stabilization of a class of stochastic differential equations with markovian switching stability of stochastic differential equations with markovian switching has been studied quite extensively for a number of years for example by basak et al j math anal appl 202 1996 604 622 ji and chizeck ieee trans automat control 35 1990 777 788 mariton jump linear systems in automatic control marcel dekker new york 1990 mao et al stochastic process appl 79 1999 45 67 bernoulli 6 2000 73 90 and yuan and lygeros in r alur g pappas eds hybrid systems computation and control seventh international workshop hscc 2004 lecture notes in computer science vol 2993 springer berlin 2004 pp 646 659 by contrast the problem of designing controllers to stabilize systems of this type has received relatively little attention in this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with markovian switching

a hybrid receding horizon control scheme for nonlinear systems a hybrid receding horizon control scheme for nonlinear discrete time systems is proposed whereas a set of optimal feedback control functions is defined at the continuous level a discrete event controller chooses the best control action depending on the current conditions of a plant and on possible external events such a two level scheme is embedded in the structure of abstract hybrid systems thus making it possible to prove a new asymptotic stability result for the hybrid receding horizon control approach

on tracking control of a class of complementary slackness hybrid mechanical systems abstract in this note we consider the problem of feedback control of n dof degree of freedom rigid manipulators subject to a scalar frictionless unilateral constraint f x 0 x r n is the vector of generalized coordinates the stability analysis relies on a stability concept that incorporates the hybrid and nonsmooth dynamical feature of the overall system it is shown that stability of the closed loop system can be obtained this work generalizes the results in brogliato et al ieee trans automat control 42 2 1997 200 215 which were mainly restricted to the 1 dof case it also clarifies some concepts related to the hybrid nature of closed loop complementary slackness mechanical systems

distributive network utility maximization over time varying fading channels distributed network utility maximization num has received an increasing intensity of interest over the past few years distributed solutions e g the primal dual gradient method have been intensively investigated under fading channels as such distributed solutions involve iterative updating and explicit message passing it is unrealistic to assume that the wireless channel remains unchanged during the iterations unfortunately the behavior of those distributed solutions under time varying channels is in general unknown in this paper we shall investigate the convergence behavior and tracking errors of the iterative primal dual scaled gradient algorithm pdsga with dynamic scaling matrices dsc for solving distributive num problems under time varying fading channels we shall also study a specific application example namely the multicommodity flow control and multicarrier power allocation problem in multihop ad hoc networks our analysis shows that the pdsga converges to a limit region rather than a single point under the finite state markov chain fsmc fading channels we also show that the order of growth of the tracking errors is given by o t n where t and n are the update interval and the average sojourn time of the fsmc respectively based on this analysis we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices which can be implemented distributively at each transmitter the numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes such as the regular primal dual gradient algorithm

necessary conditions of asymptotic stability for unilateral dynamical systems in this paper we develop a mathematical tool that can be used to state necessary conditions of asymptotic stability of isolated stationary solutions of a class of unilateral dynamical systems more precisely nonlinear evolution variational inequalities are considered instability criteria are also given applications can be found in mechanics or electrical circuits

an approach for finding the most preferred alternative in the presence of multiple criteria abstract an interactive approach for discrete multiple criteria decision making problems is developed the approach requires the decision maker to compare pairs of presented alternatives these alternatives may be existing alternatives or dummy alternatives created from existing alternatives inferior alternatives are sequentially eliminated by either using the responses of the decision maker directly or by constructing cones of inferior solutions based on these responses the approach converges to the most preferred solution so long as the decision maker has a nondecreasing quasiconcave value function the aim is to keep the number of pairwise comparisons required of the decision maker as small as possible computational experience on randomly generated problems is reported and the results are compared with the results of similar approaches

hybrid static output feedback stabilization of second order linear time invariant systems for second order linear time invariant lti systems which are not stabilizable via a single static output feedback we study the open problem whether there exists a finite state hybrid static output feedback to asymptotically stabilize the system we show that the answer to this question is affirmative for a class of second order lti systems by constructing a 2 state static output feedback incorporated with a conic switching law

consistency of finite systems of convex inequalities we give necessary and sufficient conditions for the existence of a convex functionu which satisfies a finite list of inequalities of the typeu a u b oru a u b wherea b are finite dimensional vectors

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

solving the discrete multiple criteria problem using linear prospect theory abstract prospect theory developed by kahneman and tversky is a popular model of choice in decision problems under uncertainty prospect theory has recently been extended to multiple criteria choice problems in this paper an interactive method for solving discrete multiple criteria decision problems based on prospect theory type value functions has been developed piecewise linear marginal value functions are assumed to approximate the s shaped value functions of prospect theory therefore the proposed procedure is valid only for convex preferences

some qualitative properties of sampled data control systems the authors consider sampled data control systems which consist of an interconnection of a continuous time nonlinear plant and a digital controller which has quantizers but is otherwise linear along with the required interface elements a d and d a converters in the present paper the authors study the qualitative effects of the quantizers and the plant nonlinearities of these systems

synchronization of impacting mechanical systems with a single constraint abstract this paper addresses the synchronization problem of mechanical systems subjected to a single geometric unilateral constraint the impacts of the individual systems induced by the unilateral constraint generally do not coincide even if the solutions are arbitrarily close to each other the mismatch in the impact time instants demands a careful choice of the distance function to allow for an intuitively correct comparison of the discontinuous solutions resulting from the impacts we propose a distance function induced by the quotient metric which is based on an equivalence relation using the impact map the distance function obtained in this way is continuous in time when evaluated along jumping solutions the property of maximal monotonicity which is fulfilled by most commonly used impact laws is used to significantly reduce the complexity of the distance function based on the simplified distance function a lyapunov function is constructed to investigate the synchronization problem for two identical one dimensional mechanical systems sufficient conditions for the uncoupled individual systems are provided under which local synchronization is guaranteed furthermore we present an interaction law which ensures global synchronization also in the presence of grazing trajectories and accumulation points zeno behavior the results are illustrated using numerical examples of a 1 dof mechanical impact oscillator which serves as stepping stone in the direction of more general systems

stability of discontinuous retarded functional differential equations with applications we present lyapunov stability results including converse theorems for a class of discontinuous dynamical systems dds determined by the solutions of retarded functional differential equations we demonstrate the applicability of these results in the analysis of several specific important classes of dds determined by functional differential equations and differential difference equations

solutions to hybrid inclusions via set and graphical convergence with stability theory applications motivated by questions in stability theory for hybrid dynamical systems we establish some fundamental properties of the set of solutions to such systems using the notion of a hybrid time domain and general results on set and graphical convergence we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and upper semicontinuous with respect to initial conditions and system perturbations the general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets these results parallel what is already known for differential inclusions and difference inclusions for example the basin of attraction for a compact attractor is relatively open the attractivity is uniform from compact subsets of the basin of attraction and asymptotic stability is robust with respect to small perturbations

a rank based approach to the sequential selection and assignment problem abstract in the classical sequential assignment problem machines are to be allocated sequentially to jobs so as to maximize the expected total return where the return from an allocation of job j to machine k is the product of the value xj of the job and the weight pk of the machine the set of m machines and their weights are given ahead of time but n jobs arrive in sequential order and their values are usually treated as independent identically distributed random variables from a known univariate probability distribution with known parameter values in the paper we consider a rank based version of the sequential selection and assignment problem that minimizes the sum of weighted ranks of jobs and machines the so called secretary problem is shown to be a special case of our sequential assignment problem i e m 1 due to its distribution free property our rank based assignment strategy can be successfully applied to various managerial decision problems such as machine scheduling job interview kidney allocations for transplant and emergency evacuation plan of patients in a mass casualty situation

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

an interactive evolutionary multi objective optimization algorithm with a limited number of decision maker calls this paper presents a preference based method to handle optimization problems with multiple objectives with an increase in the number of objectives the computational cost in solving a multi objective optimization problem rises exponentially and it becomes increasingly difficult for evolutionary multi objective techniques to produce the entire pareto optimal front in this paper an evolutionary multi objective procedure is combined with preference information from the decision maker during the intermediate stages of the algorithm leading to the most preferred point the proposed approach is different from the existing approaches as it tries to find the most preferred point with a limited budget of decision maker calls in this paper we incorporate the idea into a progressively interactive technique based on polyhedral cones the idea is also tested on another progressively interactive approach based on value functions results are provided on two to five objective unconstrained as well as constrained test problems

stability and instability matrices for linear evolution variational inequalities this paper deals with the characterization of the stability and instability matrices for a class of unilaterally constrained dynamical systems represented as linear evolution variational inequalities levi such systems can also be seen as a sort of differential inclusion or in special cases as linear complementarity systems which in turn are a class of hybrid dynamical systems examples show that the stability of the unconstrained system and that of the constrained system may drastically differ various criteria are proposed to characterize the stability or the instability of levi

invariance principles for hybrid systems with connections to detectability and asymptotic stability this paper shows several versions of the lasalle s invariance principle for general hybrid systems the broad framework allows for nonuniqueness of solutions zeno behaviors and does not insist on continuous dependence of solutions on initial conditions instead only a mild structural property involving graphical convergence of solutions is posed the general invariance results are then specified to hybrid systems given by set valued data further results involving invariance as well as observability detectability and asymptotic stability are given

passivity and stability of switched systems a multiple storage function method this paper presents a concept of passivity for switched systems using multiple storage functions this passivity property is invariant under compatible feedback interconnection branicky s stability theorem of multiple lyapunov functions is generalized by relaxing the non increasing condition on values of lyapunov like functions using this result we show that a passive switched system is stable in the sense of lyapunov moreover asymptotic stability is reached if all subsystems are asymptotically detectable

tracking control for hybrid systems with state triggered jumps this paper addresses the tracking problem in which the controller should stabilize time varying reference trajectories of hybrid systems despite the fact that discrete events or jumps in hybrid systems can often not be controlled directly as e g is the case in impacting mechanical systems the controller should still stabilize the desired trajectory a major complication in the analysis of this hybrid tracking problem is that in general the jump times of the plant do not coincide with those of the reference trajectory consequently the conventional euclidean tracking error does not converge to zero even if trajectories converge to the reference trajectory in between jumps and the jump times converge to those of the reference trajectory hence standard control approaches can not be applied we propose a novel definition of the tracking error that overcomes this problem and formulate lyapunov based conditions for the global asymptotic stability of the hybrid reference trajectory using these conditions we design hysteresis based controllers that solve the hybrid tracking problem for two exemplary systems including the well known bouncing ball problem

the impact of stochastic noisy feedback on distributed network utility maximization the implementation of distributed network utility maximization num algorithms hinges heavily on information feedback through message passing among network elements in practical systems the feedback is often obtained using error prone measurement mechanisms and suffers from random errors in this paper we investigate the impact of noisy feedback on distributed num we first study the distributed num algorithms based on the lagrangian dual method and focus on the primal dual p d algorithm which is a single time scale algorithm in the sense that the primal and dual parameters are updated simultaneously assuming strong duality we study both cases when the stochastic gradients are unbiased or biased and develop a general theory on the stochastic stability of the p d algorithms in the presence of noisy feedback when the gradient estimators are unbiased we establish via a combination of tools in martingale theory and convex analysis that the iterates generated by distributed p d algorithms converge with probability one to the optimal point under standard technical conditions in contrast when the gradient estimators are biased we show that the iterates converge to a contraction region around the optimal point provided that the biased terms are asymptotically bounded by a scaled version of the true gradients we also investigate the rate of convergence for the unbiased case and find that in general the limit process of the interpolated process corresponding to the normalized iterate sequence is a stationary reflected linear diffusion process not necessarily a gaussian diffusion process we apply the above general theory to investigate stability of cross layer rate control for joint congestion control and random access next we study the impact of noisy feedback on distributed two time scale num algorithms based on primal decomposition we establish via the mean ode method the convergence of the stochastic two time scale algorithm under mild conditions for the cases where the gradient estimators in both time scales are unbiased numerical examples are used to illustrate the finding that compared to the single time scale counterpart the two time scale algorithm although having lower complexity is less robust to noisy feedback

further developments and tests of a progressive algorithm for multiple criteria decision making p korhonen h moskowitz and j wallenius 1986 developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives a special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker s dm s preference structure or value function the algorithm is based on progressively sampling the decision space obtaining preference information from the dm determining the likelihood of finding possibly surely better alternatives and based on this information continuing the search or terminating it by making the final choice we describe a computerized implementation and extensive computational tests of the algorithm as well as some of our experiences in applying and field testing it in practice we also consider several improvements and developments of the algorithm to further facilitate its use in practice

cut a multicriteria approach for concavifiable preferences we consider the problem of helping a decision maker dm choose from a set of multiattributed objects when her preferences are concavifiable i e representable by a concave value function we establish conditions under which preferences or preference intensities are concavifiable we also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the dm this can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure we report on the practical use of this procedure with several dms for a flat choice problem and its computational performance on a set of project portfolio selection problem instances the use of preference intensities is found to provide significant improvements to the performance of the procedure

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

dynamical properties of hybrid systems simulators this paper analyzes the dynamical properties of a class of hybrid systems simulators a hybrid system is a dynamical system with a state that can both flow and jump its simulator attempts to generate its solutions approximately the paper presents mild regularity conditions on the hybrid system and its simulator to guarantee that simulated solutions are close to actual solutions on compact hybrid time intervals and that asymptotically stable compact sets are preserved in a semiglobal practical sense under simulation in fact it is established that asymptotically stable compact sets are continuous in the integration step size parameter of the simulator that is as the step size of the simulator converges to zero the asymptotically stable set observed in simulations approaches the asymptotically stable compact set of the true hybrid system examples are used to illustrate concepts and results

multi attribute sequential decision problem with optimizing and satisficing attributes abstract we deal with the multi attribute decision problem with sequentially presented decision alternatives our decision model is based on the assumption that the decision maker has a major attribute that must be optimized and minor attributes that must be satisficed in the vendor selection problem for example the product price could be the major factor that should be optimized while the product quality and delivery time could be the minor factors that should satisfy certain aspiration levels we first derive the optimal selection strategy for the discrete time case in which one alternative is presented at each time period the discrete time model is then extended to the continuous time case in which alternatives are presented sequentially at random times a numerical example is used to analyze the effects of the satisficing condition and the uncertainty on the optimal selection strategy

existence uniqueness and stability of stochastic neutral functional differential equations of sobolev type in this paper we are mainly concerned with a class of stochastic neutral functional differential equations of sobolev type with poisson jumps under two different sets of conditions we establish the existence of the mild solution by applying the leray schauder alternative theory and the sadakovskii s fixed point theorem respectively furthermore we use the bihari s inequality to prove the osgood type uniqueness also the mean square exponential stability is investigated by applying the gronwall inequality finally two examples are given to illustrate the theory results

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

on the control of uncertain impulsive systems approximate stabilization and controlled invariance the problems of stabilization and controlled invariance of a fairly wide class of uncertain hybrid systems is considered uncertainty enters in the form of a disturbance input that can affect both the continuous and the discrete dynamics a method for designing piecewise constant feedback controllers for this class of systems is developed in the case of controlled invariance the controller ensures that the state of the system remains arbitrarily close to a desired set over an arbitrarily long time horizon in the case of stabilization the controller ensures approximate exponential convergence of the runs of the closed loop system to the zero level set of a lyapunov function

asymptotic stability and boundedness of delay switching diffusions multiple lyapunov functions are used to establish sufficient conditions for locating the limit sets of switching diffusions the conditions lead to a number of useful results on stochastic asymptotic stability and boundedness for this class of stochastic hybrid systems

a note on the stability of bimodal systems in with discontinuous vector fields this paper presents the necessary and sufficient conditions for global asymptotic stability of a class of bimodal piecewise linear systems in r3 the approach being used allows the vector field to be discontinuous on the switching plane it is shown that the discontinuity of the vector field plays a crucial role in global asymptotic stability this point is illustrated by examples where the change in the discontinuity of the vector field without changing the eigenvalues of subsystems can cause the system to be globally asymptotically stable or unstable

stability of primal dual gradient dynamics and applications to network optimization this paper considers dynamic laws that seek a saddle point of a function of two vector variables by moving each in the direction of the corresponding partial gradient this method has old roots in the classical work of arrow hurwicz and uzawa on convex optimization and has seen renewed interest with its recent application to resource allocation in communication networks this paper brings other tools to bear on this problem in particular krasovskii s method to find lyapunov functions and recently obtained extensions of the lasalle invariance principle for hybrid systems these methods are used to obtain stability proofs of these primal dual laws in different scenarios and applications to cross layer network optimization are exhibited

stability analysis of discontinuous dynamical systems determined by semigroups we present lyapunov stability results for discontinuous dynamical systems dds determined by linear and nonlinear semigroups defined on banach space dds of the type considered herein arise in the modeling of a variety of finite and infinite dimensional systems including certain classes of hybrid systems discrete event systems switched systems systems subjected to impulse effects and the like we apply our results in the analysis of several important specific classes of dds

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

robust stability analysis of nonlinear hybrid systems we present a methodology for robust stability analysis of nonlinear hybrid systems through the algorithmic construction of polynomial and piecewise polynomial lyapunov like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials several improvements compared to previous approaches are discussed such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems

a parallel decomposition method for nonconvex stochastic multi agent optimization problems this paper considers the problem of minimizing the expected value of a possibly nonconvex cost function parameterized by a random vector variable when the expectation cannot be computed accurately e g because the statistics of the random variables are unknown and or the computational complexity is prohibitive classical stochastic gradient methods for solving this problem may suffer from slow convergence in this paper we propose a stochastic parallel successive convex approximation based best response algorithm for general nonconvex stochastic sum utility optimization problems which arise naturally in the design of multi agent networks the proposed novel decomposition approach enables all users to update their optimization variables in parallel by solving a sequence of strongly convex subproblems one for each user almost sure convergence to stationary points is proved we then customize the algorithmic framework to solve the stochastic sum rate maximization problem over single input single output siso frequency selective interference channels multiple input multiple output mimo interference channels and mimo multiple access channels numerical results corroborate that the proposed algorithms can converge faster than state of the art stochastic gradient schemes while achieving the same or better sum rates

smooth lyapunov functions for hybrid systems part i existence is equivalent to robustness hybrid systems are dynamical systems where the state is allowed to either evolve continuously flow on certain subsets of the state space or evolve discontinuously jump from other subsets of the state space for a broad class of such systems characterized by mild regularity conditions on the data we establish the equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth lyapunov function this result unifies and generalizes previous results for differential and difference inclusions with outer semicontinuous and locally bounded right hand sides furthermore we give a description of forward completeness of a hybrid system in terms of a smooth lyapunov like function

distributed nash equilibrium seeking this paper presents an asynchronous gossip based algorithm for finding a nash equilibrium ne of a game in a distributed multi player network the algorithm is designed in such a way that players make decisions based on estimates of the other players actions obtained from local neighbors using a set of standard assumptions on the cost functions and communication graph the paper proves almost sure convergence to a ne for diminishing step sizes for constant step sizes an error bound on expected distance from a ne is established the effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes

testing the efficiency of pairwise comparison methods in discrete multiple criteria problems we test the efficiency of two pairwise comparison methods the methods studied are salminen s piecewise linear prospect theory plp method and the convex cone method by korhonen wallenius and zionts kwz the plp method is based on a piecewise linear difference function the kwz method assumes a quasi concave utility or value function these methods are tested using randomly generated data sets with 50 100 150 and 200 alternatives and from 2 up to 6 criteria the dm s preference statements are simulated using linear quadratic and chebycheff value functions and piecewise linear difference functions both methods lose their efficiency very rapidly with increasing number of criteria our results indicate that pairwise comparison methods are not as efficient as reported in literature

asymptotic behavior of internet congestion controllers in a many flows regime congestion controllers for the internet are typically designed based on deterministic delay differential equation models in this paper we consider the case of a single link accessed by many tcp like congestion controlled flows and uncontrolled flows that are modeled as stochastic disturbances we show that if the number of flows is large and the link capacity is scaled in proportion to the number of users then under appropriate conditions the trajectory of the stochastic system is eventually well approximated by the trajectory of a delay differential equation our analysis also throws light on the choice of various parameters that ensureglobal asymptotic stability of the limiting deterministic system in the presence of feedback delay numerical examples with some popular congestion feedback mechanisms validate the parameter choices from the analysis the results indicate that a system with multiple tcp like flows is globally stable and thus that a deterministic model is reasonable if the number of flows is large as long asthe product of the throughput and feedback delay per flow is not very small

interactive approaches for discrete alternative multiple criteria decision making with monotone utility functions in this paper we develop interactive approaches for the discrete alternative multiple criteria decision making problem we develop an algorithm that finds the most preferred alternative of a decision maker dm assuming only that the dm has a monotonic utility function the algorithm divides the criteria space into a number of smaller subspaces and then uses the ideal points of these subspaces to eliminate alternatives we also develop a more efficient version of the algorithm for the more restrictive case of a monotonic quasiconcave utility function we present favorable computational results in terms of the required number of pairwise comparisons for both versions of the algorithm we then develop a general algorithm that first identifies the type of the dm s utility function and then employs the approach that is compatible with the identified utility function type we also present computational results for the general algorithm

a bi reference procedure for interactive multiple criteria programming the paper presents an interactive procedure to search the set of nondominated outcomes of a multiple criteria linear programming problem the procedure requires the decision maker to specify the worst outcome then the ideal outcome is identified and the improvement direction from the worst to ideal outcomes is constructed a trial solution is found by moving from a current solution along the improvement direction while maximizing the step size for a trial solution the decision maker is requested to partition the set of objective functions into three categories those to be improved those which may remain unchanged those which may be relaxed based on this partition the procedure displaces the worst and ideal outcomes calculates the new improvement direction and the entire process is repeated the method terminates when two successive trial solutions are reasonably similar

stability tests and stabilization for piecewise linear systems based on poles and zeros of subsystems this paper provides several stability tests for piecewise linear systems and proposes a method of stabilization for bimodal systems in particular we derive an explicit and exact stability test for planar systems which is given in terms of coefficients of transfer functions of subsystems restricting attention to the bimodal and planar case we show simple stability tests in addition we drive a necessary stability condition and a sufficient stability condition for higher order and bimodal systems they are given in terms of the eigenvalue loci and the observability of subsystems all the stability tests provided in this paper are computationally tractable and our results are applied to the stabilizability problem we confirm the exactness and effectiveness of our approach by illustrative examples

a progressive algorithm for modeling and solving multiple criteria decision problems we consider a decision maker dm who has a set of possible decision alternatives from which one a best is to be chosen however all decision alternatives are not at the dm s disposal initially nor is full knowledge of his her utility value function therefore the dm evaluates only the available subset of all decision alternatives from which he she chooses a most preferred one obviously this decision is not necessarily globally best two natural questions arise how good is the most preferred solution what are the chances of finding better solutions by considering additional alternatives we describe and illustrate a general progressive algorithm and the supporting theory for modeling and solving this problem when alternatives are introduced dynamically

lyapunov stability of complementarity and extended systems a linear complementarity system lcs is a piecewise linear dynamical system consisting of a linear time invariant ordinary differential equation ode parameterized by an algebraic variable that is required to be a solution to a finite dimensional linear complementarity problem lcp whose constant vector is a linear function of the differential variable continuing the authors recent investigation of the lcs from the combined point of view of system theory and mathematical programming this paper addresses the important system theoretic properties of exponential and asymptotic stability for an lcs with a c 1 state trajectory the novelty of our approach lies in our employment of a quadratic lyapunov function that involves the auxiliary algebraic variable of the lcs when expressed in the state variable alone the lyapunov function is piecewise quadratic and thus nonsmooth the nonsmoothness feature invalidates standard stability analysis that is based on smooth lyapunov functions in addition to providing sufficient conditions for exponential stability we establish a generalization of the well known lasalle invariance theorem for the asymptotic stability of a smooth dynamical system to the lcs which is intrinsically a nonsmooth system sufficient matrix theoretic copositivity conditions are introduced to facilitate the verification of the stability properties properly specialized the latter conditions are satisfied by a passive like lcs and certain hybrid linear systems having common quadratic lyapunov functions we provide numerical examples to illustrate the stability results we also develop an extended local exponential stability theory for nonlinear complementarity systems and differential variational inequalities based on a new converse theorem for odes with b differentiable right hand sides the latter theorem asserts that the existence of a b differentiable lyapunov function is a necessary and sufficient condition for the exponential stability of an equilibrium of such a differential system

stability preserving mappings for stochastic dynamical systems we first formulate a general model for stochastic dynamical systems that is suitable in the stability analysis of invariant sets this model is sufficiently general to include as special cases most of the stochastic systems considered in the literature we then adapt several existing stability concepts to this model and we introduce the notion of stability preserving mapping of stochastic dynamical systems next we establish a result which ensures that a function is a stability preserving mapping and we use this result in proving a comparison stability theorem for general stochastic dynamical systems we apply the comparison stability theorem in the stability analysis of dynamical systems determined by ito differential equations

stability of markov modulated discrete time dynamic systems motivated by various control applications this paper develops stability analysis of discrete time systems with regime switching in which the dynamics are modulated by markov chains with two time scales using the high contrast of the different transition rates among the markovian states singularly perturbed markov chains are used in the formulations taking into consideration of the regime changes and time scale separation makes the stability analysis a difficult task in this work asymptotic stability analysis is carried out using perturbed liapunov function techniques it is demonstrated that if the limit system is stable then the original system is also stable in addition we examine path excursion derive bounds on mean recurrence time and obtain the associated probability bounds

analysis of adaptive step size sa algorithms for parameter tracking we present proofs and data for adaptive step size algorithms for tracking time varying parameters when recursive stochastic approximation type algorithms are used a classical problem in adaptive control and communication theory concerns the tracking of the best fit of a given form when the statistics or the parameters change slowly a major and yet unresolved problem has been the choice of the step sizes in the tracking algorithm an algorithm for adapting the step size using the same system measurements which are used for the tracking was suggested by benveniste and various examples worked out by brossier the numerical results were very encouraging but proofs were lacking these proofs are supplied here together with supporting numerical data the proofs are based on recent results in stochastic approximation the adaptive step size technique works very well indeed much supporting analysis is presented particularly concerning the interpretation of certain stationary processes as stationary pathwise derivatives finite difference forms are also treated these are mathematically simpler and can be applied to a wide variety of systems even when the system is not well modeled the data shows that they work well

semistability theory for spatially distributed systems abstract the concepts of semistability and exponential semistability are well developed for finite dimensional systems with nonisolated equilibrium points where asymptotic or exponential stability is not possible definitions of semistability and exponential semistability have recently been formulated for networks with time delays this paper further extends the semistability theory to continuous and discrete spatially distributed systems this requires the definition of the notions of exact and approximate semicontrollability and semiobservability and discrete approximate semicontrollability and semiobservability also introduced is the property of weak semistability necessary and sufficient conditions are given for exponential semistability and weak semistability and sufficient conditions are given for semistability

on optimal control problems of a class of impulsive switching systems with terminal states constraints abstract the global optimal control problem is proposed for a special class of hybrid dynamical systems i e impulsive switching systems then the necessary condition of the above problem the minimum principle is given ekeland s variational principle and the matrix cost functional structure expression are utilized in the process of the proof based on the main result a special linear hybrid impulsive and switching system hiss is illustrated and the optimal control algorithm is presented moreover the cases of pure impulsive systems and pure switched systems are included in this paper

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

hybrid feedback control and robust stabilization of nonlinear systems in this paper we show for any nonlinear system that is asymptotically controllable to a compact set that a logic based hybrid feedback can achieve asymptotic stabilization that is robust to small measurement noise actuator error and external disturbance the construction of such a feedback hinges upon recasting a stabilizing patchy feedback in a hybrid framework by making it dynamic with a discrete state while insisting on semicontinuity and closedness properties of the hybrid feedback and of the resulting closed loop hybrid system the robustness of stability is then shown as a generic property of hybrid systems having the said regularity properties auxiliary results give uniformity of convergence and of overshoots for hybrid systems and give a characterization of asymptotic stability of compact sets

rate of convergence for constrained stochastic approximation algorithms there is a large literature on the rate of convergence problem for general unconstrained stochastic approximations typically one centers the iterate theta n about the limit point bar theta and then normalizes by dividing by the square root of the step size epsilon n then some type of convergence in distribution or weak convergence of un the centered and normalized iterate is proved for example one proves that the interpolated process formed by the un converges weakly to a stationary gaussian diffusion and the variance of the stationary measure is taken to be a measure of the rate of convergence see the references in a benveniste m metivier and p priouret adaptive algorithms and stochastic approximation springer verlag berlin new york 1990 l gerencer siam j control optim 30 1992 pp 1200 1227 h j kushner and d s clark stochastic approximation for constrained and unconstrained systems springer verlag berlin new york 1978 h j kushner and g yin stochastic approximation algorithms and applications springer verlag berlin new york 1997 m t wasan stochastic approximation cambridge university press cambridge uk 1969 for algorithms where the step size either goes to zero or is small and constant large deviations provide an alternative approach to the rate of convergence problem p dupuis and h j kushner siam j control optim 23 1985 pp 675 696 p dupuis and h j kushner siam j control optim 27 1989 pp 1108 1135 p dupuis and h j kushner probab theory related fields 75 1987 pp 223 244 a p korostelev stochastic recurrent processes nauka moscow 1984 h j kushner and g yin stochastic approximation algorithms and applications springer verlag berlin new york 1997 when the iterates of the algorithm are constrained to lie in some bounded set the limit point is frequently on the boundary with the exception of the large deviations type p dupuis and h j kushner siam j control optim 23 1985 pp 675 696 p dupuis and h j kushner probab theory related fields 75 1987 pp 223 244 the rate of convergence literature is essentially confined to the case where the limit point is not on a constraint boundary when the limit point is on the boundary of the constraint set the usual steps are hard to carry out in particular the stability methods which are used to prove tightness of the normalized iterates cannot be carried over in general and there is the problem of proving tightness of the normalized process and characterizing the limit process this paper develops the necessary techniques and shows that the stationary gaussian diffusion is replaced by an appropriate stationary reflected linear diffusion whose variance plays the same role as a measure of the rate of convergence an application to constrained function minimization under inequality constraints q i x le 0 i le p is given where both the objective function and the constraints are observed in the presence of noise the iteration is on both the basic state variable and a lagrange multiplier which is constrained to be nonnegative if a limit multiplier value for an active constraint is zero then the classical method for computing the rate cannot be used but under appropriate conditions it is a special case of our results rate of convergence results are important because among other reasons they immediately yield the advantages of iterate averaging methods as noted in h j kushner and g yin stochastic approximation algorithms and applications springer verlag berlin new york 1997

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

exponential stability of switched linear hyperbolic initial boundary value problems we consider the initial boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes the switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time we show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching we also provide an explicit dwell time bound for guaranteeing exponential stability of the switching system when for each mode the system is exponentially stable our stability conditions only depend on the system parameters and boundary data these conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption we present tutorial examples to illustrate the instabilities that can result from switching

stability of discontinuous cauchy problems in banach space abstract we present lyapunov stability results including converse theorems for a class of discontinuous dynamical systems dds determined by differential equations in banach space or cauchy problems on abstract spaces we demonstrate the applicability of our results in the analysis of several important classes of dds including systems determined by functional differential equations volterra integro differential equations and partial differential equations

boundary observer based control for hyperbolic pde ode cascade systems with stochastic jumps abstract this work is concerned with the boundary observer based control for a category of cascade systems with stochastic jumps the cascade system consists of ordinary differential equations odes entering the hyperbolic partial differential equations pdes through the boundary a continuous time discrete state homogeneous markov process models the jumping parameters of the system and its right continuous trajectory candidate values are taken from a finite set a boundary observer is designed which relies only on limited quantity of sensors at the boundary of the pdes based on the lyapunov functional approach the observer error system is firstly proved to be exponentially mean square stable then the controller is presented by utilizing the estimated states of the odes as feedback variables the evolution profiles of the pdes in the closed loop are proved to be exponentially mean square stable at the desired steady state the existence conditions of the boundary observer and the stability conditions of the pdes in the closed loop form are presented via a set of compact space varying linear matrix inequalities svlmis the svlmis are then approximated by a finite number of lmis which guarantee the svlmis and the computational cost is reduced greatly finally the obtained theoretical results are applied to a traffic flow control system which confirms that the proposed estimation and control methods are effective

simplex methods for nonlinear uncertain sliding mode control we develop a new analysis of the behavior of simplex control methods applied to multiple input multiple output nonlinear control systems under uncertainties according to such sliding mode control methods the control vector is constrained to belong to a finite set of fixed or varying vectors with an appropriate switching logic to guarantee the specified sliding condition bounded uncertainties acting on the nominal system are allowed the proposed sliding control methodology relies on the knowledge of the nominal system only we prove rigorously the convergence of these methods to the sliding manifold in a finite time under explicit quantitative conditions on the system parameters and the available bounds of the uncertainty application to a robotic problem is discussed and a nonlinear example is presented