fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

fault estimation observer design for discrete time takagi sugeno fuzzy systems based on piecewise lyapunov functions this paper studies the problem of robust fault estimation fe observer design for discrete time takagi sugeno t s fuzzy systems via piecewise lyapunov functions both the full order fe observer ffeo and the reduced order fe observer rfeo are presented the objective of this paper is to establish a novel framework of the fe observer with less conservatism first under the multiconstrained design an ffeo is proposed to achieve fe for discrete time t s fuzzy models then using a specific coordinate transformation an rfeo is constructed which results in a new fault estimator to realize fe using current output information furthermore by the piecewise lyapunov function approach less conservative results on both ffeo and rfeo are derived by introducing slack variables simulation results are presented to illustrate the advantages of the theoretic results that are obtained in this paper

an optimal fault detection approach for piecewise affine systems via diagnostic observers abstract in this paper the design issues of diagnostic observer based fault detection fd for piecewise affine systems are investigated to be specific the diagnostic observer based fd approaches are developed to satisfy the specified disturbance attenuation and optimize the fault detectability at the same time considering the fact that the measurements are generally corrupted with noises or disturbances the proposed approaches are mainly dedicated to the case that the process and its fd system are non synchronous in transition from one region to another moreover aiming at improving the fd performance a mode observer is integrated to relax the design condition for the residual generator an example is given in the end to show the effectiveness of the proposed approaches

new characterisations of positive realness and static output feedback control of discrete time systems this article is concerned with the problems of positive real analysis and control synthesis for discrete time systems new linear matrix inequality lmi characterisations of positive realness are derived which enable one to check the positive realness by using parameter dependent lyapunov function the relationship between the proposed characterisations and the existing ones are clarified which shows that our new results are of less conservatism for characterising the positive realness of discrete time systems with polytopic uncertainty in addition sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities numerical examples are included for illustration

novel stability criteria for t s fuzzy systems in this paper novel stability conditions for takagi sugeno t s fuzzy systems are presented the so called nonquadratic membership dependent lyapunov function is first proposed which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature then new membership dependent stability conditions are developed by the new lyapunov function approach it is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical results

a second order cone programming formulation for two player zero sum games with chance constraints abstract we consider a two player finite strategic zero sum game where each player has stochastic linear constraints we formulate the stochastic constraints of each player as chance constraints we show the existence of a saddle point equilibrium in mixed strategies if the row vectors of the random matrices defining the stochastic constraints are elliptically symmetric distributed random vectors we further show that a saddle point equilibrium can be obtained from the optimal solutions of a primal dual pair of second order cone programs

random payoff two person zero sum game with joint chance constraints abstract we study a two person zero sum game where the payoff matrix entries are random and the constraints are satisfied jointly with a given probability we prove that for the general random payoff zero sum game there exists a weak duality between the two formulations i e the optimal value of the minimizing player is an upper bound of the one of the maximizing player under certain assumptions we show that there also exists a strong duality where their optimal values are equal moreover we develop two approximation methods to solve the game problem when the payoff matrix entries are independent and normally distributed finally numerical examples are given to illustrate the performances of the proposed approaches

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

lagrangian decomposition and mixed integer quadratic programming reformulations for probabilistically constrained quadratic programs abstract probabilistically constrained quadratic programming pcqp problems arise naturally from many real world applications and have posed a great challenge in front of the optimization society for years due to the nonconvex and discrete nature of its feasible set we consider in this paper a special case of pcqp where the random vector has a finite discrete distribution we first derive second order cone programming socp relaxation and semidefinite programming sdp relaxation for the problem via a new lagrangian decomposition scheme we then give a mixed integer quadratic programming miqp reformulation of the pcqp and show that the continuous relaxation of the miqp is exactly the socp relaxation this new miqp reformulation is more efficient than the standard miqp reformulation in the sense that its continuous relaxation is tighter than or at least as tight as that of the standard miqp we report preliminary computational results to demonstrate the tightness of the new convex relaxations and the effectiveness of the new miqp reformulation

fault diagnosis of dynamical systems using recurrent fuzzy systems with application to an electrohydraulic servo axis this paper presents a novel approach for fault isolation based on discrete time recurrent fuzzy systems dtrfs extending the well known static fuzzy systems for fault isolation the dtrfs additionally allows for the isolation of faults causing dynamic residuals and the isolation of multiple subsequently occurring faults due to the flexibility of the dtrfs multiplicative as well as additive faults can be handled the approach is applied to an electrohydraulic servo axis with a duplex valve system experimental results at the testbed underline the effectiveness and applicability of the approach and show the enhanced performance compared to static fuzzy systems and state automata

convex combinations in terms of triangular norms a characterization of idempotent bisymmetrical and self dual compensatory operators it is observed that most of the well known compensatory operators are defined in terms of convex transformations of the values of triangular norms and conorms or other operators in this paper the characterization and the applicability of parametrized operators constructed again in terms of triangular norms and conorms but as transformations of their arguments are studied it turns out that these operators are closely related to the ordinary convex combination moreover when idempotency is required these operators can be characterized algebraically as bisymmetrical and self dual operators that satisfy the cancellation law

fuzzy model based piecewise mathscr h _ infty static output feedback controller design for networked nonlinear systems this paper investigates the problem of robust h output feedback control for a class of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s uncertain fuzzy model and the communication links between the plant and controller are assumed to be imperfect i e data packet dropouts occur intermittently which is often the case in a network environment stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon and the attention is focused on the design of a piecewise static output feedback sof controller such that the closed loop system is stochastically stable with a guaranteed h performance based on a piecewise lyapunov function combined with some novel convexifying techniques the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are also provided to illustrate the effectiveness of the proposed approaches

pole assignment for uncertain systems in a specified disk by state feedback this paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system the uncertainty being norm bounded for this the quadratic d stabilizability concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived this condition expressed as a parameter dependent discrete riccati equation enables one to design the control gain matrix by solving iteratively a discrete riccati equation

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

reliable state feedback control of t s fuzzy systems with sensor faults this paper is concerned with reliable state feedback control synthesis for takagi and sugeno t s fuzzy systems with sensor multiplicative faults by considering the influence of sensor faults on both the system states and premise variables of fuzzy controllers a class of new convex reliable stabilization conditions are proposed for t s fuzzy systems using the properties of fuzzy product inference engines furthermore the obtained result is extended to the h infty reliable control case the resulting controllers are reliable in that they provide guaranteed asymptotic stability and h infty performance when all sensors are operational as well as when some sensor experiences failures different from the proposed approach the influence of sensor faults on premise variables is not considered in the existing results then it might not guarantee the stability and control performance for t s fuzzy systems with premise variables dependent on the system states a numerical example is given to illustrate the effectiveness of the proposed method

multi constrained fault estimation observer design with finite frequency specifications for continuous time systems the design of a multi constrained full order fault estimation observer ffeo with finite frequency specifications is studied for continuous time systems by constructing an augmented system a multi constrained ffeo in finite frequency domain is proposed to achieve fault estimation meanwhile the presented ffeo can avoid the overdesign problem generated by the entire frequency domain by the generalised kalman yakubovich popov lemma furthermore by introducing slack variables improved results on ffeo design in different frequency domains are obtained such that different lyapunov matrices can be separately designed for each constraint simulation results are presented to demonstrate the effectiveness and potentials of the proposed techniques

extension of karmarkar s algorithm onto convex quadratically constrained quadratic problems convex quadratically constrained quadratic problems are considered it is shown that such problems can be transformed to aconic form the feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with a hyperplane the analogue of a simplex and a linear subspace for a problem of such form the analogue of karmarkar s projective transformation and logarithmic barrier function are built this allows us to extend word by word the method of karmarkar for lp to qcqp and allows us to obtain a similar polynomial worst case bound for the number of iterations

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

comments on finite time h_ infty fuzzy control of nonlinear jump systems with time delays via dynamic observer based state feedback this paper studies the finite time h control problem for time delay nonlinear jump systems via dynamic observer based state feedback by the fuzzy lyapunov krasovskii functional approach the takagi sugeno t s fuzzy model is first employed to represent the presented nonlinear markov jump systems mjss with time delays based on the selected lyapunov krasovskii functional the observer based state feedback controller is constructed to derive a sufficient condition such that the closed loop fuzzy mjss is finite time bounded and satisfies a prescribed level of h disturbance attenuation in a finite time interval then in terms of linear matrix inequality lmis techniques the sufficient condition on the existence of the finite time h fuzzy observer based controller is presented and proved the controller and observer can be obtained directly by using the existing lmis optimization techniques finally a numerical example is given to illustrate the effectiveness of the proposed design approach

a linear decision based approximation approach to stochastic programming stochastic optimization especially multistage models is well known to be computationally excruciating moreover such models require exact specifications of the probability distributions of the underlying uncertainties which are often unavailable in this paper we propose tractable methods of addressing a general class of multistage stochastic optimization problems which assume only limited information of the distributions of the underlying uncertainties such as known mean support and covariance one basic idea of our methods is to approximate the recourse decisions via decision rules we first examine linear decision rules in detail and show that even for problems with complete recourse linear decision rules can be inadequate and even lead to infeasible instances hence we propose several new decision rules that improve upon linear decision rules while keeping the approximate models computationally tractable specifically our approximate models are in the forms of the so called second order cone soc programs which could be solved efficiently both in theory and in practice we also present computational evidence indicating that our approach is a viable alternative and possibly advantageous to existing stochastic optimization solution techniques in solving a two stage stochastic optimization problem with complete recourse

optimized bonferroni approximations of distributionally robust joint chance constraints a distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold epsilon over a given family of probability distributions of the uncertain parameters a conservative approximation of a joint chance constraint often referred to as a bonferroni approximation uses the union bound to approximate the joint chance constraint by a system of single chance constraints one for each original uncertain constraint for a fixed choice of violation probabilities of the single chance constraints such that their sum does not exceed epsilon it has been shown that under various settings a distributionally robust single chance constraint admits a deterministic convex reformulation thus the bonferroni approximation approach can be used to build convex approximations of distributionally robust joint chance constraints in this paper we consider an optimized version of bonferroni approximation where the violation probabilities of the individual single chance constraints are design variables rather than fixed a priori we show that such an optimized bonferroni approximation of a distributionally robust joint chance constraint is exact when the uncertainties are separable across the individual inequalities i e each uncertain constraint involves a different set of uncertain parameters and corresponding distribution families unfortunately the optimized bonferroni approximation leads to np hard optimization problems even in settings where the usual bonferroni approximation is tractable when the distribution family is specified by moments or by marginal distributions we derive various sufficient conditions under which the optimized bonferroni approximation is convex and tractable we also show that for moment based distribution families and binary decision variables the optimized bonferroni approximation can be reformulated as a mixed integer second order conic set finally we demonstrate how our results can be used to derive a convex reformulation of a distributionally robust joint chance constraint with a specific non separable distribution family

analysis and design of fuzzy reduced dimensional observer and fuzzy functional observer on the basis of the t s fuzzy model this paper discusses the following three problems the fuzzy reduced dimensional observer the general structure of the fuzzy observer the fuzzy functional observer for both the continuous and discrete case respectively the separation property that is the fuzzy controller and the fuzzy observer can be independently designed is also addressed the numerical simulation and the experiment on an inverted pendulum system are given to illustrate the soundness of these results

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

a convex optimization approach to fixed order controller design for disturbance rejection in siso systems the problem of rejection of persistent unknown but bounded disturbances can be solved using the well known l sup 1 design approach however in spite of its success this theory suffers from the fact that the resulting controller may have arbitrarily high order even in the state feedback case in addition system performance is optimized under the assumption of zero initial conditions in this paper we propose a new approach to the problem of synthesizing fixed order controllers to optimally reject persistent disturbances the main result of the paper shows that this approach leads to a finite dimensional convex optimization problem that can be efficiently solved

on safe tractable approximations of chance constraints abstract a natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 while being attractive from modeling viewpoint chance constrained problems as they are are in general computationally intractable in this survey paper we overview several simulation based and simulation free computationally tractable approximations of chance constrained convex programs primarily those of chance constrained linear conic quadratic and semidefinite programming

nonfragile control with guaranteed cost of t s fuzzy singular systems based on parallel distributed compensation this paper investigates the nonfragile guaranteed cost control problem for a class of uncertain nonlinear singular state delayed systems that is described by takagi sugeno models the upper bound of state delay is assumed to be available a linear quadratic cost function is specified as the performance index of the closed loop system attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme which not only guarantees the regular impulse free and asymptotically stable of the closed loop fuzzy singular delay system but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties all derived sufficient conditions are given in terms of linear matrix inequalities some numerical examples are provided to illustrate the effectiveness of the proposed design scheme

convexity and convex approximations of discrete time stochastic control problems with constraints we investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time we consider minimization of an expected value cost subject to probabilistic constraints we study the convexity of a finite horizon optimization problem in the case where the control policies are affine functions of the disturbance input we propose an expectation based method for the convex approximation of probabilistic constraints with polytopic constraint function and a linear matrix inequality lmi method for the convex approximation of probabilistic constraints with ellipsoidal constraint function finally we introduce a class of convex expectation type constraints that provide tractable approximations of the so called integrated chance constraints performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example

visual characterization of associative quasitrivial nondecreasing operations on finite chains abstract in this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains we also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains finally we estimate the number of operations belonging to the previous classes

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

filtering and fault detection for nonlinear systems with polynomial approximation this paper is concerned with polynomial filtering and fault detection problems for a class of nonlinear systems subject to additive noises and faults the nonlinear functions are approximated with polynomials of a chosen degree different from the traditional methods the approximation errors are not discarded but formulated as low order polynomial terms with norm bounded coefficients the aim of the filtering problem is to design a least squares filter for the formulated nonlinear system with uncertain polynomials and an upper bound of the filtering error covariance is found and subsequently minimized at each time step the desired filter gain is obtained by recursively solving a set of riccati like matrix equations and the filter design algorithm is therefore applicable for online computation based on the established filter design scheme the fault detection problem is further investigated where the main focus is on the determination of the threshold on the residual due to the nonlinear and time varying nature of the system under consideration a novel threshold is determined that accounts for the noise intensity and the approximation errors and sufficient conditions are established to guarantee the fault detectability for the proposed fault detection scheme comparative simulations are exploited to illustrate that the proposed filtering strategy achieves better estimation accuracy than the conventional polynomial extended kalman filtering approach the effectiveness of the associated fault detection scheme is also demonstrated

design of observer based h_ infty control for fuzzy time delay systems this paper addresses the problem of observer based hinfin control for nonlinear systems with time varying delay represented by takagi sugeno t s fuzzy model it presents a single step linear matrix inequality lmi method for the fuzzy control design which overcomes the drawback of the two step lmi approach often encountered in the literature the derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict lmis when restricted to delay free fuzzy systems the present results improve or reduce to existing ones illustrative examples show the effectiveness and merits of the present results

static output feedback h control of a class of nonlinear discrete time systems this paper is concerned with the problem of designing robust h static output feedback sof controllers for a class of discrete time nonlinear systems which are represented by t s fuzzy models by considering the properties of system output matrices a method for h sof control synthesis is developed in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing techniques for designing sof controllers the new proposed method can give less conservative results by removing the constraint that the considered lyapunov matrix is diagonal numerical examples are given to illustrate the effectiveness of the proposed design method

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

delayed output feedback control for nonlinear systems with two layer interval fuzzy observers in this paper the design problem of a delayed output feedback control scheme using two layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated the takagi sugeno type fuzzy linear model with an online update law is used to approximate the nonlinear system based on the fuzzy model a two layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices subsequently a delayed output feedback adaptive fuzzy controller is developed to overcome the nonlinearities time delays and external disturbances such that h infty tracking performance is achieved the linguistic information is developed by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly using linear analytical results instead of estimating nonlinear system functions the tracking error dynamics are designed to enable our adaptive controller to avoid the filtering of the basis vectors whose dimension is much larger than that of the state vector of the controlled system this is achieved by not imposing the strictly positive real condition based on the lyapunov stability criterion and linear matrix inequalities some sufficient conditions are derived so that all the states of the system are uniformly ultimately bounded therefore the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and h infty tracking control is achieved building on our previous work in this area the proposed control scheme is extended to handle a class of uncertain nonlinear systems with state and output delays and external disturbances this is achieved through the use of a robust variable structure scheme and h infty control techniques finally a numerical example of a two link robot manipulator is studied to illustrate the effectiveness of the proposed control scheme

fault detection and isolation for a class of uncertain state feedback fuzzy control systems this paper investigates the fault detection and isolation fdi problem for a class of nonlinear state feedback control systems with parameter uncertainties first the considered nonlinear systems are described by multiple t s fuzzy models with uncertain grades of membership and local nonlinear parts in normal case and faulty cases then a switching technique is introduced to address the uncertain grades of membership external disturbances local nonlinear parts faults and the coupling of them in a multiple model scheme a bank of fdi observers are constructed each of which is based on the t s model that describes the system in the presence of a particular fault such that one of them can track the current system state and the corresponding observer estimate error can converge exponentially to zero finally two examples are given to illustrate the effectiveness and advantages of the new results

on the associativity functional equation abstract let a b be any bounded closed real interval the class of all continuous nondecreasing associative functions m a b 2 a b fulfilling the boundary conditions m a a a and m b b b is described

stochastic robustness of linear time invariant control systems a simple numerical procedure for estimating the stochastic robustness of a linear time invariant system is described monte carlo evaluation of the system s eigenvalues allows the probability of instability and the related stochastic root locus to be estimated this analysis approach treats not only gaussian parameter uncertainties but also nongaussian cases including uncertain but bound variations confidence intervals for the scalar probability of instability address computational issues inherent in monte carlo simulation trivial extensions of the procedure admit consideration of alternate discriminants thus the probabilities that stipulated degrees of instability will be exceeded or that closed loop roots will leave desirable regions can also be estimated results are particularly amenable to graphical presentation

probabilistically constrained linear programs and risk adjusted controller design the focal point of this paper is the probabilistically constrained linear program pclp and how it can be applied to control system design under risk constraints the pclp is the counterpart of the classical linear program where it is assumed that there is random uncertainty in the constraints and therefore the deterministic constraints are replaced by probabilistic ones it is shown that for a wide class of probability density functions called log concave symmetric densities the pclp is a convex program an equivalent formulation of the pclp is also presented which provides insight into numerical implementation this concept is applied to control system design it is shown how the results in this paper can be applied to the design of controllers for discrete time systems to obtain a closed loop system with a well defined risk of violating the so called property of superstability furthermore we address the problem of risk adjusted pole placement

sequential convex approximations to joint chance constrained programs a monte carlo approach when there is parameter uncertainty in the constraints of a convex optimization problem it is natural to formulate the problem as a joint chance constrained program jccp which requires that all constraints be satisfied simultaneously with a given large probability in this paper we propose to solve the jccp by a sequence of convex approximations we show that the solutions of the sequence of approximations converge to a karush kuhn tucker kkt point of the jccp under a certain asymptotic regime furthermore we propose to use a gradient based monte carlo method to solve the sequence of convex approximations

finite horizon estimation of randomly occurring faults for a class of nonlinear time varying systems this paper is concerned with the finite horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time varying the faults are assumed to occur in a random way governed by two sets of bernoulli distributed white sequences the stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well studied nonlinearities the aim of the problem is to estimate the random faults over a finite horizon such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an h norm in the mean square sense by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are established for the existence of the desired finite horizon h fault estimator whose parameters are then obtained by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

brief paper optimal fault detection for linear discrete time varying systems this paper deals with the problem of observer based fault detection for linear discrete time varying ldtv systems a problem formulation is first proposed to address the optimization of the fault detection filter fdf design which is expressed in terms of maximizing a finite horizon h h or h h performance index this formulation can be applied to fdf design of ldtv systems subject to l 2 norm bounded unknown inputs or stochastic noise sequences it is shown that a unified optimal solution to the fdf can be obtained by solving the discrete time riccati equation and the optimal fdf is not unique a numerical example is given to illustrate the proposed method

a fault detection approach for nonlinear systems based on data driven realizations of fuzzy kernel representations this paper is devoted to the data driven fault detection of nonlinear systems for our purpose the definition of takagi sugeno fuzzy data driven forms of kernel representations for nonlinear systems is introduced first which builds the basis of our work the major contributions consist of two parts in the first part a data driven method for fuzzy process modeling is proposed and associated with it some modeling issues are addressed with the aid of the so called randomized algorithm technique in the probabilistic framework it is followed by a data driven realization of fuzzy kernel representation and its implementation in the fault detection system design to link the data driven methods to the well established observer based fault detection approaches the recursive form of the fuzzy kernel representation is proposed in the second part the fuzzy observer based fault detection design scheme is investigated based on the recursive fuzzy kernel representation the main results of our study are illustrated by an experimental study on the laboratory setup of a three tank system

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

robust fault detection of t s fuzzy systems with time delay using fuzzy functional observer abstract this paper presents a new fuzzy functional observer based fault detection technique for fuzzy systems with time delay subject to exogenous disturbance the estimation error of the fuzzy functional observer is used to obtain a residual to detect the fault the proposed fault detection scheme does not require any threshold to compare with the residual the exogenous disturbance is decoupled from the error dynamics using the concept of unknown input observers to ensure the robustness of the residual generator the time delay is considered to be time varying and bounded sufficient conditions are presented to ensure the asymptotic stability of the observer by linear matrix inequality approach the proposed design technique is illustrated and verified using examples to demonstrate its effectiveness for fault diagnosis

nonsynchronized state estimation of multichannel networked nonlinear systems with multiple packet dropouts via t s fuzzy affine dynamic models this paper investigates the problem of robust h state estimation for a class of multichannel networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables with general probability distributions are adopted to characterize the data missing phenomenon in output channels the objective is to design an admissible state estimator guaranteeing the stochastic stability of the resulting estimation error system with a prescribed h disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the estimator implementation with state space partition may not be synchronized with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexifying techniques two different approaches are developed to robust filtering design for the underlying t s fuzzy affine systems with unreliable communication links all the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

characterizations of idempotent discrete uninorms in this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only conservativeness symmetry and nondecreasing monotonicity we also provide an alternative characterization involving the bisymmetry property finally we provide a graphical characterization of these operations in terms of their contour plots and we mention a few open questions for further research

on designing h_ infty fault detection filter for linear discrete time varying systems this technical note deals with the problem of finite horizon h fault detection for linear discrete time varying systems using an observer based fault detection filter fdf with residual feedback as a residual generator a new problem formulation of fault detection is first presented then the design of finite horizon h fdf is converted into a minimum problem of certain quadratic form through building a relationship with krein space projection and applying innovation analysis a sufficient and necessary condition for the minimum is derived and a solution to the h fdf is obtained by recursively computing riccai recursions numerical examples are given to show the effectiveness of the proposed method

a robust h_ infty non pdc design scheme for singularly perturbed t s fuzzy systems with immeasurable state variables this paper addresses an observer based robust h infty fuzzy controller design method for singularly perturbed nonlinear systems with external disturbances which are represented by uncertain takagi sugeno t s fuzzy models for a practical output feedback design the premise variables of the fuzzy controller and the fuzzy observer are considered unknown in general a fuzzy lyapunov function is utilized for the synthesis of the nonparallel distributed compensation based controller the closed loop singularly perturbed t s fuzzy system is asymptotically robustly stable in the absence of disturbances and satisfies an h infty norm condition in the presence of disturbances for all positive values of the singular perturbation parameter within the given desired bound using the descriptor redundancy approach some strict linear matrix inequality lmi conditions are derived for the h infty robustness of the closed loop system when uncertainties are simultaneously considered in all state space matrices of each fuzzy subsystem the main disadvantage of a fuzzy lyapunov function based design is that the bounds on the derivatives of the membership functions must be known a priori inspired by a recent work that provides the bounds of the membership derivatives for a given arbitrary compact set on the state space a new method is proposed that guarantees that the closed loop observer based uncertain singularly perturbed t s fuzzy system remains robustly stable in the compact set using finsler s lemma the resulting design conditions are converted to lmis two numerical examples are provided to show the effectiveness of the proposed method

an efficient algorithm for minimizing a sum of euclidean norms with applications in recent years rich theories on polynomial time interior point algorithms have been developed these theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications in this paper the problem of minimizing a sum of euclidean norms is studied this problem is convex but not everywhere differentiable by transforming the problem into a standard convex programming problem in conic form we show that an epsilon optimal solution can be computed efficiently using interior point algorithms as applications to this problem polynomial time algorithms are derived for the euclidean single facility location problem the euclidean multifacility location problem and the shortest network under a given tree topology in particular by solving the newton equation in linear time using em gaussian elimination on leaves of a tree we present an algorithm which computes an epsilon optimal solution to the shortest network under a given full steiner topology interconnecting n regular points in o n sqrt n log bar c epsilon log n arithmetic operations where bar c is the largest pairwise distance among the given points the previous best known result on this problem is a graphical algorithm which requires o n2 arithmetic operations under certain conditions

a novel observer based output feedback controller design for discrete time fuzzy systems this paper addresses the problem of observer based output feedback controller designs for discrete time t s fuzzy systems based on a relaxed approach in which the fuzzy lyapunov functions are used different from the existing two step method a single step linear matrix inequality method is provided for the observer based controller design it is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software the new design method not only overcomes the drawback induced by the two step approach but also provides less conservative results over some existing results finally the effectiveness of the proposed approach is demonstrated by an example

characterizing autodistributive aggregation operations defined on finite linearly ordered scales abstract observe that for continuous strictly increasing binary means defined on a unit interval autodistributivity and bisymmetry are equivalent bisymmetric aggregation operations defined on finite linearly ordered scales have been studied in the past and their behavior is unlike that of corresponding operations defined on the unit interval 0 1 this paper investigates two families of autodistributive aggregation operations defined on finite linearly ordered scales one with a neutral element and the other under some partial smoothness related conditions the former is fully described as the family of idempotent uninorms and the latter is completely characterized as the family of idempotent t operators through these results we can deduce that compared with bisymmetry autodistributivity is much stronger and the behavior of autodistributive aggregation operations defined on finite linearly ordered scales is significantly different from that of corresponding operations defined on 0 1

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

a chance constrained programming framework to handle uncertainties in radiation therapy treatment planning abstract a stochastic programming framework is proposed for radiation therapy treatment planning this framework takes into account uncertainty in setting up or positioning patients identically day to day during the treatment period because uncertainties are unavoidable constraint violations are tolerated to some degree in practice under this assumption a chance constrained programming ccp framework is developed to handle setup uncertainties in treatment planning the proposed framework can be employed under different distributional assumptions the goal of the proposed approach is to maximize both the statistical confidence level of a treatment plan and the homogeneity of the dose distributions this novel perspective provides a user centric and personalized optimization model that allows a trade off between sufficient tumor coverage and sparing healthy tissues under uncertainty we describe testing of the performance of the proposed ccp models in terms of plan quality robustness and homogeneity and confidence level of the constraints using clinical data for a prostate cancer patient optimized ccp plans are also compared to plans developed using a deterministic approach that does not take uncertainties into account numerical experiments confirmed that the ccp is able to control setup uncertainties in target coverage and sparing of organs at risk

on the discrete bisymmetry it is known that bisymmetry generalizes the simultaneous commutativity and associativity in the framework of the unit interval in this work we will completely characterize two classes of bisymmetric aggregation operators one with a neutral element and the other with the vertical and horizontal sections of the idempotent elements being smooth on a finite chain but not necessarily smooth and commutative thus the previous results based on the smoothness that is known as a very restrictive condition are improved for example there is only one smooth archimedean t norm on a finite chain in this paper the discrete bisymmetric aggregation operators are explored without the limit of the smoothness as a by product it is deduced that for smooth aggregation operators on a finite chain the bisymmetry is equivalent to the commutativity and associativity which improves the conclusion obtained by mas et al that associativity and bisymmetry are equivalent for commutative smooth aggregation operators on a finite chain

on the accessibility controllability of fuzzy control systems accessibility controllability are very important concepts in the design of fuzzy logic control systems flcs from both theoretical and practical perspectives this paper proposes a systematic methodology that utilizes differential geometry lie algebra that has not been investigated in the literature for analyzing the accessibility controllability of ts flcs first we linearize ts flcs and show that this process although it is straightforward has limitations when analyzing some flcs structures thus we propose a novel algorithm by consolidating the linearization and lie algebra techniques that provides a systematic approach to assess accessibility controllability the advantage of the proposed algorithm is that in the case of nonaccessibility those associated trajectories are found the proposed approach is generic and does not require assumptions on flcs s rules or structures as is common with the few existing fuzzy systems controllability analysis methods in the literature moreover we show that unlike exiting methods our approach is not limited to small rule bases but is also applicable for systems with large number of rules to validate the effectiveness of the proposed method we present several illustrative benchmark examples that will be of practical use to control engineers and can as well enable wider scale use of flcs in various engineering applications

random convex programs random convex programs rcps are convex optimization problems subject to a finite number n of random constraints the optimal objective value j of an rcp is thus a random variable we study the probability with which j is no longer optimal if a further random constraint is added to the problem violation probability v it turns out that this probability rapidly concentrates near zero as n increases we first develop a theory for rcps leading to explicit bounds on the upper tail probability of v then we extend the setup to the case of rcps with r a posteriori violated constraints rcpvs a paradigm that permits us to improve the optimal objective value while maintaining the violation probability under control explicit and nonasymptotic bounds are derived also in this case the upper tail probability of v is upper bounded by a multiple of a beta distribution irrespective of the distribution on the random constraints all results are derived under no feasibility assumptions on the problem further the relation between rcpvs and chance constrained problems ccp is explored showing that the optimal objective j of an rcpv with the generic constraint removal rule provides with arbitrarily high probability an upper bound on the optimal objective of a corresponding ccp moreover whenever an optimal constraint removal rule is used in the rcpvs then appropriate choices of n and r exist such that j approximates arbitrarily well the objective of the ccp

on bisymmetric operators on a finite chain the bisymmetry property is studied for operators defined on a finite chain in particular a characterization of all bisymmetric commutative and smooth binary operators is given it is deduced from this characterization that bisymmetry and associativity are equivalent for finite chains under these additional conditions

dob fuzzy controller design for non gaussian stochastic distribution systems using two step fuzzy identification this paper presents a novel non gaussian stochastic control framework for the problem of disturbance estimation and rejection by combining fuzzy identification technology with disturbance observer design first fuzzy logic models are used to approximate the output probability density functions pdfs of non gaussian processes such that the task of pdf shape control can be reduced to a fuzzy weight dynamics modeling and control problem next takagi sugeno fuzzy models with multiple disturbances are employed to describe the nonlinear relations between fuzzy weight dynamics and the control input in which a novel disturbance observer based pi type fuzzy feedback controller is designed to ensure the system stability and convergence of the tracking error to zero meanwhile the disturbance estimation and attenuation performance as well as the state constrained requirement can also be guaranteed moreover the novel composite observer is constructed by augmenting the disturbance estimation into the full state estimation the satisfactory tracking performance and full state observation effect can be achieved by the designed optimization algorithm finally simulations for paper making process are given to show the efficiency of the proposed approach

weighted fuzzy observer based fault detection approach for discrete time nonlinear systems via piecewise fuzzy lyapunov functions the main focus of this paper is on the analysis and integrated design of mathcal l 2 observer based fault detection fd systems for discrete time nonlinear industrial processes to gain a deeper insight into this fd framework the existence condition is introduced first then an integrated design of mathcal l 2 observer based fd approach is realized by solving the proposed existence condition with the aid of takagi sugeno fuzzy dynamic modeling technique and piecewise fuzzy lyapunov functions most importantly a weighted piecewise fuzzy observer based residual generator is proposed aiming at achieving an optimal integration of residual evaluation and threshold computation into fd systems the core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors in comparison with the standard norm based fuzzy observer based fd methods the proposed scheme may lead to a significant improvement of the fd performance in the end the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant

fuzzy approximation based adaptive control of strict feedback nonlinear systems with time delays this paper focuses on the problem of adaptive control for a class of nonlinear time delay systems with unknown nonlinearities and strict feedback structure based on the lyapunov krasovskii functional approach a state feedback adaptive controller is constructed by backstepping the proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal and all the signals of the closed loop system remain bounded compared with the results that exist the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy membership functions therefore a priori knowledge of fuzzy approximators is not necessary for control design and the proposed approach requires only one adaptive law for an nth order system two numerical examples are used to illustrate the effectiveness of the proposed approach

stochastic control with uncertain parameters via chance constrained control chance constrained methods handle problem uncertainty by formulating the constraints probabilistically and only guaranteeing their satisfaction up to a given violation level this paper extends existing chance constrained methods to handle both uncertainty in the system state as well as in the constraint parameters due to the imperfect knowledge of the system state caused by motion sensor and environment uncertainty the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically prior work has primarily only dealt with uncertainty in the system state or constraint parameters but not both simultaneously however in many motivating applications both frequently occur to handle this case previous approaches either approximate the distribution leading to a nonconvex optimization program or use sampling alone to represent the uncertainty which requires a large number of samples to accurately represent the distribution to address these limitations a novel hybrid method is proposed that uses both analytical functions and sampling to represent the uncertainty it is shown that under certain conditions the resulting optimization program using this hybrid representation is convex to check the convexity an efficient a priori sufficient condition is developed furthermore by using this hybrid representation this method drastically reduces the computational complexity over previous methods which is demonstrated through two examples consequently this method has the ability to enable real time stochastic control for the motivating applications

full and reduced order observer based controller design for h_2 optimization in this paper the most general h2 control problem is considered we derive necessary and sufficient conditions when the infimum is attained by state feedback we do the same for the measurement feedback case where we derive necessary and sufficient conditions when the infimum is attained by proper dynamic compensators we also investigate reduced order compensators if some states are observable without noise we discuss for all of these cases the freedom that the non uniqueness of optimal compensators gives us in assigning the closed loop eigenvalues the second half of this paper investigates the case when the infimum cannot be attained we give a constructive algorithm to find a minimizing sequence of stabilizing controllers and discuss the freedom in the asymptotic locations of the closed loop eigenvalues again we do the above for three different cases static state feedback full order measurement feedback and reduced order measurement feedback

lmi based nonlinear fuzzy observer controller design for uncertain mimo nonlinear systems based on the variable structure system theory we develop a nonlinear fuzzy observer controller design method for a class of uncertain nonlinear systems that can be represented by a takagi sugeno fuzzy model we use a sliding mode observer and a sliding mode controller as the local state observer and the local controller in terms of linear matrix inequalities lmis we derive sufficient conditions for the existence of the fuzzy observer and the fuzzy controller we also derive lmi conditions for the existence of the fuzzy observer and the fuzzy controller guaranteeing the alpha stability or generalized h2 hinfin performance constraints we show that the observer and the controller can be independently designed i e the separation property holds finally we give simple lmi based design algorithms together with an example

network based robust passive control for fuzzy systems with randomly occurring uncertainties this paper investigates the problem of robust passive control for networked fuzzy systems where randomly occurring uncertainties variable sampling intervals and constant network induced delay are taken into account a discontinuous lyapunov functional is introduced for the closed loop systems which takes full advantage of the sawtooth structure of the time varying interval delay induced by sample and hold and signal transmission a sufficient condition is proposed to ensure the closed loop system to be robustly stochastically passive then the problem of robust passive control is solved two examples are utilized to illustrate the advantages and effectiveness of the results that are proposed in this paper