finite horizon ℋ 2 ℋ control for a class of nonlinear markovian jump systems with probabilistic sensor failures this article is concerned with the mixed 2 control problem over a finite horizon for a class of nonlinear markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures the stochastic nonlinearities described by statistical means could cover several types of well studied nonlinearities and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval the purpose of the addressed problem is to design state feedback controllers such that the closed loop system achieves the expected 2 performance requirement with a guaranteed disturbance attenuation level the solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations the controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations a numerical example is given to illustrate the effectiveness and applicability of the proposed al

caratheodory toeplitz and nehari problems for matrix valued almost periodic functions in this paper the positive and strictly contractive extension problems for almost periodic matrix functions are treated we present nece ssary and sufficient conditions for the existence of extensions in terms of toeplit z and hankel operators on besicovitch spaces and lebesgue spaces furthermore when a solution exists a special extension the band extension is constructed which enjoys a maximum entropy property a linear fractional parameterization of the set of all extensions is also provided the techniques used xn the proofs include factorizations of matrix valued almost periodic functions and a general algebraic scheme called the band method

stochastic h2 h control with x u v dependent noise finite horizon case in this paper the finite horizon mixed h 2 h control problem is studied for the systems governed by ito type nonlinear stochastic differential equations with state control and external disturbance dependent noise it is shown that the mixed h 2 h control under consideration is associated with the four cross coupled hamilton jacobi equations a discrete approximation algorithm is presented for solving the coupled generalized differential riccati equations arising from linear stochastic h 2 h control a necessary condition and a sufficient condition for the existence of the finite horizon stochastic h 2 h control are derived in particular some previous results on deterministic and stochastic h 2 h control can be viewed as corollaries of our main theorems

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

matroids are immune to braess paradox the famous braess paradox describes the counterintuitive phenomenon in which in certain settings an increase of resources such as a new road built within a congested network may in fact lead to larger costs for the players in an equilibrium in this paper we consider general nonatomic congestion games and give a characterization of the combinatorial property of strategy spaces for which the braess paradox does not occur in short matroid bases are precisely the required structure we prove this characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

hankel integral operators and isometric interpolants on the line abstract the problem of finding an m n continuous isometric matrix valued function with entries from the wiener algebra on the line and with prespecified fourier inverse transform on the half line is studied conditions for existence uniqueness and formulas for the solution of this problem are presented connections are made between the positive factorization indices of certain solutions to this problem and the dimensions of the kernels of hankel operators based on the prespecified data alluded to above the paper uses techniques and results developed in an earlier study of an interpolation problem on the circle the main theorems are in fact continuous analogues of the latter

mixed nash equilibria in selfish routing problems with dynamic constraints we study the problem of routing traffic through a congested network consisting of m parallel links each having a certain speed moreover we are given n selfish non cooperative agents each of them willing to route her own piece of traffic on exactly one link agents are selfish in that they only pick a link which minimize the delay of their own piece of traffic in this context much effort has been lavished in the framework of mixed nash equilibria where the agent s routing choices are regulated by probability distributions one for each agent which let the system thus enter a steady state from which no agent is willing to unilaterally deviate in this work we consider situations in which some agents have constraints on the routing choice in a sense they are forbidden to route their traffic on some links we show that at most one nash equilibrium may exist and in some cases with equal speed links and where each agent is forbidden to route on at most one link we give necessary and sufficient conditions on its existence these conditions correlate the traffic load of the agents we consider also a dynamic behaviour of the network when the constraints may vary in particular when a constraint is removed we establish under which conditions the network is still in equilibrium these conditions are all effective in the sense that given a set of yes no routing constraints on each link for each agent we provide the probability distributions corresponding to the unique nash equilibrium associated to the constraints if it exists moreover these conditions and the possible nash equilibrium are computed in time o mn

a complete parameterization of all positive rational extensions of a covariance sequence in this paper we formalize the observation that filtering and interpolation induce complementary or dual decompositions of the space of positive real rational functions of degree less than or equal to n from this basic result about the geometry of the space of positive real functions we are able to deduce two complementary sets of conclusions about positive rational extensions of a given partial covariance sequence on the one hand by viewing a certain fast filtering algorithm as a nonlinear dynamical system defined on this space we are able to develop estimates on the asymptotic behavior of the schur parameters 1918 of positive rational extensions on the other hand we are also able to provide a characterization of all positive rational extensions of a given partial covariance sequence indeed motivated by its application to signal processing speech processing and stochastic realization theory this characterization is in terms of a complete parameterization using familiar objects from systems theory and proves a conjecture made by georgiou 1983 1987 our basic result however also enables us to analyze the robustness of this parameterization with respect to variations in the problem data the methodology employed is a combination of complex analysis geometry linear systems and nonlinear dynamics

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

a minority game with bounded recall this paper studies a repeated minority game with public signals symmetric bounded recall and pure strategies we investigate both public and private equilibria of the game with fixed recall size we first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de bruijn graph then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases we also show that private equilibria behave badly a private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff

factorization and approximation problems for matrix functions the purpose of this paper is to develop a new approach to certain approximation and factorization problems for matrix valued functions the approach is based on studying properties of maximizing vectors of hankel operators with matrix valued symbols and on the solution of the so called recovery problem for unitary valued matrix functions in the case of scalar functions such problems were studied in detail in pk it turns out however that the case of matrix functions is considerably more complicated than the scalar case in this paper we solve the recovery problem with the help of hankel operators this solution also allows us to give a new approach to wiener hopf factorization problems and obtain some new results another application we consider here is the problem of finding a superoptimal analytic approximation to a matrix function on the unit circle we improve earlier results on hereditary properties of such approximations see py1 and on continuity properties of the operator of superoptimal approximation see py3 recall that for a bounded m x n matrix function b on the unit circle tf the hankel operator hp is defined on the hardy class h2 cn of cn valued functions by hdf padf f e h cn

a risk sensitive maximum principle the case of imperfect state observation the risk sensitive maximum principle for optimal stochastic control derived by the author in an earlier work system control letters vol 15 1990 is restated this is an immediate generalization of the classic pontryagin principle to which it reduces in the deterministic case and is expressed immediately in terms of observables it is derived on the assumption that the criterion function is the exponential of an additive cost function and is exact under linear quadratic gaussian assumptions but is otherwise valid as a large deviation approximation the principle is extended to the case of imperfect state observation after preliminary establishment of a certainty equivalence principle the derivation yields as byproduct a large deviation version of the updating equation for nonlinear filtering the development is heuristic it is believed that the mathematical arguments given are the essential ones and provide a self contained treatment at this level

the uniqueness property for networks with several origin destination pairs abstract we consider congestion games on networks with nonatomic users and user specific costs we are interested in the uniqueness property defined by milchtaich 2005 as the uniqueness of equilibrium flows for all assignments of strictly increasing cost functions he settled the case with two terminal networks as a corollary of his result it is possible to prove that some other networks have the uniqueness property as well by adding common fictitious origin and destination in the present work we find a necessary condition for networks with several origin destination pairs to have the uniqueness property in terms of excluded minors or subgraphs as a key result we characterize completely bidirectional rings for which the uniqueness property holds it holds precisely for nine networks and those obtained from them by elementary operations for other bidirectional rings we exhibit affine cost functions yielding to two distinct equilibrium flows related results are also proven for instance we characterize networks having the uniqueness property for any choice of origin destination pairs

on the optimal solutions in spectral commutant lifting theory abstract in this note we give a property of the optimal solutions to the spectral commutant lifting theorem of h bercovici c foias and a tannenbaum trans amer math soc in press which shows that such solutions are spectral analogues of inner functions which appear as optimal solutions in classical dilation theory

a state space algorithm for the solution of the 2 block superoptimal distance problem a state space algorithm for computing the solution of the 2 block superoptimal distance problem sodp is presented given a rational and antistable matrix function r s r 11 s r 12 s find all stable approximations q s that lexicographically minimize the singular values of the error function e s r 11 s r 12 s q s conditions are given for which the superoptimal approximation is unique in addition an a priori upper bound on the macmillan degree of the approximation is given the algorithm may be stopped after minimizing a given number of singular values this premature termination of the algorithm carries with it an expected saving in the computational effort and a predictable reduction in the macmillan degree of the approximation the algorithm only requires standard linear algebraic computations and is therefore easily implemented

topological uniqueness of the nash equilibrium for selfish routing with atomic users we consider the problem of selfish routing in a congested network shared by several users where each user wishes to minimize the cost of its own flow users are atomic in the sense that each has a nonnegligible amount of flow demand and flows may be split over different routes the total cost for each user is the sum of its link costs which in turn may depend on the user s own flow as well as the total flow on that link our main interest here is network topologies that ensure uniqueness of the nash equilibrium for any set of users and link cost functions that satisfy some mild convexity conditions we characterize the class of two terminal network topologies for which this uniqueness property holds and show that it coincides with the class of nearly parallel networks that was recently shown by milchtaich milchtaich i 2005 topological conditions for uniqueness of equilibrium in networks math oper res 30 225 244 to ensure uniqueness in nonatomic or wardrop routing games we further show that uniqueness of the link flows holds under somewhat weaker convexity conditions which apply to the mixed nash wardrop equilibrium problem we finally propose a generalized continuum game formulation of the routing problem that allows for a unified treatment of atomic and nonatomic users

necessary and sufficient conditions for mixed h sub 2 and h sub infinity optimal control it is shown that d s bernstein and w m hadad s ibid vol 34 no 3 p 293 1989 necessary condition for full order mixed h sub 2 and h sub infinity optimal control is also sufficient and that j c doyle et al s proc amer control conf p 2065 1989 sufficient condition for full order mixed h sub 2 and h sub infinity optimal control is also necessary they are duals of one another

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest

generic uniqueness of equilibrium in large crowding games a crowding game is a noncooperative game in which the payoff of each player depends only on the player s action and the size of the set of players choosing that particular action the larger the set the smaller the payoff finite n player crowding games often have multiple equilibria however a large crowding game generically has just one equilibrium and the equilibrium payoffs in such a game are always unique moreover the sets of equilibria of them replicas of a finite crowding game generically converge to a singleton asm tends to infinity this singleton consists of the unique equilibrium of the limit large crowding game this equilibrium generically has the following graph theoretic property the bipartite graph in which each player in the original finite crowding game is joined with all best response actions for copies of that player does not contain cycles

optimal multiple objective resource allocation using hybrid particle swarm optimization and adaptive resource bounds technique the multiple objective resource allocation problem morap seeks for an allocation of resource to a number of activities such that a set of objectives are optimized simultaneously and the resource constraints are satisfied morap has many applications such as resource distribution project budgeting software testing health care resource allocation etc this paper addresses the nonlinear morap with integer decision variable constraint to guarantee that all the resource constraints are satisfied we devise an adaptive resource bound technique to construct feasible solutions the proposed method employs the particle swarm optimization pso paradigm and presents a hybrid execution plan which embeds a hill climbing heuristic into the pso for expediting the convergence to cope with the optimization problem with multiple objectives we evaluate the candidate solutions based on dominance relationship and a score function experimental results manifest that the hybrid pso derives solution sets which are very close to the exact pareto sets the proposed method also outperforms several representatives of the state of the art algorithms on a simulation data set of the morap

a maximum entropy principle for contractive interpolants abstract in this paper a maximum entropy principle is established for a class of continuous contractive m n matrix valued functions g with preassigned fourier coefficients gj j for j 0 1 the function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a hankel operator based on the prescribed matrices 0 1 a pair of seemingly new szego type formulas are obtained enroute and some applications to nevanlinna pick interpolation are indicated

on certain minimal entropy extensions appearing in dilation theory i abstract we consider certain natural isometric intertwining dilations which appear in the context of the commutant lifting theorem these results are based on the authors previous work on a strengthened version of the parrott theorem since our extensions are isometric or coisometric the minimize the classical entropy integral

optimal load balancing on sonet bidirectional rings in this paper we consider the ring loading problem which arises in the design of sonet bidirectional rings the issue of demand splitting divides the ring loading problem into the two kinds one allows a demand to be split and routed in two different directions and the other does not the former kind becomes a relaxation of the latter we present an efficient exact solution procedure for the case with demand splitting and a two approximation algorithm for the case without demand splitting computational results are also shown to prove the efficiency of the proposed procedures

constrained traffic equilibrium in routing we study noncooperative routing in which each user is faced with a multicriterion optimization problem formulated as the minimization of one criterion subject to constraints on others we address the questions of existence and uniqueness of equilibrium we show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem we obtain uniqueness in some weaker sense under appropriate conditions we show that the link utilizations are uniquely determined at equilibrium we further study the normalized constrained equilibrium and apply it to pricing

the caratheodory fejer pisarenko decomposition and its multivariable counterpart when a covariance matrix with a toeplitz structure is written as the sum of a singular one and a positive scalar multiple of the identity the singular summand corresponds to the covariance of a purely deterministic component of a time series whereas the identity corresponds to white noise this is the caratheacuteodory fejeacuter pisarenko cfp decomposition in the present paper we study multivariable analogs for block toeplitz matrices as well as for matrices with the structure of state covariances of finite dimensional linear systems which include block toeplitz ones to this end we develop theory which addresses questions of existence uniqueness and realization of multivariable power spectra possibly having deterministic components we characterize state covariances which admit only a deterministic input power spectrum and we explain how to realize multivariable power spectra which are consistent with singular state covariances via decomposing the contribution of the singular part we then show that multivariable decomposition of a state covariance in accordance with a deterministic component white noise hypothesis for the input does not exist in general we finally reinterpret the cfp dictum and consider replacing the scalar multiple of the identity by a covariance of maximal trace which is admissible as a summand the summand can be either block diagonal corresponding to white noise or have a short range correlation structure corresponding to a moving average component the trace represents the maximal variance energy that can be accounted for by a process at the input e g noise with the aforementioned structure and this maximal solution can be computed via convex optimization the decomposition of covariances and spectra according to the range of their time domain correlations is an alternative to the cfp dictum with potentially great practical significance

topological conditions for uniqueness of equilibrium in networks equilibrium flow in a physical network with a large number of users e g transportation communication and computer networks need not be unique if the costs of the network elements are not the same for all users such differences among users may arise if they are not equally affected by congestion or have different intrinsic preferences whether or not forall assignments of strictly increasing cost functions each user s equilibrium cost is the same in all nash equilibria can be determined from the network topology specifically this paper shows that in a two terminal network the equilibrium costs are always unique if and only if the network is one of several simple networks or consists of several such networks connected in series the complementary class of all two terminal networks with multiple equilibrium costs forsome assignment of user specific strictly increasing cost functions is similarly characterized by an embedded network of a particular simple type

spectral factorization of rectangular rational matrix functions with application to discrete wiener hopf equations the properties of a discrete wiener hopf equation are closely related to the factorization of the symbol of the equation we give a necessary and sufficient condition for existence of a canonical wiener hopf factorization of a possibly nonregular rational matrix function w relative to a contour which is a positively oriented boundary of a region in the finite complex plane the condition involves decomposition of the state space in a minimal realization of w and if it is satisfied we give explicit formulas for the factors the results are generalized by means of centered realizations to arbitrary rational matrix functions the proposed approach can be used to solve discrete wiener hopf equations whose symbols are rational matrix functions which admit canonical factorization relative to the unit circle

pareto optimal strategy for linear stochastic systems with h constraint in finite horizon abstract in this paper we derive conditions for the existence of pareto efficient strategy and pareto solution under h constraint for the linear quadratic lq finite horizon cooperative differential game of stochastic systems with state control and disturbance multiplicative noise firstly we present a stochastic bounded real lemma sbrl with any initial condition for the considered stochastic system next a necessary and sufficient condition for pareto optimal strategy under the h constraint is researched by two cross coupled generalized differential riccati equations gdres which is the key contribution of this paper another contribution is that the pareto solution for every controller is given under the pareto efficient strategy and worst case external disturbance finally a practical example is given to illustrate the effectiveness of our results

generic uniqueness of equilibrium points abstract let x be a nonempty convex and compact subset of normed linear space e respectively let x be a nonempty bounded closed and convex subset of banach space e and a be a nonempty convex and compact subset of x and f x x r be a given function the uniqueness of equilibrium point for equilibrium problem which is to find x x respectively x a such that f x y 0 for all y x respectively f x y 0 for all y a is studied with varying f respectively with both varying f and varying a the results show that most of equilibrium problems in the sense of baire category have unique equilibrium point

on the existence of pure nash equilibria in weighted congestion games we study the existence of pure nash equilibria in weighted congestion games let c denote a set of cost functions we say that c is consistent if every weighted congestion game with cost functions in c possesses a pure nash equilibrium our main contribution is a complete characterization of consistency of continuous cost functions we prove that a set c of continuous functions is consistent for two player games if and only if c contains only monotonic functions and for all nonconstant functions c1 c2 c there are constants a b r such that c1 x a c2 x b for all x r 0 for games with at least three players we prove that c is consistent if and only if exactly one of the following cases holds a c contains only affine functions b c contains only exponential functions such that c x ac e x bc for some ac bc r where ac and bc may depend on c while must be equal for every c c the latter characterization is even valid for three player games finally we derive several characterizations of consistency of cost functions for games with restricted strategy spaces such as weighted network congestion games or weighted congestion games with singleton strategies

decentralized bandwidth control subject to two layer constraints abstract this paper is concerned with the new bandwidth allocation model that considers the structural allocation constraints suppose that a system is composed of finite groups of users and the bandwidth assigned to each user and to each group of users has pre specified upper and lower bounds if each user is granted with the utility function satisfying the standard continuity and concavity conditions the existence uniqueness fairness and optimality properties of the nash equilibrium point in the allocation game are studied to identify the equilibrium point an algorithm proved to converge globally is proposed and illustrated with a numerical example

generalized interpolation in h infty with a complexity constraint in a seminal paper sarason generalized some classical interpolation problems for h infinity functions on the unit disc to problems concerning lifting onto h 2 of an operator t that is defined on k

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

an effective modified binary particle swarm optimization mbpso algorithm for multi objective resource allocation problem morap a modified binary particle swarm optimization mbpso algorithm is proposed for solving the multi objective resource allocation problem morap first the generation mechanism for initial particles is established to guarantee that the algorithm can begin to search optimal particle in the feasible solution space second we develop the update mechanism for iterative particles which includes setting up the memory array modifying sig function and verifying the constraint condition to assure that the regenerated particles meet the constraint and algorithm can quickly converge third the selection mechanism for pbesti and gbest is proposed which uses the dynamic neighborhood strategy to ensure that the algorithm to find pareto optimal solutions through comparing the example simulation results of our mbpso with hga and aco published in references we find that proposed mbpso outperforms hga and aco finally the effectiveness of the different improved methods is analyzed and the synergism effect and the convergence behavior of the mbpso algorithm show its good performances

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

state space algorithm for the computation of superoptimal matrix interpolating functions a state space algorithm is studied which generates the unique superoptimal nehari extension of a general rational matrix the procedure is to use a set of all pass transformations to sequentially minimize each frequency dependent singular value of the interpolating function in a dimension peeling algorithm these all pass transformations are determined by the maximal schmidt pairs of a sequence of hankel operators the process terminates when the original problem is reduced to one of rank one at this stage all the available degrees of freedom have been exhausted the work is an extension of that by young 1986 and gives a concrete state space implementation of his operator theoretic arguments in addition bounds are given on the minimum achievable values for s1 e sup ersi e j i 1 2 rank g0 and also the mcmillan degree of the final superoptimal extension here si denotes the ith singular value of a frequency dependent matrix and the numbering is taken to be in decrea

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

unit canonical correlations between future and past on considere des processus arma stationnaires x t de rang complet et le cas ou il y a des fonctions lineaires du futur x t t 0 et du passe x t t 0 qui ont une correlation unite on montre que le nombre de paires de ce type lineairement independantes est le nombre de zeros du determinant des fonctions de transfert sur le cercle unite

a maximum entropy principle in the general framework of the band method abstract a maximum entropy principle is developed in the general framework of the band method known maximum entropy principles appear as corollaries and new ones are derived

algorithms for distributing telecommunication traffic on a multiple ring sonet based network abstract we examine a problem arising in the assignment of telecommunication traffic to a set of synchronous optical network sonet rings prior sonet design algorithms determine node to ring assignments while concurrently prescribing an assignment of traffic to the rings however due to uncertain voice and data demand among client nodes it may become necessary to revise the planned routing scheme once the true values of this data are realized we develop a minimum cost flow algorithm for the case in which demands may be split across multiple rings and provide a transformation to a maximum flow problem for specially structured data the case in which each demand pair may be routed on only one ring is proven to be np hard and we accordingly provide a powerful heuristic and an effective standard valid inequality generation scheme to optimally solve this problem within reasonable computational limits the effectiveness of our approach is demonstrated on a set of randomly generated test data

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

unitary interpolants and factorization indices of matrix functions abstract for an n n bounded matrix function we study unitary interpolants u i e unitary valued functions u such that u j j j u for which the toeplitz operator t u is fredholm we give a new approach based on superoptimal singular values and thematic factorizations we describe wiener hopf factorization indices of u in terms of superoptimal singular values of and thematic indices of f where f is a superoptimal approximation of by bounded analytic matrix functions the approach essentially relies on the notion of a monotone thematic factorization introduced in ap in the last section we discuss hereditary properties of unitary interpolants in particular for matrix functions of class h c we study unitary interpolants u of class qc

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

unitary interpolants factorization indices and infinite hankel block matrices abstract the existence uniqueness and construction of unitary n n matrix valued functions j j j in wiener like algebras on the circle with prescribed matrix fourier coefficients j j for j 0 are studied in particular if j then such an exists with j if and only if 0 1 where v denotes the infinite block hankel matrix j k v j k 0 1 acting in the sequence space l n 2 one of the main results is that the nonnegative factorization indices of every such are uniquely determined by the given data in terms of the dimensions of the kernels of i v v whereas the negative factorization indices are arbitrary it is also shown that there is a unique such if and only if the data forces all the factorization indices to be nonnegative and simple conditions for that and a formula for in terms of certain schmidt pairs of 0 are given the results depend upon a fine analysis of the structure of the kernels of i v v and of the one step extension problem of adamjan arov and krein funct anal appl 2 1968 1 18 isometric interpolants for the nonsquare case are also considered

factorization of all pass matrix functions we consider the factorization of an all pass matrix function e s into proper stable minimum phase factors this is achieved by applying the state space wiener hopf factorization theory of bart et al 1983 to the state space characterization of all pass matrix functions given by glover 1984 important connections are made between the properties of e s as a nehari extension its partial wiener hopf factorization indices and its hankel singular values

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

solutions to the h general distance problem which minimize an entropy integral abstract we pose and solve the problem of minimizing the entropy of an h norm bounded and stabilized closed loop solution proceeds via the equivalent error system distance problem the central member of the admissible class is shown to minimize the entropy at infinity and in that case an explicit state space formula is derived for the minimum value of the entropy links between entropy h 2 norms and h 2 optimal control are given

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

a polynomial time algorithm for the weighted link ring loading problem with integer demand splitting we are given an n node undirected ring network in which each link of the ring is associated with a weight traffic demand is given for each pair of nodes in the ring each demand is allowed to be split into two integer parts which are then routed in different directions clockwise and counterclockwise respectively the load of a link is the sum of the flows routed through the link and the nonnegative weighted load of a link is the product of its weight and its load the objective is to find a routing scheme such that the maximum weighted load on the ring is minimized based on some useful structural properties of the decision version of the problem we design a polynomial time combinatorial algorithm for the optimization problem

output feedback h2 h consensus control for stochastic time varying multi agent systems with x u v dependent noises abstract in this paper the output feedback h 2 h consensus control problem is investigated for discrete time varying stochastic multi agent systems with state control and disturbance dependent noises also called x u v dependent noises two new concepts for the h 2 and h consensus requirements are proposed to quantify the transient behavior of the consensus over a finite horizon for the addressed time varying multi agent systems we aim to design an output feedback consensus controller such that the closed loop multi agent systems achieve the prescribed h 2 and h consensus performances over a finite horizon by using the completing squares method and stochastic analysis techniques sufficient conditions are derived for the existence of the desired output feedback h 2 h consensus controller in terms of the solution to two coupled backward recursive riccati difference equations rdes moreover an iterative algorithm is proposed for solving the rdes by resorting to the moore penrose pseudo inverse a numerical example is utilized to illustrate the effectiveness of the proposed h 2 h consensus control strategy

an effective genetic algorithm approach to multiobjective resource allocation problems moraps dynamic programming dp is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller and hence computationally simpler subproblems in solving multiple objectives dynamic programming problem modp classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives the determination of these weights indicate the relative importance of the various objective also if the problem scale increases it become difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered in this paper we investigated the possibility of using genetic algorithms gas to solve multiobjective resource allocation problems moraps this procedure eliminates the need of any user defined weight factor for each objective also the proposed approach is developed to deal with the problems with both single or multiple objectives the simulation results for multiobjective resource allocation problems morap shows that genetic algorithms gas may hopefully be a new approach for such kinds of problems

discounted linear exponential quadratic gaussian control in this note we describe a recursive formulation of discounted costs for a linear quadratic exponential gaussian linear regulator problem which implies time invariant linear decision rules in the infinite horizon case time invariance in the discounted case is attained by surrendering state separability of the risk adjusted costs

continuum and finite player noncooperative models of competition the anonymous interaction of large numbers of economic agents is a kind of noncooperative situation which is markedly different from small numbers strategic conflict the mathematical model of a nonatomic game or a game with a continuum of players has been introduced as a model for these many agent situations on the basis that its equilibria should closely approximate those of games with large finite numbers of players this paper contains a precise definition of what it means for a nonatomic game to be the limit of a sequence of finite player games and a theorem which states when the limit of equilibria of finite player games will be an equilibrium of the nonatomic limit game this is analogous to theorems prompted by edgeworth s conjecture in core theory it is derived from a general set of sufficient conditions for the graph of a noncooperative equilibrium correspondence to be closed

risk sensitive estimation and a differential game a large deviation result is employed to solve the state estimation problem of a continuous time gauss markov system with an exponential cost the exponential cost is the expected value of an exponential function of the state estimation error a scalar spl theta appearing in the cost termed as the risk factor determines the penalty on the higher order moments of the error in contrast to the minimum variance estimate penalty on large deviations of the estimation error is possible

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

a spectral commutant lifting theorem 1991 american mathematical society first published in transactions of the american mathematical society vol 325 no 2 june 1991 by the american mathematical society

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

an entropy formula for time varying discrete time control systems the results of this paper generalize the formula for the entropy of a transfer function to time varying systems this is done through the use of some results on spectral factorizations due to arveson and properties of the cw transform which generalizes the usual cz transform for time varying systems using the formula defined it is shown that for linear fractional transformations like those that arise in time varying f control there exists a unique bounded contraction which maximizes the entropy this generalizes known results in the time invariant case possible extensions are discussed along with state space formulae

a hybrid binary particle swarm optimization for the obnoxious p median problem abstract the obnoxious p median problem can be formulated as a constrained binary linear program it is np hard and has a lot of real world applications in this paper a hybrid binary particle swarm optimization is proposed to solve the obnoxious p median problem a new position updating rule is presented to inherit the good structure of previous high quality solutions furthermore two tabu based mutation operators are used to avoid the premature convergence and guide the search to a promising area a greedy repair procedure is developed to repair infeasible solutions in addition an iterated greedy local search procedure is utilized to enhance the exploitation ability extensive experiments are done on a set of 72 benchmark instances from the literature experimental results and comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm in particular the proposed algorithm finds new best solutions for 15 instances compared with existing algorithms the proposed algorithm is able to find better average objective function value in a short average computing time

structure of model uncertainty for a weakly corrupted plant in this paper we investigate the structure of the transfer function set which includes all the transfer functions deduced from the plant available information it is shown that when an upper bound of the plant transfer function s h sup spl infin norm has been supplied and the noise contaminating the time domain identification experiment data is not too significant such a transfer function set can be parameterized by a linear fractional transformation of two transfer function matrices one of them is a fixed transfer function matrix which is completely determined by the plant available information and the noise magnitude the other is a norm bounded structure fixed free transfer function matrix moreover it is shown that the problem of analytically obtaining the fixed complexity nominal model that best approximates this transfer function set is as difficult as the spl mu synthesis problem

competitive routing in networks with polynomial costs we study a class of noncooperative general topology networks shared by n users each user has a given flow which it has to ship from a source to a destination we consider a class of polynomial link cost functions adopted originally in the context of road traffic modeling and show that these costs have appealing properties that lead to predictable and efficient network flows in particular we show that the nash equilibrium is unique and is moreover efficient these properties make the polynomial cost structure attractive for traffic regulation and link pricing in telecommunication networks we finally discuss the computation of the equilibrium in the special case of the affine cost structure for a topology of parallel links

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

a risk sensitive maximum principle abstract a stochastic maximum principle is derived which is formally of general application and so not restricted to the diffusion case it moreover differs from the classic deterministic principle only by a modification of the hamiltonian and so requires no solution of stochastic differential equations or calculation of conditional expectations the two essential points in its construction are that one considers the family of criterion functions exponential in an additive cost function of which the conventional expected cost case is a degenerate member and that in the non lqg case appeal to large deviation theory must be valid

relations between maximum entropy h control and combined h lqg control abstract the maximum entropy h control problem and a combined h lqg control problem are presented in a unified way and shown to be equivalent in the case of a full order controller and equalized h lqg weights the result links two separate approaches which have distinctly different methods of solution only two decoupled algebraic riccati equations are needed to state the controller maximum value of the entropy and minimum value of the auxiliary cost

an analysis of the pole zero cancellations in h optimal control problems of the first kind the aim of this paper is to study the pole zero cancellations which occur in a class of h infty optimal control problems which may be embedded in the configuration of fig 1 h infty control problems are said to be of the first kind if both p 12 s and p 21 s are square but not necessarily of the same size it is primarily this class of problems which will concern us here a general bound on the mcmillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies bf mathcal r s infty leqq rho rho need not be optimal in the l infty norm sense is derived as illustrated in fig 1 bf mathcal r s is the transfer function relating y 1 s to u 1 s if the mcmillan degree of p s in fig 1 is n we show that in the single loop siso case the corresponding unique h infty optimal controller never requires more than n 1 states in the multivariable case there is a continuum of optimal controllers whose mcmil

on the uniqueness of equilibrium in atomic splittable routing games in routing games with infinitesimal players it follows from well known convexity arguments that equilibria exist and are unique in routing games with atomic players with splittable flow equilibria exist but uniqueness of equilibria has been demonstrated only in limited cases in two terminal nearly parallel graphs when all players control the same amount of flow and when latency functions are polynomials of degree at most three there are no known examples of multiple equilibria in these games in this work we show that in contrast to routing games with infinitesimal players atomic splittable routing games admit multiple equilibria we demonstrate this multiplicity via two specific examples in addition we show that our examples are topologically minimal by giving a complete characterization of the class of network topologies for which multiple equilibria exist our proofs and examples are based on a novel characterization of these topologies in terms of sets of circulations

a hamiltonian formulation of risk sensitive linear quadratic gaussian control we consider the optimal control problem with time homogeneous linear and in general non markov dynamics and risk sensitive criterion appeal to the extremal principle prescribed by the risk sensitive certainty equivalence principle rscep yields a symmetric equation system indicating that the extended hamiltonian formulation generalizes naturally to the risk sensitive case the conjugate variable of a hamiltonian formulation now has an interpretation in terms of forecasted process noise and the rscep in fact provides a stochastic maximum principle for which all variables have a clear interpretation and the desired measurability properties in the infinite horizon case meaningful under generalized controllability conditions optimal control is determined explicitly in terms of a canonical factorization for the case of imperfect process observation the rscep leads to coupled equation systems that can again be solved in terms of canonical factorizations in the time invariant stationary case