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

adaptive control of linear systems with markov perturbations the stochastic model considered is a linear jump diffusion process x for which the coefficients and the jump processes depend on a markov chain z with finite state space first we study the optimal filtering and control problem for these systems with non gaussian initial conditions given noisy observations of the state x and perfect measurements of z we derive a new sufficient condition which ensures the existence and the uniqueness of the solution of the nonlinear stochastic differential equations satisfied by the output of the filter we study a quadratic control problem and show that the separation principle holds next we investigate an adaptive control problem for a state process x defined by a linear diffusion for which the coefficients depend on a markov chain the processes x and z being observed in independent white noises suboptimal estimates for the process x z and approximate control law are investigated for a large class of probability distributions of the initial state asymptotic properties of these filters and this control law are obtained upper bounds for the corresponding error are given

on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control abstract existence of maximal solution is proved for a generalized version of the well known standard algebraic riccati equations which arise in certain stochastic optimal control problems

stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic riccati equation this note addresses the jump linear quadratic problem of markov jump linear systems and the associated algebraic riccati equation necessary and sufficient conditions for stability of the optimal control and positiveness of riccati solutions are developed we show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory but also a necessary one this together with a characterization developed here for the kernel of the riccati solution allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable and that the riccati solution is positive definite if and only if the system is weakly observable the connection between the algebraic riccati equation and the control problem is made as far as the minimal positive semidefinite solution for the algebraic riccati equation is identified with the optimal solution of the linear quadratic problem illustrative numerical examples and comparisons are included

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

stability of solutions for stochastic impulsive systems via comparison approach this note studies stability problem of solutions for stochastic impulsive systems by employing lyapunov like function method and it s formula comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established based on these comparison principles the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system as the application the stability results are used to design impulsive control for the stabilization of unstable stochastic systems finally one example is given to illustrate the obtained results

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

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

robust jump linear quadratic control a mode stabilizing solution this correspondence is concerned with optimal feedback control of a class of linear stochastic systems for a quadratic performance index the solution to this problem is known but the resulting optimal regulator does not ensure stability in every mode of operation to improve robustness a new mode stabilizing solution is defined an example illustrates the advantages of the proposed controller

mean square stability for discrete bounded linear systems in hilbert space the asymptotic behaviour for infinite dimensional discrete linear systems driven by white noise is considered in this paper both the evolution and convergence of the state correlation operators sequence are analysed mean square stability conditions are investigated including a comparison with the deterministic stability problem the particular case of compact operators is considered in some detail

testing the correlation for clustered categorical and censored discrete time to event data when covariates are measured without with errors summary in the analysis of clustered categorical data it is of common interest to test for the correlation within clusters and the heterogeneity across different clusters we address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models for clustered nominal and ordinal categorical responses we extend the results to accommodate clustered censored discrete time to event data we next consider such tests in the situation where covariates are measured with errors we propose using the simex method to construct the score tests for the null hypothesis that the variance components are zero key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates the asymptotic properties of the proposed tests are studied we illustrate these tests by analyzing two data sets and evaluate their performance with simulations

the weight distribution of a class of linear codes from perfect nonlinear functions in this correspondence the weight distribution of a class of linear codes based on perfect nonlinear functions also called planar functions is determined the class of linear codes under study are either optimal or among the best codes known and have nice applications in cryptography

bias analysis and simex approach in generalized linear mixed measurement error models abstract we consider generalized linear mixed models glmms for clustered data when one of the predictors is measured with error when the measurement error is additive and normally distributed and the error prone predictor is itself normally distributed we show that the observed data also follow a glmm but with a different fixed effects structure from the original model a different and more complex random effects structure and restrictions on the parameters this characterization enables us to compute the biases that result in common glmms when one ignores measurement error for instance in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases both for regression coefficients and for variance components parameter estimation is described using the simex method a relatively new functional method that makes no assumptions about the structure of the unobservable predictors simulations and an example illustrate the results

optimal control of discrete time bilinear systems with applications to switched linear stochastic systems abstract this paper aims at characterizing the most destabilizing switching law for discrete time switched systems governed by a set of bounded linear operators the switched system is embedded in a special class of discrete time bilinear control systems this allows us to apply the variational approach to the bilinear control system associated with a mayer type optimal control problem and a second order necessary optimality condition is derived optimal equivalence between the bilinear system and the switched system is analyzed which shows that any optimal control law can be equivalently expressed as a switching law this specific switching law is most unstable for the switched system and thus can be used to determine stability under arbitrary switching based on the second order moment of the state the proposed approach is applied to analyze uniform mean square stability of discrete time switched linear stochastic systems numerical simulations are presented to verify the usefulness of the theoretic results

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

almost sure and moments stability of jump linear systems abstract the stability of piecewise deterministic linear systems driven by an underlying finite markov chain is analyzed necessary and sufficient conditions for moment stability are obtained by means of an explicit formula for the corresponding liapunov exponent the relationship between almost sure and moment stability is elucidated revealing the possible occurrence of high order moment instability and large deviations from a stable sample path behavior

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

on the phase portrait of the matrix riccati equation arising from the periodic control problem a comprehensive description is provided of the properties of the matrix riccati differential equation in which the coefficient matrices are t periodic for some t 0 the main results include 1 a classification of all the periodic equilibria t periodic solutions 2 necessary and sufficient conditions for convergence to the uniformly asymptotically stable completely unstable periodic equilibrium as t to infty t to infty 3 necessary and sufficient conditions for a solution to escape in finite forward or backward time 4 a description of every almost periodic solution 5 a proof that every solution which does not escape in finite time is asymptotically almost periodic and an explicit formula for the limiting almost periodic solution

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

gradient projection based performance improvement for jlq problems this article is concerned with a class of continuous time markovian jump linear systems where the regime transition rates are determined through an initial policy the purpose is to study the jump linear quadratic regulator for such class of systems a two level regulating method is adopted to design the state feedback controller and the policy separately the problem of tuning the existing policy with respect to a prescribed quadratic performance criterion is formulated as a gradient projection based iterative optimisation this method leads to a near optimal policy whose performance is better than that of the initial one useful characteristics of such a policy are also developed the efficiency of the main results is elucidated by two numerical examples

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

lyapunov coupled equations for continuous time infinite markov jump linear systems this paper deals with lyapunov equations for continuous time markov jump linear systems mjls out of the bent which wends most of the literature on mjls we focus here on the case in which the markov chain has a countably infinite state space it is shown that the infinite mjls is stochastically stabilizable ss if and only if the associated countably infinite coupled lyapunov equations have a unique norm bounded strictly positive solution it is worth mentioning here that this result do not hold for mean square stabilizability mss since ss and mss are no longer equivalent in our set up see e g j baczynski optimal control for continuous time lq problems with infinite markov jump parameters ph d thesis federal university of rio de janeiro ufrj coppe 2000 to some extent a decomplexification technique and tools from operator theory in banach space and in particular from semigroup theory are the very technical underpinning of the paper

on the covering structures of two classes of linear codes from perfect nonlinear functions in this paper the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from fqm to itself are determined using a unified approach all the minimal codewords of these codes are characterized according to their weights which suggests that their covering structures are determined finally all the minimal access sets of the secret sharing schemes based on their dual codes are obtained

controllability of linear stochastic systems abstract we discuss several concepts of controllability for stochastic systems and derive sufficient and in most cases also necessary algebraic conditions for the controllability of the state and the output of white and colored noise linear systems these criteria reduce to the well known deterministic ones in the absence of noise

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

robust stability ℋ2 analysis and stabilisation of discrete time markov jump linear systems with uncertain probability matrix the stability and the problem of 2 guaranteed cost computation for discrete time markov jump linear systems mjls are investigated assuming that the transition probability matrix is not precisely known it is generally difficult to estimate the exact transition matrix of the underlying markov chain and the setting has a special interest for applications of mjls the exact matrix is assumed to belong to a polytopic domain made up by known probability matrices and a sequence of linear matrix inequalities lmis is proposed to verify the stability and to solve the 2 guaranteed cost with increasing precision these lmi problems are connected to homogeneous polynomially parameter dependent lyapunov matrix of increasing degree g the mean square stability mss can be established by the method since the conditions that are sufficient eventually turns out to also be necessary provided that the degree g is large enough the 2 guaranteed cost under mss is also studied here and an extension to cope with th

robust kalman filtering for discrete time markovian jump systems with parameter uncertainty in this paper we examine the problem of robust kalman filtering for a class of linear uncertain discrete time systems with markovian jump parameters the underlying system is subjected to norm bounded time varying uncertainties in the state and measurement equations first stochastic quadratic stability of the system is studied then a linear state estimator is constructed such that the estimation error covariance is guaranteed to lie within certain bound for all admissible uncertainties the solution is given in terms of two coupled algebraic riccati equations

functional inference in frailty measurement error models for clustered survival data using the simex approach we consider frailty models for clustered survival data in the presence of measurement errors in covariates we first show that when the measurement error is accounted for in a full likelihood analysis but the distribution of the unobserved covariate is misspecified the maximum likelihood estimators are asymptotically biased especially for the variance component whose bias can be substantial we then discuss making inference using functional estimation via the simex method where no distribution of the unobserved error prone covariate is assumed the simex method is easy to implement by repeatedly fitting standard frailty models we study the asymptotic properties of the simex estimates and show that they are consistent and asymptotically normal in simulation studies we compare the simex method and the likelihood method in terms of efficiency and robustness we also propose a simex score test for the variance component to test for the within cluster correlation and evaluate its performance through simu

simex variance component tests in generalized linear mixed measurement error models in the analysis of clustered data with covariates measured with error a problem of common interest is to test for correlation within clusters and heterogeneity across clusters we examined this problem in the framework of generalized linear mixed measurement error models we propose using the simex method to construct a score test for the null hypothesis that all variance components are zero a key feature of this simex score test is that no assumptions need to be made regarding the distributions of the random eects and the unobserved covariates we illustrate this test by analyzing framingham heart disease data and evaluate its performance by simulation we also propose individual simex score tests for testing the variance components separately both tests can be easily implemented using existing statistical software

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

efficient estimation of first passage time density function for jump diffusion processes the first passage time problem has attracted considerable research interest in the field of stochastic processes it concerns the estimation of the probability density of the time for a random process to cross a specified boundary level even though there are many theoretical advances in solving this problem for many classes of random processes no analytical solution exists the jump diffusion process jdp is one such class recent research in finance theory has renewed the interest in jdps and the first passage time problem for such processes is applicable to several finance problems in this paper we develop fast monte carlo type numerical methods for computing the first passage density function for jdps compared with the standard monte carlo approach our approaches are about 10 30 times faster

a new look at the robust control of discrete time markov jump linear systems abstractin this paper we make a foray in the role played by a set of four operators on the study of robust h2 and mixed h2 h control problems for discrete time markov jump linear systems these operators appear in the study of mean square stability for this class of systems by means of new linear matrix inequality lmi characterisations of controllers which include slack variables that to some extent separate the robustness and performance objectives we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of h2 performance since each operator provides a different degree of conservatism the results are unified in the form of an iterative lmi technique for designing robust h2 controllers whose convergence is attained in a finite number of steps the method yields a new way of computing mixed h2 h controllers whose conservatism decreases with iteration two numerical examples illustrate the applicability

properties and applications of preimage distributions of perfect nonlinear functions the preimage distributions of perfect nonlinear functions from an abelian group of order n to an abelian group of order 3 or 4 respectively are studied based on the properties of the preimage distributions of perfect nonlinear functions from an abelian group of order 3r to an abelian group of order 3 the weight distributions of the ternary linear codes c pi from the perfect nonlinear functions pi x from f 3 r to itself are determined these results suggest that two open problems proposed by carlet ding and yuan in 2005 and 2006 respectively are answered

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

a locally most powerful test for homogeneity with many strata summary a locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting the test is based on the difference between the square of the score and the observed information about the nuisance parameters all evaluated at the null hypothesis several examples including constant normal mean with possibly different variances and matched case control studies are presented in detail the relative efficiencies of the unstratified estimator of parameter of interest versus the stratified one are calculated two data sets on matched case control studies are used for illustration

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

array algorithm for filtering of discrete time markovian jump linear systems this note develops an array algorithm for optimal filtering of discrete time markovian jump linear systems dtmjlss the known advantages of this kind of algorithm which was originally developed for normal state space systems remain valid when it is applied to linear systems subject to markovian jumps it is numerically more stable in the sense that it presents better conditioning and reduced dynamical range a numerical example based on fixed point implementations is presented in order to demonstrate the advantage of this algorithm

policy iteration based feedback control it is well known that stochastic control systems can be viewed as markov decision processes mdps with continuous state spaces in this paper we propose to apply the policy iteration approach in mdps to the optimal control problem of stochastic systems we first provide an optimality equation based on performance potentials and develop a policy iteration procedure then we apply policy iteration to the jump linear quadratic problem and obtain the coupled riccati equations for their optimal solutions the approach is applicable to linear as well as nonlinear systems and can be implemented on line on real world systems without identifying all the system structure and parameters

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem 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 of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

uncoupled riccati iterations for the linear quadratic control problem of discrete time markov jump linear systems this paper deals with recursive methods for solving coupled riccati equations arising in the linear quadratic control for markovian jump linear systems two algorithms based on solving uncoupled riccati equations at each iteration are presented the standard method for this problem relies on finite stage approximations with receding horizon whereas the methods presented here are based on sequences of stopping times to define the terminal time of the approximating control problems the methods can be ordered in terms of rate of convergence comparisons with other methods in the current literature are also presented

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

maximal solution of a certain class of periodic riccati differential equations this paper deals with a generalized version of the well known periodic riccati differential equation which arises in certain optimal filtering problems for linear periodic systems a monotonicity property for symmetric periodic equilibrium solutions is established and it is proved that there exists a maximal symmetric periodic equilibrium solution

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

finite horizon quadratic optimal control and a separation principle for markovian jump linear systems in this note we consider the finite horizon quadratic optimal control problem of discrete time markovian jump linear systems driven by a wide sense white noise sequence we assume that the output variable and the jump parameters are available to the controller it is desired to design a dynamic markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time as in the case with no jumps we show that an optimal controller can be obtained from two coupled riccati difference equations one associated to the optimal control problem when the state variable is available and the other one associated to the optimal filtering problem this is a principle of separation for the finite horizon quadratic optimal control problem for discrete time markovian jump linear systems when there is only one mode of operation our results coincide with the traditional separation principle for the linear quadratic gaussian control of discrete time linear systems

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

monte carlo td λ methods for the optimal control of discrete time markovian jump linear systems in this paper we present an iterative technique based on monte carlo simulations for deriving the optimal control of the infinite horizon linear regulator problem of discrete time markovian jump linear systems for the case in which the transition probability matrix of the markov chain is not known we trace a parallel with the theory of td l algorithms for markovian decision processes to develop a td l like algorithm for the optimal control associated to the maximal solution of a set of coupled algebraic riccati equations care it is assumed that either there is a sample of past observations of the markov chain that can be used for the iterative algorithm or it can be generated through a computer program our proofs rely on the spectral radius of the closed loop operators associated to the mean square stability of the system being less than 1

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

information filtering and array algorithms for discrete time markovian jump linear systems this technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete time markovian jump linear systems a numerical example for a two mode markovian jump linear system to show the advantage of using array algorithms to filter this class of systems is provided

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

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

optimal control of jump linear gaussian systems this paper investigates the problem of controlling a discrete time linear system with jump parameters a review of the literature is presented as well as a development of the application of dynamic programming to this class of control problems dynamic programming has been applied by many researchers and it was observed that no closed form analytical solution could be constructed because of the dual aspects of the controller the main contribution of the present work is an algorithm suitable for computer implementation for the optimal dual control the construction of the algorithm is based on transforming the dynamic programming relations into a space of sufficient statistics and using a finite dimensional optimization procedure to obtain the optimal control as a function of the statistics this is achieved by first developing a suitable recursive realization of a filter which generates the sufficient statistics for the problem and then embedding this filter into the dynamic programming equations

team optimal control of stochastically switched systems with local parameter knowledge this paper considers the optimal decentralized control of linear systems with stochastically switched cost and system matrices depending on local parameters two types of dynamic switched problems are considered with partially nested and one step delayed sharing information structures for the former case parameters and measurements follow a partially nested structure with the parameters possibly being correlated across all stages for the latter case parameters are assumed to be markov processes with their values along with measurements available instantaneously to local controllers but with a one time step delay to others the solution to both these problems rely on the optimal solution to a static one stage stochastic parameter problem with local type dependent gaussian measurements and for this purpose the static quadratic team problem is examined in some generality using an operator theoretic framework it is shown that the sequential update scheme always converges to the team optimal strategy for general static quadratic team setups this when applied to the static stochastic parameter problem yields the team optimal strategy the corresponding strategy is affine in the measurements with the parameter dependent coefficients obtained by solving a set of linear equations these equations are immediately solvable when the total number of parameter values is finite however for the case of infinite parameter values the update scheme also provides a mechanism to determine an approximation to the team optimal strategy

on the detectability and observability of discrete time markov jump linear systems abstract this paper presents a new detectability concept for discrete time markov jump linear systems with finite markov state which generalizes the ms detectability concept found in the literature the new sense of detectability can similarly assure that the solution of the coupled algebraic riccati equation associated to the quadratic control problem is a stabilizing solution in addition the paper introduces a related observability concept that also generalizes previous concepts a test for detectability based on a coupled matrix equation is derived from the definition and a test for observability is presented which can be performed in a finite number of steps the results are illustrated by examples including one that shows that a system may be detectable in the new sense but not in the ms sense

controllability of stochastic linear systems in the paper necessary and sufficient conditions for various types of stochastic controllability of the linear stochastic system of the form d x ax d t bu d t c d w r x 0 x 0 are given some possible extensions are indicated as well

linear codes from perfect nonlinear mappings and their secret sharing schemes in this paper error correcting codes from perfect nonlinear mappings are constructed and then employed to construct secret sharing schemes the error correcting codes obtained in this paper are very good in general and many of them are optimal or almost optimal the secret sharing schemes obtained in this paper have two types of access structures the first type is democratic in the sense that every participant is involved in the same number of minimal access sets in the second type of access structures there are a few dictators who are in every minimal access set while each of the remaining participants is in the same number of minimal access sets

optimal design of networked control systems computer control via asynchronous communication channels we study a linear discrete time partially observed system perturbed by white noises the observations are transmitted to the controller and its outputs are sent to the actuators via communication channels that provide random transmission times and may lose messages various signals may incur independent delays and arrive at the destination point out of order under certain assumptions a recursive minimum variance state estimator is proposed a finite horizon linear quadratic optimal control problem is also solved

a separation principle for the continuous time lq problem with markovian jump parameters in this paper we devise a separation principle for the finite horizon quadratic optimal control problem of continuous time markovian jump linear systems driven by a wiener process and with partial observations we assume that the output variable and the jump parameters are available to the controller it is desired to design a dynamic markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time as in the case with no jumps we show that an optimal controller can be obtained from two coupled riccati differential equations one associated to the optimal control problem when the state variable is available and the other one associated to the optimal filtering problem this is a separation principle for the finite horizon quadratic optimal control problem for continuous time markovian jump linear systems for the case in which the matrices are all time invariant we analyze the asymptotic behavior of the solution of the derived interconnected riccati differential equations to the solution of the associated set of coupled algebraic riccati equations as well as the mean square stabilizing property of this limiting solution when there is only one mode of operation our results coincide with the traditional ones for the lqg control of continuous time linear systems

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

on a partially observable lqg problem for systems with markovian jumping parameters in this paper a variant of the lqg problem for systems with markovian jumping parameters is studied it is assumed that the system is partially observable in the sense that we do not have access to the jumping parameter via nonlinear filtering the problem is recast as one with complete information it is then shown that a certain averaged control is an optimal policy vis a vis a modified quadratic cost apart from its intrinsic theoretical interest this result has an important bearing on a number of different analyses related with the original quadratic cost

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

lq control of discrete time jump systems with markov chain in a general borel space in this technical note it is studied the lq optimal control problem for discrete time markov jump linear systems considering the case in which the markov chain takes values in a general borel space cal m it is shown that the solution of the lq optimal control problem is obtained in terms of the positive semi definite solution s ell ell in cal m of cal m coupled algebraic riccati equations by cal m coupled we mean that the algebraic riccati equations are coupled via an integral over a transition probability kernel cal g cdot vert cdot having a density g cdot vert cdot with respect to a sigma finite measure mu on cal m it is obtained sufficient conditions based on the concept of stochastic stabilizability and stochastic detectability for the existence and uniqueness of this positive semi definite solution these results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

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

test of homogeneity of binary data with explanatory variables summary apparent heterogeneity of the risk of a disease in different groups may be explained by subjectspecific risk factors unequally distributed in these groups we propose a score test of homogeneity that allows adjustment for known risk factors of the disease the test is based oni a random effect logistic regression model and requires only simple computations in addition to a conventional logistic regression method the score test is applied to the study of geographical heterogeneity of cognitive impairment in elderly using a sample of 3 318 subjects scattered in 75 parishes it is shown that an apparent heterogeneity disappears when taking into account subject specific risk factors this test may also be useful for studying familial aggregation of a disease testing homogeneity of the distribution of binary traits in different groups has long been recognized as an important problem particularly in conventional genetics smith 1951 and in genetic epidemiology where it may be used to investigate the familial aggregation of a disease the presence of familial aggregation suggests a genetic determinant testing homogeneity of geographical units is also of interest the presence of heterogeneity suggests the presence of an unmeasured environmental factor another application occurs if the possible correlation of the data is treated as a nuisance it is useful to test whether the groups are homogeneous before performing ordinary regression models liang 1987 chi squared tests are used for testing homogeneity when the number of groups is small however the chi squared test is not applicable when the sizes of the groups are not large haldane 1940 and when the number of groups is large in such cases random effect models are preferred the probability of disease within a group have a common distribution thus the null hypothesis is specified by a null variance of the random effect and alternative hypotheses are specified by a unique parameter the variance of the random effect whatever the number of groups see potthoff and whittinghill 1966 wisniewsky 1968 and tarone 1979 in epidemiologic studies however we often need to test for homogeneity while adjusting for other risk factors of the disease indeed risk factors if differently distributed in the different groups may play the role of confounding factors relative to the group effect it is of paramount importance in genetic studies to investigate whether an apparent familial aggregation may be explained by nongenetic factors such as educational level or nutritional habits which may also segregate in families similarly geographical clusters may be explained by nonenvironmental factors unequally distributed in the geographical units based on a random effect logistic regression model we derive a score test of homogeneity that allows adjustment on explanatory variables the score statistic is the same as that proposed by hamerle 1990 in the context of repeated measurements but the variance proposed in the present paper is different simulations show that it leads to a more powerful test we use this test to investigate the possible geographical heterogeneity of cognitive impairment as measured by the mini mental state score in 3 318 subjects scattered in 75 parishes in southwestern france

weak detectability and the linear quadratic control problem of discrete time markov jump linear systems the paper deals with the stochastic concepts of weak detectability and weak observability for markov jump linear systems which is an special class of composite linear systems the concepts are explored here to strengthen the similarities with the corresponding concepts of deterministic detectability and observability we introduce a collection of matrices referred to as the observability matrices we show that weak observability is equivalent to full rank of each matrix in the set of observability matrices in addition we present a stochastic counterpart of the well known result on the invariance of trajectories within non observable subspaces these characterizations allow us to clarify the relationship between weak detectability and mean square detectability and to provide a testable condition for weak detectability relying on the assumption of weak detectability we develop a method for solving the linear quadratic problem that is based on iterations of uncoupled algebraic riccati equations which

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