the new control design method provides less conservative results than the corresponding ones via the parallel distributed compensation pdc scheme a numerical example is given to illustrate the effectiveness of the proposed method

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints the aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent in addition the related dual problems for which the set of feasible parameters and the solvability set are studied these fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers the existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of a pareto optimality an illustrative example is given to clarify the obtained results

on variational problems characterization of solutions and duality in this paper we introduce a new class of pseudoinvex functions for variational problems using this new concept we obtain a necessary and sufficient condition for a critical point of the variational problem to be an optimal solution illustrated with an example also weak strong and converse duality are established

duality and sufficiency in control problems with invexity recently mond chandra and husain 3 established duality results for a variational problem under more general convexity conditions called invex than mond and hanson 4 in a similar fashion the results of mond and hanson s for duality in control problems are extended to more general convex or invex functions it is also shown that for invex functions the necessary conditions for optimality in the control problem are also sufficient

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

flexible stability criteria for a linguistic fuzzy dynamic system abstract this paper considers the stability problems of continuous and discrete type fuzzy control systems respectively on the basis of matrix measures and matrix norms several stability criteria for the systems are proposed some of these criteria are flexible with different chosen parameter p that means the trade off between the conservativeness and the computing convenience of the criteria depends on the chosen value of p totally

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

generalized fractional minimax programming with b p r invexity optimality conditions are proved for a class of generalized fractional minimax programming problems involving b p r invexity functions subsequently these optimality conditions are utilized as a basis for constructing various duality models for this type of fractional programming problems and proving appropriate duality theorems

new results on delay dependent robust stability criteria of uncertain fuzzy systems with state and input delays this paper focuses on the delay dependent stability analysis and stabilization for uncertain t s fuzzy control systems with state and input delays the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology in fact these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis finally some examples are included to show that the proposed criteria improve the existing results significantly

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

nonsmooth multiple objective optimization in separable hilbert spaces abstract this paper provides new necessary and sufficient optimality conditions for nonsmooth multiple objective optimization programs in separable hilbert spaces

a new approach to robust and non fragile h control for uncertain fuzzy systems this paper investigates the robust h control and non fragile control problems for takagi sugeno t s fuzzy systems with linear fractional parametric uncertainties the robust h control problem is to design a state feedback controller such that the robust stability and a prescribed h performance of the resulting closed loop system is ensured and the non fragile h control problem is to design a state feedback controller with parameter uncertainties based on the linear matrix inequality lmi approach new sufficient conditions for the solvability of the two problems are obtained it is shown that the desired state feedback fuzzy controller can be constructed by solving a set of lmis numerical examples are also provided to demonstrate the effectiveness of the proposed design method

symmetric duality with p r ρ η θ invexity abstract in this paper we introduce a new type of generalized invex function called p r invex function and study symmetric duality results under these assumptions in our study the nonnegative orthants for the constraints are replaced by closed convex cones and their polars we establish weak and strong duality theorems under p r invexity assumptions for the symmetric dual problems we also give many examples to justify our results

penalty function methods and a duality gap for invex optimization problems abstract in this paper the penalty function method is used to study duality in nonconvex mathematical programming problems in particular we prove the zero duality gap between optimization problems involving invex functions with respect to the same function and their lagrangian dual problems the results proved in the paper are illustrated by suitable examples of nonconvex optimization problems

filtering continuous time linear systems with time varying measurement delay we consider the filtering problem of lti continuous time systems with known and bounded measurement delays the aim of the technical note is the design of a finite dimensional sub optimal filter whose performance in terms of the estimation error is comparable to optimal infinite dimensional approaches we show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error in the time varying case no restrictive hypotheses on the delay function are needed the proposed filter can therefore be applied to delay functions for which traditional infinite dimensional approaches cannot be straightforwardly applied

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

robust h spl infin filter design for uncertain linear systems with multiple time varying state delays the problem of robust h spl infin filtering for continuous time uncertain linear systems with multiple time varying delays in the state variables is investigated the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain the aim is to design a stable linear filter assuring asymptotic stability and a prescribed h spl infin performance level for the filtering error system irrespective of the uncertainties and the time delays sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities which can be efficiently solved by means of powerful convex programming tools with global convergence assured an example illustrates the proposed methodology

necessary and sufficient conditions in constrained optimization additional conditions are attached to the kuhn tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization under appropriate constraint qualifications necessary and sufficient conditions are also given for optimality of the dual problem duality and converse duality are treated accordingly

exact penalty functions method for mathematical programming problems involving invex functions in this paper some new results on the exact penalty function method are presented simple optimality characterizations are given for the differentiable nonconvex optimization problems with both inequality and equality constraints via exact penalty function method the equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable invexity assumption furthermore the equivalence between a saddle point in the invex mathematical programming problem and an optimal point in its exact penalized optimization problem is also proved

stable and optimal adaptive fuzzy control of complex systems using fuzzy dynamic model a design method is presented for the stabilization of multivariable complex nonlinear systems which can be represented by fuzzy dynamic model firstly an adaptive fuzzy control law is addressed then the closed loop fuzzy system is robustly stabilized under some bounded perturbations and disturbances by adding a supervising controller based on the variable structure control theory of uncertain systems a sufficient condition for the stability of the closed loop fuzzy system is also derived using the concept of connective stability in decentralized control of large scale systems under this condition an optimal fuzzy controller is designed with genetic algorithms two examples are given to illustrate the application of the method

robust fuzzy stabilization of dithered chaotic systems using island based random optimization algorithm applying dither to highly nonlinear systems may suppress chaotic phenomena but dynamic performance such as convergence rate and disturbance attenuation is usually not guaranteed this paper presents a dithered h robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds in the proposed scheme takagi sugeno t s fuzzy linear models are used to describe the relaxed models of the dithered chaotic system and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation pdc sufficient condition for the existence of the h robust fuzzy controllers is presented in terms of a novel linear matrix inequalities lmi form which takes full consideration of modeling error and disturbances but cannot be solved by the standard procedures in order to solve the lmi problem and to identify the chaotic systems as t s fuzzy modes we propose a compound optimization strategy called the island based random walk algorithm ira the algorithm is composed of a set of communicating random walk optimization procedures concatenated with the down hill simplex method the design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system

stability analysis and design of takagi sugeno fuzzy systems this work presents stable composite control criteria for multivariable takagi sugeno t s fuzzy systems on the basis of the linear matrix inequality lmi control strategy and parametric optimization the composite fuzzy control algorithms are derived unlike earlier studies of fuzzy control systems on an lmi framework this investigation develops a supervisory control approach such that a fuzzy controller can be synthesized more efficiently moreover a robust control scheme is applied to the t s fuzzy model with parametric uncertainties the sufficient conditions are deduced in the form of reduced lmis and adaptive tuning rules finally numeric simulations are given to validate the proposed approach

pseudo invexity and symmetric duality in nonlinear fractional programming abstract the purpose of this paper is to study the symmetric dual fractional programming problem for pseudo invex functions and arbitrary cones several known results are obtained as special cases

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

robust adaptive critic control of nonlinear systems using fuzzy basis function networks an lmi approach abstract this paper proposes an adaptive critic tracking control design for a class of nonlinear systems using fuzzy basis function networks fbfns the key component of the adaptive critic controller is the fbfn which implements an associative learning network aln to approximate unknown nonlinear system functions and an adaptive critic network acn to generate the internal reinforcement learning signal to tune the aln another important component the reinforcement learning signal generator requires the solution of a linear matrix inequality lmi which should also be satisfied to ensure stability furthermore the robust control technique can easily reject the effects of the approximation errors of the fbfn and external disturbances unlike traditional adaptive critic controllers that learn from trial and error interactions the proposed on line tuning algorithm for aln and acn is derived from lyapunov theory thereby significantly shortening the learning time simulation results of a cart pole system demonstrate the effectiveness of the proposed fbfn based adaptive critic controller

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

further robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delay via relaxed integral inequality abstract this paper focuses on robust stability analysis for uncertain takagi sugeno fuzzy systems with time varying delays two delay product type terms are introduced for constructing a new lyapunov krasovskii functional which contains more information of time varying delay and a novel relaxed integral inequality is applied to estimate the derivative of lkf for achieving reduction of estimation gap as a result several further robust stability criteria with less conservativeness are proposed finally three numerical examples and an application to control of a truck trailer are provided to show the effectiveness and advantages of the presented methods

nondifferentiable multiobjective programming under generalized di invexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce new concepts of d i invexity and generalized d i invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d i new fritz john type necessary and karush kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient efficient or properly efficient moreover we prove weak strong converse and strict duality results for a mond weir type dual under various types of generalized d i invexity assumptions

takagi sugeno fuzzy model based indirect adaptive fuzzy observer and controller design this paper proposes the design scheme of the alternative adaptive observer and controller based on the takagi sugeno t s fuzzy model the t s fuzzy modeling and the state feedback control technique are adopted for the simple structure the proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators in addition with the simple adaptive state feedback controller it solves the singularity problem which occurs in the inverse dynamics based on the feedback linearization method using lyapunov theory and lipschitz condition the stability analysis is conducted and the adaptive law is derived the proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance

symmetric duality with invexity in variational problems abstract weak and strong duality results are established under invexity hypotheses for symmetric dual variational problems without positivity constraints self dual problems and static symmetric dual programs are included as special cases

h state feedback controller design for continuous time t s fuzzy systems in finite frequency domain this paper is concerned with finite frequency h state feedback controller designs for continuous time takagi sugeno t s fuzzy systems a parallel distributed compensation pdc controller is designed in finite frequency domain with the aid of the generalized kalman yakubovich popov gkyp lemma the design problem is formulated as solving a set of linear matrix inequalities lmis simulation examples illustrate that the finite frequency design approach proposed in this paper receives better results than those of existing full frequency approaches

symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear symmetric dual variational problems for the single objective problems our problems become the symmetric dual pair of i smart and b mond j math anal appl 152 1990 536 545 under invexity assumptions we establish the weak strong converse and self duality theorems for our variational problems by using the concept of efficiency also we give the static case of our symmetric duality results

design of robust fuzzy model based controller with sliding mode control for siso nonlinear systems in this paper we present the design of a new type of fuzzy controllers for controlling complex single input single output systems by incorporating sliding mode control theory with fuzzy control technology first a fuzzy model of the given nonlinear system is constructed to represent the local dynamic behaviors of the given nonlinear system a global controller is then constructed by combining all local state feedback controllers and a global supervisory sliding mode controller improved robustness and tracking performance are obtained by a seamless integration of fuzzy model based control and sliding mode control in addition stability of controlling the original underlying nonlinear systems is guaranteed owing to the robustness of the sliding mode control method to system parameter uncertainties two simulation examples are included to show the effectiveness and feasibility of the developed integrated controller

optimal filtering for rm it mathhat o stochastic continuous time systems with multiple delayed measurements this technical note focuses on optimal filtering for ito stochastic continuous time systems with multiple delayed measurements stochastic analysis and calculus of stochastic variables are the main tools employed for the analysis and design for an ito stochastic system its stochastic differential and integral have a significant place and are different from that for other stochastic systems owing to the wiener or the brownian process in this technical note an ito stochastic continuous time system with multiple delayed measurements is first reduced to an equivalent system with delay free measurements by solving stochastic equation via the non singularity of the transition matrix instead of reorganizing the innovation then based on the delay free measurements the optimal filter is derived through calculation of the conditional expectation it is should be stressed that the optimal filter follows directly from the manipulation of the performance finally a short interest rate model in mathematical finance is chosen to demonstrate the design of the optimal filter via the approach proposed in the technical note

optimal estimation for continuous time systems with delayed measurements this note focuses on the traditional problem of the kalman filtering for linear continuous time systems although the problem has been studied widely in the past decades little work has been done for the time delayed systems and some fundamental problems remain to be solved this note proposes a new tool namely reorganization innovation analysis approach to investigate the filtering problem for systems with delayed measurements the kalman filter is given in terms of the solution of standard riccati equations the performance is clearly demonstrated through analytical results and simulation the solved problem in this note is related with some more complicated problems such as h sub spl infin fixed lag smoothing h sub spl infin control with preview and control with input delays

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

weakly efficient solutions and pseudoinvexity in multiobjective control problems abstract in this paper we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem called w kt pseudoinvexity and w fj pseudoinvexity we prove that all kuhn tucker or fritz john points are weakly efficient solutions if and only if these conditions are fulfilled we relate weakly efficient solutions to optimal solutions of weighting control problems we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

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 twofold spline approximation for finite horizon lqg control of hereditary systems in this paper an approximation scheme is developed for the solution of the linear quadratic gaussian lqg control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay the solution here proposed is achieved by means of two approximating subspaces the first one to approximate the riccati equation for control and the second one to approximate the filtering equations since the approximating subspaces have finite dimension the resulting equations can be implemented the convergence of the approximated control law to the optimal one is proved simulation results are reported on a wind tunnel model showing the high performance of the method

efficient solutions in v kt pseudoinvex multiobjective control problems a characterization in this paper we introduce a new condition on functionals involved in a multiobjective control problem for which we define the v kt pseudoinvex control problem we prove that a v kt pseudoinvex control problem is characterized so that a kuhn tucker point is an efficient solution we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

further studies on relaxed stabilization conditions for discrete time two dimension takagi sugeno fuzzy systems this paper investigates the stabilization problem of discrete time two dimension 2 d takagi sugeno t s fuzzy systems based on a novel non parallel distributed compensation non pdc control scheme combined with a new non quadratic lyapunov function less conservative stabilization conditions are developed the proposed non quadratic lyapunov function is homogeneous polynomially parameter dependent on membership functions as the degree of the lyapunov function increases the conservatism of the obtained stabilization conditions is gradually reduced by exploiting the algebraic property of membership functions the stabilization conditions approach to exactness in the sense of convergence compared with the existing methods no slack variables are introduced in control synthesis and hence the same or less conservative results can be obtained with a lower computational cost a numerical example is given to illustrate the effectiveness of the proposed method

new filter design for linear time delay systems abstract this paper develops new robust delay dependent filter design for a class of linear systems with time varying delays and convex bounded parameter uncertainties the design procedure hinges upon the constructive use of an appropriate lyapunov functional plus a free weighting matrices in order to exhibit the delay dependent dynamics the developed approach utilizes smaller number of lmi decision variables thereby leading to less conservative solutions to the delay dependent stability and filtering problems subsequently linear matrix inequalities lmis based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level l 2 gain all the developed results are tested on representative examples

symmetric and self duality in vector optimization problem abstract in this paper we present the first order symmetric and self duality programs in multiobjective nonlinear programming problems for these first order symmetric and dual programs we introduce the weak strong and converse duality theorems under convexity and concavity conditions where the pair of the symmetric dual multiobjective nonlinear programming problems in this paper different which in d s kim y b yun h kuk second order symmetric and self duality in multiobjective programming appl math lett 10 2 1997 17 22 also we prove the self duality theorem for these first order self dual programs and illustrate its example

spl hscr sub spl infin filtering for continuous time linear systems with delay the problem of spl hscr sub spl infin filtering for continuous time linear systems with time delayed measurement is investigated the authors develop a methodology for designing linear filters which ensure a prescribed bound on the spl lscr sub 2 induced gain from the noise signals to the estimation error filtering problems for time varying systems over a finite horizon as well as stationary infinite horizon filtering for time invariant systems are tackled in the finite horizon case our estimation procedure entails an overdesign that stems from the last d seconds of the time interval 0 t where d is the delay length this overdesign becomes smaller as t increases and it vanishes in the infinite horizon case

method for higher order polynomial sugeno fuzzy inference systems a method for higher order polynomial sugeno fuzzy inference systems formation is presented compared to other existing higher order sugeno implementations it uses fewer parameters and compared to zero and 1st order sugeno fuzzy systems it has overall improved model performance while best models are not always obtained via a higher order representation in our proposed method it is possible to choose the polynomial order which best fits the desired data its input is a previously established model found by a clustering algorithm subtractive algorithm in this case afterward parameters of all higher order polynomials are adjusted using recursive least square algorithm for experimental validation multiple benchmark datasets are tested using hold out and k fold validation as well as data forecasting various performance measures are used although akaike information criterion is used as a primary measure to demonstrate that our proposed higher order polynomials have overall better model performance over zero and 1st order polynomials

symmetric duality for invex multiobjective fractional variational problems we introduce a symmetric dual for multiobjective fractional variational problems under certain invexity assumptions we establish weak strong and converse duality theorems as well as self duality relations the paper includes an extension of previous symmetric duality results for the static case obtained by weir to the dynamic case

kalman filtering for multiple time delay systems this paper is to study the linear minimum variance estimation for discrete time systems with instantaneous and l time delayed measurements by using re organized innovation analysis a simple approach to the problem is presented in this paper it is shown that the derived estimator involves solving l 1 different standard kalman filtering with the same dimension as the original system

generalized sufficiency criteria in continuous time programming with application to a class of variational type inequalities abstract in this paper we establish a number of sufficiency criteria under generalized invexity conditions for general continuous time programming problems with nonlinear operator equality and inequality constraints as an application of these results we establish some existence criteria for solutions of a class of variational type inequalities

adaptive control of discrete time state space t s fuzzy systems with general relative degree this paper develops a new solution framework for adaptive control of general discrete time single input single output siso state space takagi sugeno t s fuzzy systems with a relative degree r email protected email protected n a new procedure is proposed to construct a normal form of a global t s fuzzy system model from local state space models in non canonical form and such a normal form system has an explicit relative degree structure and a specific input output signal causality relationship in the sense that it does not include any future values of fuzzy membership functions an adaptive feedback control scheme is designed based on the global normal form t s fuzzy model to ensure desired closed loop stability and output tracking properties a comparison is given to adaptive state tracking designs seen in the literature which require much more restrictive matching conditions and do not take into account the high relative degree cases as an illustrative example a t s fuzzy system is constructed based on the linearized local models of a transport airplane simulation results have demonstrated the developed new concepts and verified the desired performance of the new type of adaptive fuzzy control systems

fuzzy chaos hybrid controller for controlling of nonlinear systems a novel concept for controlling of nonlinear systems using chaos and fuzzy model based regulators is presented in the control of such systems we employ two phases the first of which uses open loop control forming a chaotic attractor or using chaotic inherent features in a system itself once the system states reach a predefined convex domain open loop control is cut off and a fuzzy model based controller is employed under state feedback control in the second phase the relaxed stability conditions and linear matrix inequalities lmis based design for a fuzzy regulator is introduced to construct a fuzzy attractive domain in which a global solution is obtained so as to achieve the desired stability condition of the closed loop system the proposed controller architecture has been tested using three nonlinear systems the henon map the lorenz attractor and a two link manipulator the simulation results show the effectiveness of the proposed controller

kt invex control problem abstract in this paper we introduce a new condition on functions of a control problem for which we define a kt invex control problem we prove that a kt invex control problem is characterized in order that a kuhn tucker point is an optimal solution we generalize optimality results of known mathematical programming problems we illustrate these results with examples