center manifolds and contractions on a scale of banach spaces we give a new proof for the existence of a ck center manifold at a nonhyperbolic equilibrium point of a finite dimensional vector field of class ck the problem is reduced to a fixed point problem on a scale of banach spaces these banach spaces consist of mappings with a certain maximal exponential growth at infinity we give conditions under which there is a unique fixed point depending differentiably on the parameters the main difficulty is that the mappings under consideration become only differentiable after composition with appropriate embeddings on the scale of banach spaces

robust h control of t s fuzzy systems with input time varying delays a delay partitioning method abstract addressed in this paper is the robust h control issue of t s fuzzy systems with input time varying delays by means of the delay partitioning method the delay interval is partitioned into multiple unequal subintervals whose lengths satisfy a geometric sequence on this basis a modified lyapunov krasovskii functional is presented to analyze asymptotic stability of the open loop system then a state feedback controller that ensures a prescribed h performance level for the closed loop system is proposed in linear matrix inequality format finally two numerical examples are given to illustrate the effectiveness and advantages of the obtained results

generic simplicity of the spectrum and stabilization for a plate equation in this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of mathbb r d that is given omega subset mathbb r d we show that there exists an arbitrarily small deformation of the domain u such that all the eigenvalues of the plate system in the deformed domain omega u are simple to prove this result we first prove a nonstandard unique continuation property for this system that also holds generically with respect to the perturbations of the domain both the proof of this generic uniqueness result and the generic simplicity of the spectrum use baire s lemma and shape differentiation finally we show an application of this unique continuation property to a result of generic stabilization for a plate system with one dissipative boundary condition

a branch and bound algorithm for symmetric 2 peripatetic salesman problems abstract the symmetric 2 peripatetic salesman problem 2 psp is an extension of the well known symmetric traveling salesman problem tsp in the sense that 2 edge disjoint hamiltonian cycles of minimum total length are required in a graph g with n vertices lower bound solutions are provided by 2 minimum length edge disjoint 1 trees which can be constructed in at most o n 2 log n operations if g is complete generating upper bound solutions and executing edge elimination tests takes o n 2 time a branch and bound algorithm has been developed based on these procedures to solve symmetric problems computational results are available for euclidean problems up to 60 vertices and problems with randomly generated distance matrices up to 130 vertices

existence of bounded solutions of a second order system with dissipation in this article we study the following second order system of ordinary differential equations with dissipationu cu dau khu pt u rn t r where c d and k are positive constants h rn rn is a locally lipschitz function and p r rn is a continuous and bounded function a is a n n matrix whose eigenvalues are positive under these conditions we prove that for some values of c d and k this system has a bounded solution which is exponentially asymptotically stable moreover if p t is almost periodic then this bounded solution is also almost periodic these results are applied to the spatial discretization of very well known second order partial differential equations

bounded solutions of a second order evolution equation and applications in this paper we study the following abstract second order differential equation with dissipation in a hilbert space h u cu da u kg u p t u h t r where c d and k are positive constants g h h is a lipschitzian function and p r h is a continuous and bounded function a d a h h is an unbounded linear operator which is self adjoint positive definite and has compact resolvent under these conditions we prove that for some values of d c and k this system has a bounded solution which is exponentially asymptotically stable moreover if p t is almost periodic then this bounded solution is also almost periodic these results are applied to a very well known second order system partial differential equations such as the sine gordon equation the suspension bridge equation proposed by lazer and mckenna etc

on the generalized 2 peripatetic salesman problem abstract given an undirected graph the 2 peripatetic salesman problem psp is the problem that aims to minimize the total length of 2 edge disjoint hamiltonian cycles we consider a generalization of the problem gpsp where each cycle visits each vertex at most instead of exactly once and a penalty has to be paid for each unvisited vertex we will show that the generalized problem can be solved by finding 2 edge disjoint paths the path problem in turn can be transformed into a standard psp so that the gpsp is solvable by a standard psp algorithm we will discuss some special cases of the gpsp

new stability conditions based on piecewise fuzzy lyapunov functions and tensor product transformations improvements of recent stability conditions for continuous time takagi sugeno t s fuzzy systems are proposed the key idea is to bring together the so called local transformations of membership functions and new piecewise fuzzy lyapunov functions by relying on these special local transformations the associated linear matrix inequalities that are used to prove the system s stability can be relaxed without increasing the number of conditions in addition to enhance the usefulness of the proposed methodology one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives a standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time varying delays an adaptive fuzzy controller is presented for a class of stochastic nonlinear systems an quadratic function is constructed to give the condition of the stability of systems the scheme guarantees the stability of closed loop system in the mean square sense the drawback of the quartic moment approach is overcome and the method is simplified this paper addresses the problem of adaptive tracking control for a class of stochastic strict feedback nonlinear time varying delays systems using fuzzy logic systems fls in this paper quadratic functions are used as lyapunov functions to analyze the stability of systems other than the fourth moment approach proposed by h deng and m krstic and the hyperbolic tangent functions are introduced to deal with the hessian terms this approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller based on the backstepping technique the appropriate lyapunov krasovskii functionals and the fls the adaptive fuzzy controller is well designed the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense

the undirected m capacitated peripatetic salesman problem abstract in the m capacitated peripatetic salesman problem m cpsp the aim is to determine m hamiltonian cycles of minimal total cost on a graph such that all the edges are traversed less than the value of their capacity this article introduces three formulations for the m cpsp two branch and cut algorithms and one branch and price algorithm are developed tests performed on randomly generated and on tsplib euclidean instances indicate that the branch and price algorithm can solve instances with more than twice the size of what is achievable with the branch and cut algorithms

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

exact boundary controllability for the linear korteweg de vries equation on the half line this paper is concerned with the controllability of the linear korteweg de vries equation on the domain o 0 infty the control being applied at the left endpoint x 0 it is shown that the em exact boundary controllability holds true in l 2 0 infty provided that the solutions are not required to be in l infty 0 t l 2 0 infty the proof rests on a carleman s estimate and an approximation theorem a similar result is obtained for the heat equation and for the schrodinger equation

nonfragile retarded sampled data switched control of t s fuzzy systems and its applications this article investigates the nonfragile retarded fuzzy sampled data control design of takagi sugeno t s fuzzy system when compared to the traditional sampled data control scheme a constant signal transmission delay is involved with uncertainties in control gain parameters which exploited for the first time to tackle the stabilization analysis of the closed loop t s fuzzy systems based on the switched control idea by constructing a fuzzy membership function fmf dependent lyapunov krasovskii functional lkf and utilizing the time derivative information of the fmf the sufficient conditions are carried out in terms of linear matrix inequalities lmis such that the resultant t s fuzzy systems can achieve the globally asymptotically stable under the designed control then the desired control gain is determined by solving the obtained lmis finally the numerical simulations are demonstrated to show the advantage and applicability of the derived sufficient conditions

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

existence stability and smoothness of a bounded solution for nonlinear time varying thermoelastic plate equations in this paper we study the existence stability and the smoothness of a bounded solution of the following nonlinear time varying thermoelastic plate equation with homogeneous dirichlet boundary conditions utt 2u f1 t u t 0 x t ut f2 t u t 0 x u u 0 t 0 x where 0 0 is a sufficiently regular bounded domain in rn n 1 and fe1 fe2 r l2 2 l2 define by fe t u x f t u x x x are continuous and locally lipschitz functions first we prove that the linear system f1 f2 0 generates an analytic strongly continuous semigroup which decays exponentially to zero second under some additional condition we prove that the nonlinear system has a bounded solution which is exponentially stable and for a large class of functions f1 f2 this bounded solution is almost periodic finally we use the analyticity of the semigroup generated by the linear system to prove the smoothness of the bounded solution

brief paper dynamic output feedback h control of switched linear systems this paper is devoted to dynamic output feedback h control design of switched linear systems in both continuous and discrete time domains more specifically the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed loop switched linear system globally asymptotically stable and impose a pre specified upper bound to the l 2 gain an example of practical importance is presented to illustrate the validity and efficiency of the theory

a branch and bound algorithm for the symmetric traveling salesman problem based on the 1 tree relaxation abstract in 1970 held and karp introduced the lagrangean approach to the symmetric traveling salesman problem we use this 1 tree relaxation in a new branch and bound algorithm it differs from other algorithms not only in the branching scheme but also in the ascent method to calculate the 1 tree bounds urthermore we determine heuristic solutions throughout the computations to provide upperbounds we present computational results for both a depth first and a breadth first version of our algorithm on the average our results on a number of euclidean problems from the literature are obtained in about 60 less 1 trees than the best known algorithm based on the 1 tree relaxation for random table problems up to 100 cities the average results are also satisfactory

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

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

local stability analysis of continuous time takagi sugeno fuzzy systems a fuzzy lyapunov function approach this paper proposes a strategy to estimate invariant subsets of the domain of attraction da for asymptotically stable zero equilibrium points of continuous time takagi sugeno t s fuzzy systems specifically by using lyapunov s stability theory and the linear matrix inequality lmi technique sufficient conditions for proving the local stability are provided in terms of single parameter minimization problems subject to lmi constraints or eigenvalue problems which are solvable via convex optimizations the fuzzy lyapunov functions flfs expressed by the so called multi dimensional fuzzy summations are employed to characterize invariant subsets of the da as sublevel sets of the flfs to compute a larger inner estimate of the da an iterative lmi algorithm is also developed finally illustrative examples show the efficacy of the approach

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

static output feedback controller design for fuzzy systems an ilmi approach this paper examines the problem of static output feedback control of a takagi sugeno ts fuzzy system the existence of a static output feedback control law is given in terms of the solvability of bilinear matrix inequalities an iterative algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain to reduce the conservatism of the design the structural information of the membership function of the fuzzy rules is incorporated numerical examples are used to illustrate the validity of the methods

stability analysis and state feedback control of continuous time t s fuzzy systems via anew switched fuzzy lyapunov function approach this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems first a new membership function dependent switching law is proposed and a relaxation parameter is introduced into this switching law to guarantee a minimal dwell time between two consecutive switching compared to the existing methods the most important point is that with the help of the dwell time the discretized lyapunov function dlf technique can be adopted then a new stability criterion of the t s fuzzy system with less conservatism is derived based on a fuzzy discretized lyapunov function fdlf second to estimate the domain of attraction da an algorithm with less iteration steps is proposed based on the proposed switching method sufficient conditions for existence of the state feedback controllers are presented via the switched non parallel distributed compensation non pdc scheme the effectiveness of the proposed method is illustrated through three simulation examples

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

carleman estimates for a class of degenerate parabolic operators given alpha in 0 2 and f in l 2 0 t times 0 1 we derive new carleman estimates for the degenerate parabolic problem w t x alpha w x x f where t x in 0 t times 0 1 associated to the boundary conditions w t 1 0 and w t 0 0 if 0 leq alpha 1 or x alpha w x t 0 0 if 1 leq alpha 2 the proof is based on the choice of suitable weighted functions and hardy type inequalities as a consequence for all 0 leq alpha 2 and omega subset subset 0 1 we deduce null controllability results for the degenerate one dimensional heat equation u t x alpha u x x h chi omega with the same boundary conditions as above

null controllability for a semilinear parabolic equation with gradient quadratic growth abstract this article is concerned with the null controllability of a semilinear parabolic equation with the nonlinear term involving the gradient quadratic term the technique in this paper is a combination of cole hopf transformation and some methods from a y khapalov controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term a qualitative approach siam j control optim 41 2003 1886 1900

nonfragile distributed filtering for t s fuzzy systems in sensor networks this paper is concerned with the nonfragile distributed h infty filtering problem for a class of discrete time takagi sugeno t s systems in sensor networks additive filter gain uncertainties that reflect imprecision in filter implementation are considered based on the robust control approach sufficient conditions are obtained to ensure that the filtering error system is asymptotically stable with a prescribed h infty performance level and the eigenvalues of the filtering error system in a given circular region the filter parameters are determined by solving a set of linear matrix inequalities a simulation study on the nonlinear tunnel diode circuit system is presented to show the effectiveness of the proposed design method

unique continuation for some evolution equations this work is concerned with unique continuation results for some evolution equations essentially of parabolic type to be more precise let l be an evolution operator acting on functions defined on some connected open set b of r r x r l is said to have the unique continuation property if every solution u of lu 0 which vanishes one some nonempty open set u i of fl vanishes in the horizontal component of o in 0 i e in x t e 0 3x x t e co the first general result of this type was established by mizohata 6 in the case where l is a second order parabolic operator with smooth coefficients however mizohata s proof is somewhat delicate it is based in particular on an extended class of calderon zygmund operators and does not lead obviously to a weakening of the smoothness of the coefficients on the other hand it is important for the applications to deal with nonsmooth coefficients since l is often obtained as the linearization of some nonlinear operator at a nonnecessarily smooth solution we refer to lions 4 and kernevez and lions 3 for applications to control theory and to 1 l for applications to transversality techniques let us now describe the content of this work in the first section we prove a unique continuation theorem when l is a second order parabolic equation our proof is simple and based on the derivation of a carleman estimate which is reminiscent of the classical carleman estimates for second order elliptic operators see 121 this carleman inequality allows the weakening of the 118 0022 0396187 3 00

improvement on nonquadratic stabilization of discrete time takagi sugeno fuzzy systems multiple parameterization approach this paper presents the relaxed nonquadratic stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this we propose a new fuzzy controller and lyapunov function by generalizing the nonparallel distributed compensation non pdc control law and nonquadratic lyapunov function respectively by exploiting po lya s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions an infinite family of sufficient conditions for the asymptotic stabilizability is derived these conditions are formulated in the format of linear matrix inequalities lmis and hence are numerically tractable via convex programming techniques finally an example is given to illustrate advantages of the proposed method

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

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

quantized feedback fuzzy sliding mode control design via memory based strategy this paper is concerned with the sliding mode control smc design for a class of takagi sugeno t s fuzzy nonlinear systems subject to model uncertainties and input quantization mismatch a novel memory based sliding surface is presented which includes not only the current states but also the past state information of the systems sufficient conditions for the design of the switching gains are given via linear matrix inequality lmi technique and then the reaching conditions of the sliding surface is constructed to ensure the reachability of the sliding manifold furthermore an adaptive neuro fuzzy inference system anfis is introduced for reducing the high frequency chattering induced by the signum function term in the sliding mode control the effectiveness of the proposed methodology is illustrated by matlab simulations

a note on finding minimum cost edge disjoint spanning trees let g be an undirected graph with n vertices and m edges such that each edge has a real valued cost we consider the problem of finding a set of k edge disjoint spanning trees in g of minimum total edge cost this problem can be solved in polynomial time by the matroid greedy algorithm we present an implementation of this algorithm that runs in o m log m k2n2 time if all edge costs are the same the algorithm runs in o k2n2 time the algorithm can also be extended to find the largest k such that k edge disjoint spanning trees exist in o m2 time we mention several applications of the algorithm

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

a new fuzzy lyapunov function for relaxed stability condition of continuous time takagi sugeno fuzzy systems this paper presents a new fuzzy lyapunov function flf for the stability analysis of continuous time takagi sugeno t s fuzzy systems unlike conventional flfs the proposed one depends not only on the fuzzy weighting functions of the t s fuzzy systems but on their first order time derivatives as well based on the proposed flf a sufficient stability condition is derived in the form of linear matrix inequalities depending on the upper bounds on the second order time derivative of the fuzzy weighting functions as well as the first order ones finally some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature

approximate controllability for fractional semilinear parabolic equations abstract in this paper we deal with the control systems described by a large class of fractional semilinear parabolic equations firstly we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate banach space secondly we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator nonlinear analysis method and fixed point theorem then the approximate controllability of the fractional semilinear parabolic equations is formulated and proved at the end of the paper an example is given to illustrate our main results

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

nonoptimal edges for the symmetric traveling salesman problem for the symmetric traveling salesman problem we identify a set of undirected edges that can be eliminated while still retaining at least one optimal solution of the problem the simple identification rules are based on the fact that a solution can be optimal only if it is 2 optimal the rules are less stringent than those formulated for nonoptimal arcs directed applied to the symmetric case so in general they identify more nonoptimal edges application of the theory in a 1 tree based traveling salesman algorithm roughly halves the average computation time for euclidean problems we indicate to what extent the theorems presented here can be adapted for variants of the traveling salesman problem

generalized nonquadratic stability of continuous time takagi sugeno models this paper provides generalized nonquadratic stability conditions for continuous time nonlinear models in the takagi sugeno ts form obtained by sector nonlinearity approach should global quadratic stability fail for a given nonlinear model the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear matrix inequalities lmis which are efficiently solved by convex optimization techniques illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis

exact controllability of the suspension bridge model proposed by lazer and mckenna abstract in this paper we give a sufficient condition for the exact controllability of the following model of the suspension bridge equation proposed by lazer and mckenna in a c lazer p j mckenna large amplitude periodic oscillations in suspension bridges some new connections with nonlinear analysis siam rev 32 1990 537 578 w t t c w t d w x x x x k w p t x u t x f t w u t x 0 x 1 w t 0 w t 1 w x x t 0 w x x t 1 0 t r where t 0 d 0 c 0 k 0 the distributed control u l 2 0 t 1 l 2 0 1 p r 0 1 r is continuous and bounded and the non linear term f 0 t 1 r r r is a continuous function on t and globally lipschitz in the other variables i e there exists a constant l 0 such that for all x 1 x 2 u 1 u 2 r we have f t x 2 u 2 f t x 1 u 1 l x 2 x 1 u 2 u 1 t 0 t 1 to this end we prove that the linear part of the system is exactly controllable on 0 t 1 then we prove that the non linear system is exactly controllable on 0 t 1 for t 1 small enough that is to say the controllability of the linear system is preserved under the non linear perturbation k w p t x f t w u t x

finite time h fuzzy control of nonlinear markovian jump delayed systems with partly uncertain transition descriptions abstract this paper addresses a finite time h fuzzy control problem for a class of nonlinear markovian jump delayed systems with partly uncertain transition descriptions which is represented as a takagi sugeno t s fuzzy model a new homogeneous polynomial of partly uncertain transition rates is chosen free matrix based and double integral forms of the wirtinger based integral inequalities are employed to make the proposed approach less conservative then sufficient conditions are derived such that the fuzzy nonlinear makovian jump delayed system exhibits stochastic finite time boundedness finally two numerical examples are given to illustrate the effectiveness of the proposed design methodology

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

controls insensitizing the norm of the solution of a semilinear heat equation abstract we consider here a semilinear heat equation with partially known initial and boundary conditions the insensitizing problem consists in finding a control function such that some functional of the state is locally insensitive to the perturbations of these initial and boundary data in this paper the insensitizing control of the norm of the observation of the solution in an open subset of the domain is studied under appropriate assumptions on the nonlinearity and the observation subset it is shown that the insensitivity conditions are equivalent to a particular nonlinear exact controllability problem for parabolic equations due to the smoothing effects of this type of equation exact controllability is very hard to achieve and this is why it seems natural to introduce the idea of approximately insensitizing control and then to solve a nonlinear approximate controllability problem of a special type that is done using a linearization and fixed point method solving the linear problem leads to the proof of a nontrivial uniqueness property which is abo used to characterize a particular subset of the admissible controls this characterization is made thanks to a convex duality theorem and allows us to solve a fixed point problem and get the result for the nonlinear case various comments and conclusions are eventually given with other approximately insensitizing problems that can be solved by our methods

stability analysis and systematic design of takagi sugeno fuzzy control systems abstract the stability analysis and systematic design techniques of takagi sugeno t s fuzzy control systems are discussed in this paper in order to make good use of the structural information in rule base to decrease the conservatism of the stability analysis the standard fuzzy partition of the input variables of fuzzy control systems is well defined based on the property analysis of fuzzy control systems with sfp inputs the stability of both the input free t s fuzzy systems and the closed loop t s fuzzy control systems are studied in detail with the extended lyapunov theory and two theorems to check the stability of t s fuzzy control systems are proposed these methods which only require to find a common positive definite symmetric matrix in each maximal overlapped rules group can reduce the conservatism and difficulty of the former stability analysis approaches using the method of parallel distributed compensation a systematic design approach of t s fuzzy control systems is presented the simulation results of three examples show that these methods are effective

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

some results on controllability of a nonlinear degenerate parabolic system by bilinear control in this paper we discuss the controllability of a nonlinear degenerate parabolic system with bilinear control based on the shrinking property of the solutions we prove that the system is not globally approximately controllable furthermore we give an approximate null controllability result we also prove that the system is not globally exactly null controllable by a comparison principle

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

efficient algorithms with performance guarantees for some problems of finding several discrete disjoint subgraphs in complete weighted graph some hard to solve combinatorial problems of finding several disjoint discrete structures in complete weighted graph are considered efficient algorithms with performance guarantees are constructed for the euclidean m peripatetic salesman problem m weighted clique problem and m layer planar three index assignment problem

the undirected m peripatetic salesman problem polyhedral results and new algorithms in the m peripatetic salesman problem m psp the aim is to determine m edge disjoint hamiltonian cycles of minimum total cost on a graph this article introduces new valid inequalities and polyhedral results for the m psp an improved 2 index branch and cut algorithm is developed tests performed on randomly generated and tsplib euclidean instances indicate that this algorithm can solve instances with more than double the size of what was previously achievable

boundary controllability of thermoelastic plates via the free boundary conditions controllability properties of a partial differential equation pde model describing a thermoelastic plate are studied the pde is composed of a kirchoff plate equation coupled to a heat equation on a bounded domain with the coupling taking place on the interior and boundary of the domain the coupling in this pde is parameterized by alpha 0 boundary control is exerted through the two free boundary conditions of the plate equation and through the robin boundary condition of the temperature these controls have the physical interpretation of inserted forces and moments and prescribed temperature respectively all of which act on the edges of the plate the main result here is that under such boundary control and with initial data in the basic space of well posedness one can simultaneously control the displacement of the plate exactly and the temperature approximately moreover the thermal control may be taken to be arbitrarily smooth in time and space and the thermal control region may be any nonempty subset of the boundary this controllability holds for arbitrary values of the coupling parameter alpha with the optimal controllability time in line with that seen for uncoupled kirchoff plates

a generalized multiple lyapunov functions method based non fragile guaranteed cost control for uncertain switched fuzzy systems abstract this paper is concerned with a non fragile guaranteed cost control problem for a class of uncertain switched fuzzy systems which are described by switched takagi sugeno t s fuzzy models by employing the generalized multiple lyapunov functions method we present a sufficient condition to guarantee the closed loop system asymptotically stable and possess an upper bound of the non fragile guaranteed cost function meanwhile a non fragile state feedback control law and a switching law are designed moreover an optimization problem in which the minimal non fragile guaranteed cost can be obtained is solved finally a simulation example is given to verify the feasibility and effectiveness of the proposed method

approximate controllability of a semilinear heat equation in bbb r n we prove the approximate controllability of the semilinear heat equation in bbb r n we introduce the weighted sobolev spaces of escobedo and kavian and in that functional setting we adapt the technique introduced by fabre puel and zuazua for the problem in bounded domains that is we first prove the approximate controllability of the linear equation and by a fixed point method obtain the main result

branch and cut algorithms for the undirected m peripatetic salesman problem in the m peripatetic salesman problem m psp the aim is to determine m edge disjoint hamiltonian cycles of minimum total cost on a graph this article describes exact branch and cut solution procedures for the undirected m psp computational results are reported on random and euclidean graphs

time optimal control of semilinear parabolic equations via bilinear controls abstract we establish the existence of the time optimal control for semilinear parabolic equations with gradient quadratic growth via bilinear controls it is worth pointing out that there is no restriction on the growth of the nonlinearity f s with respect to the variable s in the equation which is a remarkable difference compared to the semilinear parabolic system with locally distributed controls the technique used in this paper is the combination of the hopf cole transformation the a prior estimates on solutions of parabolic equations and the strategy of the stepwise control

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

the symmetric traveling salesman problem and edge exchanges in minimal 1 trees abstract in this article the effect of exchanging edges inside a minimal 1 tree with edges outside is analysed in combination with an upper bound this analysis enables the elimination of variables in the symmetric traveling salesman problem after discussion on a number of improvements for this analysis the implementation is described in a traveling salesman algorithm based on the 1 tree relaxation computational results show the advantages of the edges exchanges for euclidean problems up to 120 cities as well as for random table problems up to 200 cities

simultaneous fault detection and control for switched linear systems with mode dependent average dwell time this paper investigates the problem of the simultaneous fault detection and control sfdc for switched linear systems to meet the control and detection objectives the time dependent detection filters and dynamic output feedback controllers are presented in sfdc under a mixed h h framework a mode dependent average dwell time mdadt approach which means that each subsystem has its own average dwell time is adopted in this paper to reduce the conservativeness of the average dwell time method and the discretized lyapunov function dlf technique is first used to relax the mdadt constraints in sfdc some sufficient conditions for designing filters controllers which satisfy the h h performance are given in terms of linear matrix inequalities lmis what s more a two step algorithm to solve the sfdc problem is proposed the effectiveness of the proposed method is illustrated through two simulation examples

on the lack of null controllability of the heat equation on the half line we consider the linear heat equation on the half line with a dirichlet boundary control we analyze the null controllability problem more precisely we study the class of initial data that may be driven to zero in finite time by means of an appropriate choice of the l2 boundary control we rewrite the system on the similarity variables that are a common tool when analyzing asymptotic problems next the control problem is reduced to a moment problem which turns out to be critical since it concerns the family of real exponentials eit j in which the usual summability condition on the inverses of the eigenvalues does not hold roughly speaking we prove that controllable data have fourier coefficients that grow exponentially for large frequencies this result is in contrast with the existing ones for bounded domains that guarantee that every initial datum belonging to a sobolev space of negative order may be driven to zero in an arbitrarily small time

on a class of non linear parabolic control systems with memory effects this work establishes the local exact null controllability of non linear parabolic integrodifferential equations with non linearities under the integral sign in a bounded domain and with homogeneous dirichlet boundary conditions the control is assumed to be distributed along a subdomain of using a carleman type inequality we first prove the global exact null controllability of a linearized equation then by a fixed point method we obtain the main result for the non linear case this result asserts that when the non linearity is of class c 1 and globally lipschitz the system is null controllable

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

relaxed stabilization conditions for continuous time takagi sugeno fuzzy control systems this paper deals with the stabilization of continuous time takagi sugeno t s fuzzy control systems based on fuzzy lyapunov functions and nonparallel distributed compensation non pdc control laws new stabilization conditions are represented in the form of linear matrix inequalities lmis the theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature moreover in order to demonstrate the effectiveness of the non pdc control laws the problem of h controller design for t s fuzzy systems is also studied simulation examples are given to illustrate the merits of the proposed methods

almost periodic solutions of first and second order cauchy problems abstract almost periodicity of solutions of first and second order cauchy problems on the real line is proved under the assumption that the imaginary resp real spectrum of the underlying operator is countable related results have been obtained by ruess v and basit our proof uses a new idea it is based on a factorisation method which also gives a short proof of the vector valued version of loomis classical theorem saying that a bounded uniformly continuous function from r into a banach spacexwith countable spectrum is almost periodic ifc0 x our method can also be used for solutions on the half line this is done in a separate paper

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

dynamic output feedback control for positive roesser system under the switched and t s fuzzy rules abstract this paper is concerned with the dynamic output feedback controller design for the positive roesser type nonlinear system which is intrinsically characterized by the switched mechanism and subtly decomposed into the linear form under the takagi sugeno fuzzy rules firstly based on the co positive lyapunov function and the average dwell time method sufficient conditions are presented under which the resulting closed loop system is exponentially stable and has l 1 gain bound then explicit expressions are also given to derive the expected controller gain matrices with desired l 1 gain bound finally effectiveness of the proposed results is illustrated by two numerical examples