stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

linear dynamically varying lq control of nonlinear systems over compact sets linear quadratic controllers for tracking natural and composite trajectories of nonlinear dynamical systems evoluting over compact sets are developed typically such systems exhibit complicated dynamics i e have nontrivial recurrence the controllers which use small perturbations of the nominal dynamics as input actuators are based on modeling the tracking error as a linear dynamically varying ldv system necessary and sufficient conditions for the existence of such a controller are linked to the existence of a bounded solution to a functional algebraic riccati equation fare it is shown that despite the lack of continuity of the asymptotic trajectory relative to initial conditions the cost to stabilize about the trajectory as given by the solution to the fare is continuous an ergodic theory method for solving the fare is presented furthermore it is shown that wrapping the ldv controller around the nonlinear system secures a stable tracking dynamics finally an example of controlling the henon map to follow an aperiodic orbit is presented

a new general sufficient condition for almost sure stability of jump linear systems in this paper we study the almost sure stability of discrete time jump linear systems with a finite state markov form process a general condition for almost sure stability which is a necessary and sufficient condition for scalar one dimensional systems is derived many simpler testable sufficient conditions for almost sure stability are derived from this sufficient condition

nonlinear tracking over compact sets with linear dynamically varying boldmath h infty control linear dynamically varying h infty controllers are developed for tracking natural trajectories of a broad class of nonlinear systems defined over compact sets it is shown that the existence of a suboptimal h infty controller is related to the existence of a bounded solution to a functional algebraic riccati equation even though nonlinear systems running over compact sets could exhibit sensitive dependence on initial conditions the riccati solution is continuous in the suboptimal case but it may be discontinuous in the optimal case

an improved lower matrix bound of the solution of the unified coupled riccati equation a new lower matrix bound of the solution for the unified coupled algebraic riccati equation ucare is proposed this bound improves the drawback of the results presented in a previous paper

a bounded real lemma for jump systems this note presents a bounded real lemma for discrete time markovian jump linear systems mjlss we show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems for the case of one plant mode this condition reduces to the standard necessary and sufficient condition for discrete time systems we envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for mjlss

the skorohod oblique reflection problem in time dependent domains the deterministic skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection in the form studied here the multidimensional skorohod problem w

performance optimization of switched systems a model matching approach in this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n stable linear time invariant lti systems the interest is placed on optimizing the worst case performance of this model matching system over all possible switchings with either l infin induced norm or h 2 norm as the performance criterion this optimization is performed over all youla kucera parameters that switch causally in time among n stable lti systems for the particular setup at hand it is shown that the optimal youla kucera parameter need not depend on the switching trajectory in the cases of partially matched switching and unmatched switching and that it can be obtained as an lti solution to an associated standard l 1 or h 2 optimization in the case of matched switching two convergent sequences to the optimal solution from above and below are formulated in terms of linear programs and quadratic programs respectively for the l infin induced and h 2 norm optimizations an approximate solution with any given precision is possible by finite truncation applications of these results to sensitivity minimization linear switched parameter systems and cooperative control are provided

iterative solutions of coupled discrete markovian jump lyapunov equations in this paper two iterative methods are given to solve coupled discrete markovian jump lyapunov equations arising from the stability analysis of discrete time markovian jump systems when such equations have unique positive definite solutions a sufficient condition for the convergence of iterates for one iterative method is derived when such equations only have unique solutions but not necessarily positive definite the above iterative method may fail and an alterative iterative method is provided by using the solutions of discrete time lyapunov equations as its intermediate steps a sufficient condition is also presented for the convergence of the iterates

upper solution bounds of the continuous and discrete coupled algebraic riccati equations in this paper we propose upper bounds for the sum of the maximal eigenvalues of the solutions of the continuous coupled algebraic riccati equation ccare and the discrete coupled algebraic riccati equation dcare which are then used to infer upper bounds for the maximal eigenvalues of the solutions of each riccati equation by utilizing the upper bounds for the maximal eigenvalues of each equation we then derive upper matrix bounds for the solutions of the ccare and dcare following the development of each bound an iterative algorithm is proposed which can be used to derive tighter upper matrix bounds finally we give numerical examples to demonstrate the effectiveness of the proposed results making comparisons with existing results

control of discrete time hybrid stochastic systems a realistic stochastic control problem for hybrid systems with markovian jump parameters can have switching parameters in both the state and the measurement equations furthermore both the base and jump states in general are not perfectly observed there are only two existing controllers for this problem both with complexity exponentially increasing with time the authors present another control algorithm for stochastic systems with markovian jump parameters this algorithm is derived through the use of stochastic dynamic programming and is designed to be used for realistic stochastic control problems i e with noisy state observations this scheme has fixed computational requirements at each stage and a natural parallel implementation simulation results are used to compare the algorithm with previous schemes

robust finite time h control for uncertain discrete jump systems with time delay abstract this paper addresses the robust finite time h control problem for a family of uncertain discrete time markovian jump systems with time delay initially the concepts of stochastic finite time boundedness and stochastic h finite time stabilization are given then a stochastic finite time h controller is designed such that the underlying closed loop discrete jump time delay system is stochastic finite time boundedness and satisfies a prescribed h performance level in some given finite time interval based on lyapunov approach sufficient criteria on the stochastic h finite time stabilization are established for the solvability of the problem which can be handled by a feasibility problem in the form of linear matrix inequalities with a fixed parameter finally simulation examples are presented to demonstrate the validity of the developed techniques

on the solution of discrete time markovian jump linear quadratic control problems abstract a necessary and sufficient condition for the existence of a positive semidefinite solution of the coupled algebraic discrete time riccati like equation occurring in markovian jump control problems is derived by verifying a simple matrix inequality it is shown that such a solution exists and can be obtained as a limit of a monotonic sequence this leads to a straightforward numerical algorithm for the computation of the solution an example is given to illustrate the proposed method

stabilization of continuous time jump linear systems we investigate almost sure and moment stabilization of continuous time jump linear systems with a finite state markov jump form process we first clarify the concepts of spl delta moment stabilizability exponential spl delta moment stabilizability and stochastic spl delta moment stabilizability we then present results on the relationships among these concepts coupled riccati equations that provide necessary and sufficient conditions for mean square stabilization are given in detail and an algorithm for solving the coupled riccati equations is proposed moreover we show that individual mode controllability implies almost sure stabilizability which is not true for other types of stabilizability finally we present some testable sufficient conditions for spl delta moment stabilizability and almost sure stabilizability

solution of lyapunov equations by alternating direction implicit iteration abstract in this report a new procedure is presented for solving the lyapunov matrix equation first the system is reduced to tridiagonal form with gaussian similarity transformations then the resulting system is solved with alternating direction implicit adi iteration a matrix commutation property essential for model problem convergence of adi iteration applied to elliptic difference equations is not needed for this application all stable lyapunov matrix equations are model adi problems

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

directional derivatives of oblique reflection maps given an oblique reflection map and functions documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document psi chi in mathcal d lim end document the space of k valued functions that have finite left and right limits at every point the directional derivative documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document nabla chi gamma psi end document of along evaluated at is defined to be the pointwise limit as documentclass aastex usepackage amsbsy usepackage amsfonts u

a dirichlet process characterization of a class of reflected diffusions for a class of stochastic differential equations with reflection for which a certain l p continuity condition holds with p 1 it is shown that any weak solution that is a strong markov process can be decomposed into the sum of a local martingale and a continuous adapted process of zero p variation when p 2 this implies that the reflected diffusion is a dirichlet process two examples are provided to motivate such a characterization the first example is a class of multidimensional reflected diffusions in polyhedral conical domains that arise as approximations of certain stochastic networks and the second example is a family of two dimensional reflected diffusions in curved domains in both cases the reflected diffusions are shown to be dirichlet processes but not semimartingales

optimal quadratic control of jump linear systems with separately controlled transition probabilities abstract the optimal control of discrete time jump systems that would be linear but for randomly jumping parameters are considered these parameter jumps which are indexed by a finite state form process can be used to model systems subject to component failures or structural changes the control of such systems when the jump probabilities can be controlled by choice of a finite valued input is considered this input form control can be thought of as corresponding to a maintenance or repair policy the optimal control problem with quadratic costs whose weighting matrices depend on the jumping parameters and form control is formulated for such systems the optimal solution for finite and infinite time horizon problems is developed in addition sufficient conditions for the existence of a steady state stabilizing solution to the infinite time problem are given in terms of appropriately defined controllability and observability properties

a detector based approach for the h_ 2 control of markov jump linear systems with partial information in this paper we study the h 2 control for discrete time markov jump linear systems mjls with partial information we consider the case in which we do not have access to the markov jump parameter but instead there is a detector that emits signals which provides information on this parameter a salient feature of our formulation is that it encompasses for instance the cases with perfect information no information and cluster observations of the markov parameter which were previously analyzed in the markov jump control literature the goal is to derive a feedback linear control using the information provided by the detector in order to stochastically stabilize the closed loop system we present two lyapunov like equations for the stochastic stability of the system in addition we show that a linear matrix inequalities lmi formulation can be obtained in order to design a stochastically stabilizing feedback control in the sequel we deal with the h 2 control problem and we show that again an lmi optimization problem can be formulated in order to design a stochastically stabilizing feedback control with guaranteed h 2 cost we also present two special cases one of them always satisfied for the limit case in which the detector provides perfect information on the markov parameter and the bernoulli jump case under which lmi conditions become necessary and sufficient for the stochastic stabilizability of the system and the lmi optimization problems provide the optimal h 2 cost for the bernoulli jump case we show that our formulation generalizes previous ones the case with convex polytopic uncertainty on the parameters of the system and on the transition probability matrix is also considered the paper is concluded with some numerical examples

an explicit formula for the skorokhod map on 0 a the skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions in this work an explicit formula for the skorokhod map 0 a on 0 a for any a 0 is derived specifically it is shown that on the space d 0 of right continuous functions with left limits taking values in r 0 a a o 0 where a d 0 d 0 is defined by a t t sups 0 t s a infu s t u and 0 d 0 d 0 is the skorokhod map on 0 which is given explicitly by 0 t t sup s 0 t s in addition properties of a are developed and comparison properties of 0 a are established

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

brief robust one step receding horizon control of discrete time markovian jump uncertain systems this paper proposes a receding horizon control scheme for a set of uncertain discrete time linear systems with randomly jumping parameters described by a finite state markov process whose jumping transition probabilities are assumed to belong to some convex sets the control scheme for the underlying systems is based on the minimization of the worst case one step finite horizon cost with a finite terminal weighting matrix at each time instant this robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters the proposed controller is obtained using semidefinite programming

brief paper markov jump linear systems with switching transition rates mean square stability with dwell time the stability of a class of markov jump linear systems characterized by piecewise constant transition rates and system dynamics is investigated for these switching markov jump linear systems mean square stability is analyzed through the time evolution of the second order moment of the state the main result is a sufficient condition that guarantees mean square stability under constraints on the dwell time between switching instants an alternative condition based on kronecker calculus is worked out it is shown that both the stability criteria admit an lmi implementation

on the influence of noise on jump linear systems jump linear systems are considered in a random environment where they are subject to additive and multiplicative noises stochastic notions of stabilizability and detectability are introduced to characterize the asymptotic behavior of the optimal jump linear quadratic gaussian regulator and a dual kalman filter

a natural gradient descent algorithm for the solution of discrete algebraic lyapunov equations based on the geodesic distance a new framework to calculate the numerical solution of the discrete algebraic lyapunov equation is proposed by using the geometric structures on the riemannian manifold specifically two algorithms based on the manifold of positive definite symmetric matrices are provided one is a gradient descent algorithm with an objective function of the classical euclidean distance the other is a natural gradient descent algorithm with an objective function of the geodesic distance on the curved riemannian manifold furthermore these two algorithms are compared with a traditional iteration method simulation examples show that the convergence speed of the natural gradient descent algorithm is the fastest one among three algorithms

asymptotically optimal admission control of a queue with impatient customers we consider a gi gi 1 queue with impatient customers in heavy traffic we use the solution of an approximating singular diffusion control problem to construct an admission control policy for the queue the approximating control problem does not admit a so called pathwise solution hence the resulting admission control policy depends on second moment data we prove asymptotic optimality of the constructed policy using weak convergence methods rh

positive operator based iterative algorithms for solving lyapunov equations for ito stochastic systems with markovian jumps this paper studies the iterative solutions of lyapunov matrix equations associated with ito stochastic systems having markovian jump parameters for the discrete time case when the associated stochastic system is mean square stable two iterative algorithms with one in direct form and the other one in implicit form are established the convergence of the implicit iteration is proved by the properties of some positive operators associated with the stochastic system for the continuous time case a transformation is first performed so that it is transformed into an equivalent discrete time lyapunov equation then the iterative solution can be obtained by applying the iterative algorithm developed for discrete time lyapunov equation similar to the discrete time case an implicit iteration is also proposed for the continuous case for both discrete time and continuous time lyapunov equations the convergence rates of the established algorithms are analyzed and compared numerical examples are worked out to validate the effectiveness of the proposed algorithms

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

technical communique lower bounds on the solution of coupled algebraic riccati equation lower bounds for eigenvalues and matrix lower bound of a solution to continuous time coupled algebraic riccati equation and discrete time coupled algebraic riccati equation are developed as special cases of bounds for the unified coupled algebraic riccati equation they include bounds for the minimal eigenvalues the sums of the eigenvalues the trace and the determinant

jump linear quadratic control with random state discontinuities abstract in a random environment jump linear quadratic control problems are studied random state discontinuities are included in the analysis and the corresponding optimal regulator is obtained the introduction of stochastic notions of stabilizability and detectability gives a direct characterization of the asymptotic behaviour of the optimal system

output feedback h control of systems over communication networks using a deterministic switching system approach this paper proposes a new control problem of systems over asymmetric path delay configurations on arbitrary communication networks where the criterion is the h norm minimization via dynamic output feedback controllers network delay dependent switching controllers are designed via a piecewise lyapunov function approach as well as a common lyapunov function approach the controllers are found through convex optimization over linear matrix inequalities

a differential game for a multiclass queueing model in the moderate deviation heavy traffic regime we study a differential game that governs the moderate deviation heavy traffic asymptotics of a multiclass single server queueing control problem with a risk sensitive cost we consider a cost set on a finite but sufficiently large time horizon and show that this formulation leads to stationary feedback policies for the game several aspects of the game are explored including its characterization via a one dimensional free boundary problem the semi explicit solution of an optimal strategy and the specification of a saddle point we emphasize the analogy to the well known harrison taksar free boundary problem which plays a similar role in the diffusion scale heavy traffic literature

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

on stability and lq control of mjls with a markov chain with general state space we study the mean square stability and the lq control of discrete time markov jump linear systems where the markov chain has a general state space the mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a lyapunov equation and a uniformity result respectively an algorithm for testing the mean square stability is also developed based on the uniformity result the finite and infinite horizon lq problems are considered and their solutions are characterized by appropriate riccati integral equations an application to networked control systems ncs is finally presented and a simple example is studied via simulation

the modular properties and the integral representations of the multiple elliptic gamma functions abstract we show the modular properties of the multiple elliptic gamma functions which are an extension of those of the theta function and the elliptic gamma function the modular property of the theta function is known as jacobi s transformation and that of the elliptic gamma function was provided by felder and varchenko in this paper we deal with the multiple sine functions since the modular properties of the multiple elliptic gamma functions result from the equivalence between two ways to represent the multiple sine functions as infinite products we also derive integral representations of the multiple sine functions and the multiple elliptic gamma functions we introduce correspondences between the multiple elliptic gamma functions and the multiple sine functions

weighted least squares solutions to general coupled sylvester matrix equations this paper is concerned with weighted least squares solutions to general coupled sylvester matrix equations gradient based iterative algorithms are proposed to solve this problem this type of iterative algorithm includes a wide class of iterative algorithms and two special cases of them are studied in detail in this paper necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented sufficient conditions that are easy to compute are also given the optimal step sizes such that the convergence rates of the algorithms which are properly defined in this paper are maximized and established several special cases of the weighted least squares problem such as a least squares solution to the coupled sylvester matrix equations problem solutions to the general coupled sylvester matrix equations problem and a weighted least squares solution to the linear matrix equation problem are simultaneously solved several numerical examples are given to illustrate the effectiveness of the proposed algorithms

an addition type formula for the elliptic digamma function abstract eisenstein derived addition formulas for the weierstrass zeta function from the addition formula for the cotangent function and the fact that the weierstrass zeta function can be represented as an infinite sum of the cotangent functions in this paper we apply this idea of eisenstein s to the addition type formula for the double cotangent function established by the author we show that the elliptic digamma function defined by the logarithmic derivative of the elliptic gamma function satisfies an addition type formula this formula includes the addition formula for the weierstrass zeta function evaluation formulas for the double eisenstein series introduced by tsumura and the double shuffle relations for the double eisenstein series proved by gangl kaneko zagier

discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

stability of discrete time linear systems with markovian jumping parameters and constrained control the note is devoted to the study of linear discrete time systems with markovian jumping parameters and constrained control the constraints used in the note are of symmetrical inequality type the approach of positively invariant sets is used to obtain new necessary and sufficient conditions for positive invariance and sufficient conditions for stochastic stability these conditions become those given for stationary discrete time systems with one mode deterministic linear discrete time systems as known in the literature

asymptotically optimal controls for time inhomogeneous networks a framework is introduced for the identification of controls for single class time varying queueing networks that are asymptotically optimal in the so called uniform acceleration regime a related but simpler first order or fluid control problem is first formulated for a class of performance measures that satisfy a certain continuity property it is then shown that any sequence of policies whose performances approach the infimum in the fluid control problem is asymptotically optimal for the original network problem examples of performance measures with this property are described and simulations implementing asymptotically optimal policies are presented the use of directional derivatives of the reflection map for solving fluid control problems is also illustrated this work serves to complement a large body of literature on asymptotically optimal controls for time homogeneous networks

an implicit sequential algorithm for solving coupled lyapunov equations of continuous time markovian jump systems in this paper an implicit sequential algorithm is presented for solving coupled lyapunov matrix equations of continuous time markovian jump linear systems first some existing iterative algorithms which can be utilized to solve the coupled lyapunov matrix equations are reviewed and discussed next based on the existing parallel iterative algorithm an implicit sequential algorithm is proposed by using the latest updated information the proposed algorithm fills the current gap of implicit algorithms for solving continuous coupled lyapunov matrix equations it is shown that the proposed algorithm with zero initial conditions can monotonically converge to the unique positive definite solutions of the coupled lyapunov matrix equations if the associated markovian jump system is stochastically stable moreover a necessary and sufficient condition is established for the proposed algorithm to be convergent the algorithm presented in this paper has much better convergence performance than other existing iterative algorithms and requires less storage capacity finally a numerical example is given to show the effectiveness of the proposed algorithm

iterative algorithm to compute the maximal and stabilising solutions of a general class of discrete time riccati type equations in this article an iterative method to compute the maximal solution and the stabilising solution respectively of a wide class of discrete time nonlinear equations on the linear space of symmetric

brief constrained quadratic state feedback control of discrete time markovian jump linear systems in this paper we consider the quadratic optimal control problem of a discrete time markovian jump linear system subject to constraints on the state and control variables it is desired to find a state feedback controller which may also depend on the jump variable that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables related to the state and control variables of the system the transition probability of the markov chain and initial condition of the system may belong to appropriate convex sets we obtain an approximation for the optimal solution of this problem in terms of linear matrices inequalities so that convex programming can be used for numerical calculations examples are presented to illustrate the usefulness of the developed results

optimal state estimation for discrete time markovian jump linear systems in the presence of delayed output observations we investigate the design of optimal state estimators for markovian jump linear systems we consider that the output observations and the mode observations are affected by delays not necessarily identical our objective is to design optimal estimators for the current state given current and past observations we provide a solution to this paradigm by giving an optimal recursive estimator for the state in the minimum mean square sense and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output we also show that if the output delay is less then the one in observing the mode then the optimal state estimation becomes nonlinear in the output observations

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

optimal beamforming for video streaming in multiantenna interference networks via diffusion limit in this paper we consider queue aware beamforming control for video streaming applications in multiantenna interference network using heavy traffic approach we derive the diffusion limit for the discrete time queuing system and obtain an ergodic excess beamforming control problem for the diffusion limit system the ergodic control problem is to minimize the average power costs of the access points subject to the constraints on the playback interruption costs and buffer overflow costs of the mobile users to deal with the queue coupling challenge we utilize the weak interference coupling property in the network using the theories of calculus and perturbation techniques we derive a closed form approximate priority function of the optimality equation and the associated error bound based on this approximation we propose a low complexity queue aware beamforming control algorithm which is asymptotically optimal for sufficiently small cross channel path gain finally the proposed scheme is compared with various baselines through simulations and it is shown that significant performance gain can be achieved

parallel algorithm for solving coupled algebraic lyapunov equations of discrete time jump linear systems abstract a parallel iterative scheme for solving coupled algebraic lyapunov equations of discrete time jump linear systems with markovian transitions is introduced the algorithm is computationally efficient since it operates on reduced order decoupled algebraic discrete lyapunov equations furthermore the solutions at every iteration are computed by elementary matrix operations hence the number of operations is minimal monotonicity of convergence is established under the existence conditions of unique positive solutions

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

the elliptic gamma function and sl 3 z z3 abstract the elliptic gamma function is a generalization of the euler gamma function and is associated to an elliptic curve its trigonometric and rational degenerations are the jackson q gamma function and the euler gamma function respectively the elliptic gamma function appears in baxter s formula for the free energy of the eight vertex model and in the hypergeometric solutions of the elliptic qkzb equations in this paper the properties of this function are studied in particular we show that elliptic gamma functions are generalizations of automorphic forms of g sl 3 z z 3 associated to a non trivial class in h3 g z

optimal preview control of markovian jump linear systems in this technical note we investigate the design of controllers for discrete time markovian jump linear systems that achieve optimal reference tracking in the presence of preview reference look ahead for a quadratic cost and given a reference sequence we obtain the optimal solution for the full information case the optimal control policy consists of the additive contribution of two terms a feedforward term and a feedback term we show that the feedback term is identical to the standard optimal linear quadratic regulator for markovian jump linear systems we provide explicit formulas for computing the feedforward term including an analysis of convergence

almost sure and δmoment stability of jump linear systems abstract in this paper we study the almost sure stability and moment stability of discrete time jump linear systems with a finite state form process criteria for almost sure and moment stability which are necessary and sufficient conditions for scalar one dimensional systems are derived the relationship between almost sure and 6 moment stability for scalar one dimensional systems is also presented if the system matrices commute necessary and sufficient conditions for almost sure stability are obtained

extended hamiltonian algorithm for the solution of discrete algebraic lyapunov equations in this paper we use a second order learning algorithm for solving the numerical solution of the discrete algebraic lyapunov equation specifically extended hamiltonian algorithm based on the manifold of positive definite symmetric matrices is provided furthermore this algorithm is compared with the euclidean gradient algorithm the riemannian gradient algorithm and the two traditional iteration methods simulation examples show that the convergence speed of the extended hamiltonian algorithm is the fastest one among these algorithms

full informationh control for discrete time infinite markov jump parameter systems abstract in this paper we consider the full information discrete timeh control problem for the class of linear systems with markovian jumping parameters the state space of the markov chain is assumed to take values in a countably infinite set full information here means that the controller has access to both the state variables and jump variables a necessary and sufficient condition for the existence of a feedback controller that makes the l 2 induced norm of the system less than a prespecified bound is obtained this condition is written in terms of a set of infinite coupled algebraic riccati equations

recursive robust regulator for discrete time markovian jump linear systems in this paper we propose a robust regulator for discrete time markovian jump linear systems dmjls subject to structured parameter uncertainties states of markov chain are considered known at each instant and the transition probabilities matrix is time varying the framework proposed to deal with this problem is developed through a regularization approach based on robust least squares and penalty functions recursive solutions in terms of coupled riccati equations which do not depend on any auxiliary parameter to be tuned are provided these equations resemble the recursive solutions of dmjls standard regulators when the system is not subject to uncertainties conditions for convergence and stability of this robust regulator are established numerical examples present comparative studies considering the proposed robust regulator the standard linear quadratic regulator and an h infty controller for dmjls

gradient based iterative algorithm for solving coupled matrix equations abstract this paper is concerned with iterative methods for solving a class of coupled matrix equations including the well known coupled markovian jump lyapunov matrix equations as special cases the proposed method is developed from an optimization point of view and contains the well known jacobi iteration gauss seidel iteration and some recently reported iterative algorithms by using the hierarchical identification principle as special cases we have provided analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm simultaneously the optimal step size such that the convergence rate of the algorithm is maximized is also established in explicit form the proposed approach requires less computation and is numerically reliable as only matrix manipulation is required some other existing results require either matrix inversion or special matrix products numerical examples show the effectiveness of the proposed algorithm

an elliptic analogue of the multiple gamma function a hierarchy of functions including the elliptic gamma function is introduced it can be interpreted as an elliptic analogue of the multiple gamma function and its trigonometric limit coincides with a q analogue of the multiple gamma function some properties of the functions are considered

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

error bounds in the averaging of hybrid systems the authors analyze the error introduced by the averaging of hybrid systems these systems involve linear systems which can take a number of different realizations based on the state of an underlying finite state process the averaging technique based on a formula from lie algebras known as the backer campbell hausdorff bch formula provides a single system matrix as an approximation to the hybrid system the two errors discussed are 1 the error induced by the truncation of the bch series expansion and 2 the error between the actual hybrid system and its average a simple sufficient stability test is proposed to check the asymptotic behavior of this error in addition conditions are derived that allow the use of state feedback instead of averaging to arrive at a time invariant system matrix

h control for markovian jump systems with partially unknown transition rates via an adaptive method abstract this paper investigates the problem of the h control for a class of continuous time markovian jump systems with partially unknown transition rates an adaptive h performance index is defined to describe the disturbance attenuation performance of markovian jump systems by combining the linear matrix inequality lmi approach for designing h controllers and the adaptive method for estimating the unknown terms a new method for designing the h controllers is proposed where an estimation of the transition rate matrix is given and the controller parameter matrices are dependent on the known transition rates and the estimations of the unknown terms the sufficient conditions for the existence of the adaptive state feedback controller and the adaptive dynamic output feedback controller are proposed and the estimations of the unknown transition rates are obtained from the adaptive laws it is shown that the proposed adaptive controllers provide better performance than the traditional fixed gain controllers a practical example is provided to illustrate the effectiveness and advantage of the proposed method

brief control of singularly perturbed systems with markovian jump parameters an h approach in this paper we study the problem of h control for singularly perturbed linear continuous time systems with markovian jump parameters the system under consideration is described by a state space model consisting of slow and fast dynamics with a continuous time discrete state markov process taking values on a finite set on the basis of reduced order technique our attention is focused on the designing of state feedback control such that both stochastic stability and a prescribed h performance for the full order system are achieved it has been shown that the above problem can be solved if a set of coupled riccati equations has solution furthermore the asymptotic structure of composite mode dependent controller is characterized which shows that the controller is independent of the singular perturbation e when e is sufficiently small

static output feedback control of markov jump linear systems without mode observation in this paper we address infinite horizon optimal control of markov jump linear systems mjls via static output feedback because the jump parameter is assumed not to be observed the optimal control law is nonlinear and intractable therefore we assume the regulator to be linear under this assumption we first present sufficient feasibility conditions for static output feedback stabilization of mjls with nonobserved mode in the mean square sense in terms of linear matrix inequalities lmis however these conditions depend on the particular state space representation i e a coordinate transform can make the lmis feasible while the original lmis are infeasible to avoid the issues with the ambiguity of the state space representation we therefore present an iterative algorithm for the computation of the regulator gain the algorithm is shown to converge if the mjls is stabilizable via mode independent static output feedback however convergence of the algorithm is not sufficient for the stability of the closed loop which requires an additional stability check after the regulator gains have been computed a numerical example demonstrates the application of the presented results

robust h_ infty filtering for switched stochastic system with missing measurements this paper considers the design of robust h infin filtering problem for switched stochastic discrete time delay system with missing measurements via switched lyapunov function approach attention is focused on the design of an exponentially stable filter guaranteeing a prescribed noise attenuation level in the h infin sense and missing measurements probability by using switched lyapunov functionals some sufficient conditions in terms of linear matrix inequalities lmis are obtained finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

first order analytic difference equations and integrable quantum systems we present a new solution method for a class of first order analytic difference equations the method yields explicit minimal solutions that are essentially unique special difference equations give rise to minimal solutions that may be viewed as generalized gamma functions of hyperbolic trigonometric and elliptic type euler s gamma function being of rational type we study these generalized gamma functions in considerable detail the scattering and weight functions u and w functions associated to various integrable quantum systems can be expressed in terms of our generalized gamma functions we obtain detailed information on these u and w functions exploiting the difference equations they satisfy

mean square stabilizing solutions for discrete time coupled algebraic riccati equations in this paper we present new sufficient conditions for the existence of a mean square stabilizing solution for a set of coupled algebraic riccati equations which arises from the study of quadratic optimal control of discrete time linear systems with markov switching parameters the conditions are derived under the assumptions of mean square stabilizability and on the unobservable modes of the system and compared with existing results

stein iterations for the coupled discrete time riccati equations abstract we consider a set of discrete time coupled algebraic riccati equations that arise in quadratic optimal control of markovian jump linear systems two iterations for computing a symmetric maximal solution of this system are investigated we construct sequences of the solutions of the decoupled stein equations and show that these sequences converge to a solution of the considered system numerical experiments are given

jump linear quadratic gaussian control in continuous time the optimal quadratic control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes is addressed the systems are also subject to gaussian input and measurement noise the optimal solution for the jump linear quadratic gaussian jlqc problem is given this solution is based on a separation theorem the optimal state estimator is sample path dependent if the plant parameters are constant in each value of the underlying jumping process then the controller portion of the compensator converges to a time invariant control law however the filter portion of the optimal infinite time horizon jlqc compensator is not time invariant thus a suboptimal filter which does converge to a steady state solution under certain conditions is derived and a time invariant compensator is obtained

approximating the gi gi 1 gi queue with a nonlinear drift diffusion hazard rate scaling in heavy traffic we study a single server queue operating under the first in first out fifo service discipline in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time under some mild conditions on the abandonment distribution we identify a limiting heavy traffic regime in which the resulting diffusion approximation for both the offered waiting time process the process that tracks the amount of time an infinitely patient arriving customer would wait for service and the queue length process contain the entire abandonment distribution to use a continuous mapping approach to establish our weak convergence results we additionally develop existence uniqueness and continuity results for nonlinear generalized regulator mappings that are of independent interest we further perform a simulation study to evaluate the quality of the proposed approximations for the steady state mean queue length and the steady state probability of abandonment suggested by the limiting diffusion process

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

delay dependent stabilization of singularly perturbed jump linear systems this paper considers the stability and stabilization problems of continuous time singularly perturbed markov jump linear systems lmi based sufficient conditions for the system to be stochastically stable are given and using lmi approaches two methods for designing state feedback stabilizing controllers are also derived numerical examples are worked out to illustrate the usefulness of the proposed results

an iterative algorithm for discrete periodic lyapunov matrix equations abstract in this paper a novel iterative algorithm with a tuning parameter is developed to solve the forward discrete periodic lyapunov matrix equation associated with discrete time linear periodic systems an important feature of the proposed algorithm is that the information in the current and the last steps is used to update the iterative sequence the convergence rate of the algorithm can be significantly improved by choosing a proper tuning parameter it is shown that the sequence generated by this algorithm with zero initial conditions monotonically converges to the unique positive definite solution of the periodic lyapunov matrix equation if the tuning parameter is within the interval 0 1 in addition a necessary and sufficient convergence condition is given for the proposed algorithm in terms of the roots of a set of polynomial equations also a method to choose the optimal parameter is developed such that the algorithm has the fastest convergence rate finally numerical examples are provided to illustrate the effectiveness of the proposed algorithm

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

multiple model adaptive control for jump linear stochastic systems abstract the problem of stochastic control is considered for linear discrete time systems with markovian jump parameters where the parameters are included in both state and observation models and their evolutions are not observed when applying a multiple model adaptive control mmaq strategy to the problem we need in general mn sequences of control gains where m is the number of markov chain states and n is a final time this approach is clearly impractical for large n a suboptimal control method is proposed to alleviate the computational loads of the mmac approach algorithms for the elemental control gains are obtained in lerms of a set of m coupled riccati like equations while a generalized pseudo bayes algorithm gpba is used for the elemental filter mechanism simulation results are included to illustrate the effectiveness of the proposed method by comparing with some mmacs using other elemental filtering techniques

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided