robust and resilient finite time bounded control of discrete time uncertain nonlinear systems abstract finite time state feedback stabilization is addressed for a class of discrete time nonlinear systems with conic type nonlinearities bounded feedback control gain perturbations and additive disturbances first conditions for the existence of a robust and resilient linear state feedback controller for this class of systems are derived then using linear matrix inequality techniques a solution for the controller gain and the maximum allowable bound on the gain perturbation is obtained the developed controller is robust for all unknown nonlinearities lying in a known hypersphere with an uncertain center and all admissible disturbances moreover it is resilient against any bounded perturbations that may alter the controller s gain by at most a prescribed amount the paper is concluded with a numerical example showcasing the applicability of the main result

optimality conditions and algorithms for parameter design problems with two level structure we consider the parameter design problem for a central system coordinating plural semiautonomous subsystems each of which optimizes its own objective under the given parameter from the center the center makes a decision of the parameter values to be assigned to the subsystems so as to optimize its objective considering the values of optimized subsystems performances such a parameter design problem is formulated in the framework of a two level planning problem and becomes an optimization problem including optimal value functions and accordingly a nondifferentiable optimization problem in this paper based on gauvin s studies concerned with the directional derivatives of optimal value functions we derive the necessary conditions for the parameter design problem by means of a new theorem of the alternative the results obtained here are slightly different from the kuhn tucker like conditions and are adapted to the structure of the problem as the computational method for our problem we propose applying an existing generalized gradient algorithm called the bundle method in a class of nondifferentiable optimization methods and also show a numerical example

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

optimal routing under capacity and distance restrictions this paper describes an integer linear programming algorithm for vehicle routing problems involving capacity and distance constraints the method uses constraint relaxation and a new class of subtour elimination constraints two versions of the algorithm are presented depending upon the nature of the distance matrix exact solutions are obtained for problems involving up to sixty cities

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

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

stability and stabilization of a class of stochastic switching systems with lower bound of sojourn time abstract this paper is concerned with the stability and stabilization issues for a family of discrete time stochastic switching systems with bounded sojourn time the stochastic switching systems are modeled by semi markov jump linear systems and the semi markov kernel approach is employed to handle the stability and stabilization problems the sojourn time of each system mode is considered to have both upper and lower bounds which is more general than the scenarios in previous literature that only consider the upper bound of sojourn time the concept of error mean square stability is put forward in a new form by taking into account the lower bounds of sojourn time for all system modes by virtue of a lyapunov function that not only depends on the current system mode but also on the elapsed time the system has been in the current mode together with certain techniques eliminating powers of matrices numerically testable stability and stabilization criteria in the sense of the proposed error mean square stability are obtained for the closed loop stochastic switching system finally a numerical example and a practical example of a dc motor are utilized to demonstrate the effectiveness of the proposed control strategy and the superiority of allowing for the lower bound of sojourn time

facet identification for the symmetric traveling salesman polytope several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given an identification procedure accepts as input the support graph of a point which does not belong to the polytope and returns as output some of the facet inducing inequalities violated by the point a procedure which always accomplishes this task is calledexact otherwise it is calledheuristic we give exact procedures for the subtour elimination and the 2 matching constraints based on the gomory hu and padberg rao algorithms respectively efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities these procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large scale problem instances with sizes up to 2392 nodes to optimality

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

optimal control for linear systems with multiple time delays in control input this note presents the optimal linear quadratic lq regulator for a linear system with multiple time delays in the control input optimality of the solution is proved in two steps first a necessary optimality condition is derived from the maximum principle then the sufficiency of this condition is established by verifying that it satisfies the hamilton jacobi bellman equation using an illustrative example the performance of the obtained optimal regulator is compared against the performance of the optimal lq regulator for linear systems without delays and some other feasible feedback regulators that are linear in the state variables finally the note establishes a duality between the solutions of the optimal filtering problem for linear systems with multiple time delays in the observations and the optimal lq control problem for linear systems with multiple time delays in the control input

separating capacity constraints in the cvrp using tabu search abstract branch and cut methods have shown to be very successful in the resolution of some hard combinatorial optimization problems the success has been remarkable for the symmetric traveling salesman problem tsp the crucial part in the method is the cutting plane algorithm the algorithm that looks for valid inequalities that cut off the current nonfeasible linear program lp solution in turn this part relies on a good knowledge of the corresponding polyhedron and our ability to design algorithms that can identify violated valid inequalities this paper deals with the separation of the capacity constraints for the capacitated vehicle routing problem cvrp three algorithms are presented a constructive algorithm a randomized greedy algorithm and a very simple tabu search procedure as far as we know this is the first time a metaheuristic is used in a separation procedure the aim of this paper is to present this application no advanced tabu technique is used we report computational results with these heuristics on difficult instances taken from the literature as well as on some randomly generated instances these algorithms were used in a branch and cut procedure that successfully solved to optimality large cvrp instances

brief paper h estimation for discrete time piecewise homogeneous markov jump linear systems this paper concerns the problem of h estimation for a class of markov jump linear systems mjls with time varying transition probabilities tps in discrete time domain the time varying character of tps is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types arbitrary variation and stochastic variation respectively the latter means that the variation is subject to a higher level transition probability matrix the mode dependent and variation dependent h filter is designed such that the resulting closed loop systems are stochastically stable and have a guaranteed h filtering error performance index using the idea in the recent studies of partially unknown tps for the traditional mjls with homogeneous tps a generalized framework covering the two kinds of variations is proposed a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

quadratic incentive coordination for non convex optimal control problems part 1 theory non convex optimal control problems are decomposed and coordinated by using quadratic incentive functions the idea is to decompose the original problem into subproblems along the time axis so that subproblems can be solved in parallel to coordinate the subproblems a high level problem is used an equivalence is demonstrated by showing there is a one to one correspondence between the local minima of the high level problem and local minima of the original problem provided certain technical conditions are satisfied the theoretical foundation of quadratic incentive coordination is established the relationship of the quadratic incentives and the optimal cost to go functions is also established

the graphical relaxation a new framework for the symmetric traveling salesman polytope a present trend in the study of thesymmetric traveling salesman polytope stsp n is to use as a relaxation of the polytope thegraphical relaxation gtsp n rather than the traditionalmonotone relaxation which seems to have attained its limits in this paper we show the very close relationship between stsp n and gtsp n in particular we prove that every non trivial facet of stsp n is the intersection ofn 1 facets of gtsp n n of which are defined by the degree inequalities this fact permits us to define a standard form for the facet defining inequalities for stsp n that we calltight triangular and to devise a proof technique that can be used to show that many known facet defining inequalities for gtsp n define also facets of stsp n in addition we give conditions that permit to obtain facet defining inequalities by composition of facet defining inequalities for stsp n and general lifting theorems to derive facet defining inequalities for stsp n k from inequalities defining facets of stsp n

mixed coordination method for long horizon optimal control problems we present a new approach to solving long horizon discrete time optimal control problems using the mixed coordination method the idea is to decompose a long horizon problem into subproblems along the time axis the requirement that the initial state of a subproblem equal the terminal state of the preceding subproblem is relaxed by using lagrange multipliers the lagrange multipliers and initial state of each subproblem are then selected as high level variables the equivalence of the two level formulation and the original problem is proved for both convex and non convex cases the low level subproblems are solved in parallel using extended differential dynamic programming ddp an efficient way to find the gradient and hessian of a low level objective function with respect to high level variables is developed the high level problem is solved using the modified newton method an effective procedure is developed to select initial values of multipliers based on the initial trajectory the method can conv

stability and stabilization of discrete time semi markov jump linear systems via semi markov kernel approach this technical note is concerned with the problems of stability and stabilization for a class of discrete time semi markov jump linear systems s mjlss the discrete time semi markov kernel smk is introduced where the probability density function of sojourn time is dependent on both current and next system mode as a consequence different types of distributions and or different parameters in a same type of distribution of sojourn time depending on the target mode towards which the system jumps can coexist in each mode of a smk the underlying s mjlss are therefore more general than those considered in existing studies a new stability concept generalizing the traditional mean square stability is proposed such that numerically testable criteria on the basis of smk are obtained numerical examples are presented to illustrate the validity and advantage of the developed theoretical results

a polyhedral approach to the asymmetric traveling salesman problem several branch and bound algorithms for the exact solution of the asymmetric traveling salesman problem atsp based on the assignment problem ap relaxation have been proposed in the literature these algorithms perform very well for some instances e g those with uniformly random integer costs but very poorly for others the aim of this paper is to evaluate the effectiveness of a branch and cut algorithm exploiting atsp specific facet defining cuts to be used to attack hard instances that cannot be solved by the ap based procedures from the literature we present new separation algorithms for some classes of facet defining cuts and a new variable pricing technique for dealing with highly degenerate primal lp problems a branch and cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real world instances the outcome of the research is that on hard instances the branch and cut algorithm clearly outperforms the best ap based algorithms from the literature

input output finite time stability of linear systems necessary and sufficient conditions in the recent paper input output finite time stabilization of linear systems f amato a sufficient condition for input output finite time stability io fts when the inputs of the system are l2 signals has been provided such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality dlmi roughly speaking a system is said to be input output finite time stable if given a class of norm bounded input signals over a specified time interval of length t the outputs of the system do not exceed an assigned threshold during such time interval io fts constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response in this context this paper presents several novel contributions first by using an approach based on the reachability gramian theory we show that the main theorem of f amato is actually also a necessary condition for io fts at the same time we provide an alternative still necessary and sufficient condition for io fts in this case based on the existence of a suitable solution to a differential lyapunov equality dle we show that the last condition is computationally more efficient however the formulation via dlmi allows to solve the problem of the io finite time stabilization via output feedback the effectiveness and computational issues of the two approaches for the analysis and the synthesis respectively are discussed in two examples in particular our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude

a hierarchical decomposition for large scale optimal control problems with parallel processing structure abstract this paper presents a new method in solving long horizon optimal control problems the original problem is decomposed along the time axis to form many smaller subproblems and a high level problem is created that uses initial and terminal states of subproblems as coordination parameters in such a scheme the high level problem is a parameter optimization problem subproblems are optimal control problems having shorter time horizon and are completely decoupled so that they can be solved in parallel it is shown that the two level problem has the same global optimum as the original one moreover the high level problem is a convex programming problem if the original problem has a convex cost function and linear system dynamics a parallel two level optimization algorithm is then presented where the the high level problem is solved by newton s method and low level subproblems are solved by the differential dynamic programming technique numerical testings on two examples are given to illustrate the idea and to demonstrate the potential of the new method in solving long horizon problems under a parallel processing environment

input output finite time mean square stabilization of nonlinear semi markovian jump systems this paper is concerned with the input output finite time mean square stabilization problem for a class of nonlinear semi markovian jump systems smjss with time varying delay both time varying factors of transition rates and states delay are considered to be bounded our main purpose is to derive some parameter dependent sufficient criteria by designing a state feedback controller to guarantee the input output finite time mean square stabilization for the underlying systems where the nonlinear term satisfies the conic sector constraint then the stabilization conditions are obtained by employing a novel lyapunov krasovskii functional differential form gronwall s inequality and an extra slack variable which is composed of the time varying transition rates finally a simulation example is provided to illustrate the effectiveness and merits of the proposed method

stability analysis and stabilization of discrete time non homogeneous semi markov jump linear systems a polytopic approach abstract this paper addresses the issues of stability analysis and stabilizing controller design for two classes of discrete time non homogeneous semi markov jump linear systems s mjlss the first class is concerned with the sojourn time probability mass functions that are independent of jump instants while the other considers the existence of probability mass functions of sojourn time depending on jump instants new techniques are developed respectively for both classes of systems by transforming their corresponding time varying semi markov kernels into more tractable forms based on the stochastic stability allowing for bounded sojourn time the derived stability and stabilization criteria containing the probability distribution information of random sojourn time can be numerically tested in order to reduce the possible conservatism of the obtained results a novel class of polytopic quadratic lyapunov function is constructed which depends on both the current mode and the elapsed time in the current mode finally the proposed control strategies are applied to an illustrative application of automotive electronic throttle valve to show the effectiveness of the theoretical results the results also reveal the significance of considering the inhomogeneity of s mjlss and the importance of our constructed lyapunov function

a sliding mode approach to stabilization of nonlinear markovian jump singularly perturbed systems this paper presents a sliding mode control smc method for a class of nonlinear markovian jump singularly perturbed systems mjspss the system is subject to parameter uncertainties and partly unknown transition probabilities to fully employ the model characteristics of such a hybrid system a novel integral type switching function is firstly designed by adopting the e dependent stochastic lyapunov function method sufficient conditions are presented to ensure the mean square asymptotic stability of the sliding mode dynamics a mode dependent fuzzy smc law is then synthesized to induce and maintain the sliding motion despite partly unknown transition probabilities and parameter uncertainties finally the developed method is applied to stabilize a modified series dc motor system

computational aspects of discrete time optimal control our opinion is that a little known technique called differential dynamicprogramming offers the potential of enormously expanding the scale of discrete time optimal control problems which are subject to numerical solution among the attractive features of this method are that no discretization of control or state space is used the memory requirements grow as m 2 and the computational requirements as m 3 with m being the dimension of the control variable the successive approximations converge globally under lenient smoothness assumptions and the convergence is quadratic if certain convexity assumptions hold the contribution of the present paper is to demonstrate the practical merit of differential dynamic programming by reporting computational solutions to problems having as many as forty control variables and no particularly convenient structure additionally we give a more algorithmically oriented presentation of the method than hitherto available extend the basic methodto the nonconvex case and give a proof of global convergence

the stagewise kuhn tucker condition and differential dynamic programming the intention of this work is to describe and examine a differential dynamic programming ddp algorithm for constrained discrete time optimal control this algorithm has performed successfully on a large scale reservoir control problem 11 the present paper gives conditions under which convergence to the stationary policy is assured the convergence demonstration hinges upon a notion which we refer to as the stagewise kuhn tucker condition strategies generated to satisfy this condition determine policies which satisfy the conventional kuhn tucker condition this observation may be of wider importance in discrete optimal control theory for the stagewise condition might be a convenient criterion for constructing strategies

new insertion and postoptimization procedures for the traveling salesman problem this paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem the combination of the two methods results in an efficient algorithm genius which outperforms known alternative heuristics in terms of solution quality and computing time

stochastic stability and stabilization conditions of semi markovian jump systems with mode transition dependent sojourn time distributions this paper is concerned with the stochastic stability and stabilization problem for a class of continuous time semi markovian jump systems s mjss with mode transition dependent sojourn time distributions in contrast to other approaches this paper offers the possibility to explore more refined probability models on the sojourn time by considering the mode transition dependent sojourn time distributions instead of mode dependent ones here to construct a finite set of linear matrix inequalities lmis from sojourn time dependent matrix inequalities a less conservative relaxation method is proposed in such a way that all available constraints on time varying transition rates can be exploited simulation examples report the effectiveness of the proposed method

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

optimal mean variance control for discrete time linear systems with markovian jumps and multiplicative noises in this paper we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noises under two criteria the first one is an unconstrained mean variance trade off performance criterion along the time and the second one is a minimum variance criterion along the time with constraints on the expected output we present explicit conditions for the existence of an optimal control strategy for the problems generalizing previous results in the literature we conclude the paper by presenting a numerical example of a multi period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

sliding mode filter design for nonlinear polynomial systems with unmeasured states this paper addresses the mean square and mean module filtering problems for a nonlinear polynomial stochastic system with gaussian white noises the obtained solutions contain a sliding mode term signum of the innovations process it is shown that the designed sliding mode mean square filter generates the mean square estimate which has the same minimum estimation error variance as the estimate given by the conventional mean square polynomial filter basin et al 2008 8 although the gain matrices of both filters are different the designed sliding mode mean module filter generates the mean module estimate which yields a better value of the mean module criterion in comparison to the conventional mean square polynomial filter the theoretical result is complemented with an illustrative example verifying performance of the designed filters it is demonstrated that the estimates produced by the designed sliding mode mean square filter and the conventional mean square polynomial filter yield the same estimation error variance and there is an advantage in favor of the designed sliding mode mean module filter

smc design for robust stabilization of nonlinear markovian jump singular systems in this technical note the sliding mode control smc problem is investigated for t s fuzzy model based nonlinear markovian jump singular systems subject to matched unmatched uncertainties to accommodate the model characteristics of such a hybrid system a novel integral type fuzzy sliding surface is put forward by taking the singular matrix and state dependent projection matrix into account simultaneously which is the key contribution of the note the designed surface contains two important features 1 local input matrices for different subsystems in the same system mode are allowed to be different and 2 the matched uncertainties are completely compensated and the unmatched ones are not amplified during sliding motion sufficient conditions for the stochastic admissibility of the corresponding sliding mode dynamics are presented and a fuzzy smc law is constructed to ensure the reaching condition despite uncertainties the applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

extended formulations and branch and cut algorithms for the black and white traveling salesman problem in this paper we study integer linear programming models and develop branch and cut algorithms to solve the black and white traveling salesman problem bwtsp bourgeois laporte semet 2003 which is a variant of the well known traveling salesman problem tsp two strategies to model the bwtsp have been used in the literature the problem is either modeled on the original graph as tsp using a single set of binary edge variables and with additional non trivial hop and distance constraints between every pair of black nodes see ghiani laporte semat 2006 or as a sequence of constrained paths composed of white nodes connecting pairs of black nodes see muter 2015 in this paper we study and develop an intermediate approach based on the observation that it is sufficient to guarantee the required distance and hop limit of the path from a given black node to the next black node without explicitly stating which one it is thus instead of stating the two constraints after adding appropriately defined variables for each pair of black nodes they are stated for each black node only that represents the source of each path based on this idea we develop several variants of position and distance dependent reformulations together with corresponding layered graph representations branch and cut algorithms are developed for all proposed formulations and empirically compared by an extensive computational study the obtained results allow us to provide insights into individual advantages and disadvantages of the different models

a tabu search heuristic for the vehicle routing problem the purpose of this paper is to describe taburoute a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions the algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route this is done by means of a generalized insertion procedure previously developed by the authors during the course of the algorithm infeasible solutions are allowed numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics and taburoute often produces the best known solutions

the black and white traveling salesman problem the black and white traveling salesman problem bwtsp is defined on a graph g whose vertex set is partitioned into black and white vertices the aim is to design a shortest hamiltonian tour on g subject to cardinality and length constraints both the number of white vertices as well as the length of the tour between two consecutive black vertices are bounded above the bwtsp has applications in airline scheduling and in telecommunications this paper proposes an integer linear formulation for the undirected bwtsp as well as several classes of valid inequalities an exact branch and cut algorithm is then developed extensive tests show that it can solve exactly instances involving up to 100 vertices the algorithm can also be applied directly to solve unit demand vehicle routing problems of similar sizes

stability analysis of linear systems with time varying delay via intermediate polynomial based functions abstract this note is devoted to stability analysis for linear system with time varying delay by advisably introducing slack matrices novel fractional order intermediate polynomial based functions ipfs are proposed then the stability condition is derived for the time delay system from configuration on fractional order polynomials the relationships among system states are taken into account and consolidated via slack variables and the characteristics for integral inequality are synthetically considered while avoiding higher order time delays more remarkably adjusting tunable parameters also contributes to reduction of conservatism the comparisons of computational complexity and stability region on a well known numerical example are provided to validate the advantages of the resulting stability criterion

partitioned dynamic programming for optimal control parallel algorithms for the solution of linear quadratic optimal control problems are described the algorithms are based on a straightforward decomposition of the domain of the problem and are related to multiple shooting methods for two point boundary value problems their arithmetic cost is approximately twice that of the serial dynamic programming approach however they have the advantage that they can be efficiently implemented on a wide variety of parallel architectures extension to the case in which there are box constraints on the controls is simple the algorithms can be used to solve linear quadratic subproblems arising from the application of newton s method or two metric gradient projection methods to nonlinear problems

slow state variables feedback stabilization for semi markov jump systems with singular perturbations the slow state variables feedback stabilization problem for semi markov jump discrete time systems with slow sampling singular perturbations is discussed in this work a new fairly comprehensive system model semi markov jump system with singular perturbations which is more general than markov jump model is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems based on a slow state variables feedback control scheme a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated with the help of the discrete time semi markov kernel approach some sojourn time dependent and less conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed finally an illustrative example is given to show the superiority and usefulness of the proposed method

uncertain jumping systems with strong and weak functional delays this paper provides complete results on the stability behavior of a class of uncertain dynamical systems with jumping parameters and functional time delays the jumping parameters are modeled as a continuous time discrete state markov process the parametric uncertainties are norm bounded appearing in all system matrices and the delay factor depends on the mode of operation notions of weak and strong stochastic stability for the jumping system are developed depending on the available information using a prescribed h performance memoryless and delayed state feedback are considered to guarantee the closed loop stability all the results are cast into linear matrix inequalities format a numerical example is given to illustrate the developed results

technical communique input output finite time stabilization of linear systems bounded input bounded output bibo stability is usually studied when only the input output behavior of a dynamical system is of concern the present paper investigates the analogous concept in the framework of finite time stability fts namely the input output fts io fts fts has been already investigated in several papers in terms of state boundedness whereas in this work we deal with the characterization of the input output behavior sufficient conditions are given concerning the class of l 2 and l input signals for the analysis of io fts and for the design of a static state feedback controller guaranteeing io fts of the closed loop system the effectiveness of the proposed results is eventually illustrated by means of some numerical examples

a branch and cut algorithm for the symmetric generalized traveling salesman problem we consider a variant of the classical symmetric traveling salesman problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster this np hard problem is known in the literature as the symmetric generalized traveling salesman problem gtsp and finds practical applications in routing scheduling and location routing in a companion paper fischetti et al fischetti m j j salazar p toth 1995 the symmetric generalized traveling salesman polytope networks 26 113 123 we modeled gtsp as an integer linear program and studied the facial structure of two polytopes associated with the problem here we propose exact and heuristic separation procedures for some classes of facet defining inequalities which are used within a branch and cut algorithm for the exact solution of gtsp heuristic procedures are also described extensive computational results for instances taken from the literature and involving up to 442 nodes are reported

a new parallel algorithm for optimal control problems of interconnected systems parallel algorithms play a crucial role in utilizing parallel computers to overcome the difficulties of computation intensive problems this paper presents a new parallel algorithm for solving optimal control of discrete time interconnected systems the idea is to use lagrange multipliers to relax the coupling among subsystems the decomposed subproblems are solved in parallel by using the differential dynamic programming ddp method the lagrange multipliers are selected as coordinating variables and updated at the high level to ensure global optimality a method for estimating the computational complexity of the decomposition coordination approach is presented and the relationship between speed up and major system parameters is established it is shown that significant speed ups are difficult to achieve by using conventional optimization techniques at high level a large number of high level iterations may offset the reduction in computation for dealing with smaller decomposed subproblems in parallel