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

control of singularly perturbed hybrid stochastic systems we study a class of optimal stochastic control problems involving two different time scales the fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process under a fundamental ergodicity property for a class of infinitesimal control systems associated with the fast mode we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system both the finite and infinite discounted horizon cases are considered we show how an approximate optimal control law can be constructed from the solution of the limit control problem in the particular case where the infinitesimal control systems possess the so called turnpike property i e characterized by the existence of global attractors the limit control problem can be given an interpretation related to a decomposition approach

boundedly optimal control of piecewise deterministic systems abstract this paper deals with a class of undiscounted piecewise deterministic control problems with bounded state space and possibly undiscounted cost the concept of boundedly optimal control is introduced for undiscounted cost problems this optimality concept is stronger than the average cost optimality via a limit argument for a family of associated problems with discounted cost we show that a dynamic programming formalism can be developed for the characterization of boundedly optimal solutions

tracking fast trajectories along a slow dynamics a singular perturbations approach controlled coupled slow and fast motions are examined in a singular perturbations setting the objective is to minimize a cost functional that takes into account both the fast motion supposing say tracking a fast target and the slow dynamics a method is offered to cope with the possibility that the fast flow has nonstationary limits invariant measures of the fast motion are then the controlled objects on the infinitesimal scale optimal amalgamation of them on the slow scale induces the variational limit whose solutions are near optimal solutions of the perturbed system

the value of information from multiple sources of uncertainty in decision analysis abstract in decision analysis the expected value of information is a well known and used concept where the value of information about sources of uncertainty are normally considered one at a time when information is potentially available for more than one source of uncertainty in a decision problem and the decision maker must choose which sets of information to acquire the nonlinearities and discontinuities which are inherent to the problem result in general non additivity of information values additivity of the expected value of perfect information evpi occurs only under certain conditions and for a large proportion of decision problems evpis are not even approximately additive this paper presents an analysis of this class of problem some fundamental results practical implications and delineates a number of useful directions for further research

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

the haagerup property for locally compact quantum groups the haagerup property for locally compact groups is generalised to the context of locally compact quantum groups with several equivalent characterisations in terms of the unitary representations and positive definite functions established in particular it is shown that a locally compact quantum group g has the haagerup property if and only if its mixing representations are dense in the space of all unitary representations for discrete g we characterise the haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group hat g by the existence of a real proper cocycle on g and further if g is also unimodular we show that the haagerup property is a von neumann property of g this extends results of akemann walter bekka cherix valette and jolissaint to the quantum setting and provides a connection to the recent work of brannan we use these characterisations to show that the haagerup property is preserved under free products of discrete quantum groups

control of a hybrid stochastic system abstract we consider in this paper a continuous time stochastic hybrid control system with a finite time horizon the objective is to minimize a linear function of the expected state trajectory the state evolves according to a linear dynamics however the parameters of the state evolution equation may change at discrete times according to a controlled markov chain which has finite state and action spaces we use a procedure similar in form to the maximum principle this determines a control strategy which is asymptotically optimal as the number of transitions during the finite time horizon grows to infinity

h2 optimal control for linear stochastic systems the aim of the present paper is to provide an optimal solution to the h 2 state feedback and output feedback control problems for stochastic linear systems subjected both to markov jumps and to multiplicative white noise it is proved that in the state feedback case the optimal solution is a static gain which is also optimal in the class of all higher order controllers in the output feedback case the optimal h 2 controller has the same order as the given stochastic system the realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of riccati type coupled equations an effective iterative convergent algorithm to compute these stabilizing solutions is also presented the paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature

singular perturbation of a finite horizon problem with state space constraints we study the singular perturbation of optimal control problems for nonlinear systems with constraints on the fast state variables and a cost functional either of bolza type or involving the exit time of the system from a given domain under a controllability assumption on the fast variables we show that these variables become controls in the limit problem our method consists of passing to the limit in the associated hamilton jacobi bellman hjb equations by means of some tools in the theory of viscosity solutions

modeling uncertainty in multi criteria decision analysis abstract his paper provides a review of multiple criteria decision analysis mcda for cases where attribute evaluations are uncertain the main aim is to identify different tools which can be used to represent uncertain evaluations and to broadly survey the available decision models that can be used to support uncertain decision making the review includes models using probabilities or probability like quantities explicit risk measures such as quantiles and variances fuzzy numbers and scenarios the practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed

production control of manufacturing systems with production rate dependent failure rates it is known that for single part type production systems with homogeneous markovian machine failure rates special single threshold feedback policies called hedging point policies are optimal and the stationary probability distribution of the part type surplus for given tentative hedging point values can be obtained analytically this approach is extended to multiple threshold policies with production rate dependent machine failure rates it is shown that the stationary distribution of the part type surplus can be obtained under the extended policy and in the presence of production rate dependent failure rates the advantage of multiple threshold policies is that they can provide a piecewise constant step function approximation of any feedback policy it is observed that hedging point policies are not always optimal and in fact feedback policies are not always optimal either

a crame spl acute r rao type estimation lower bound for systems with measurement faults a crame spl acute r rao type lower bound is presented for systems with measurements prone to discretely distributed faults which are a class of hybrid systems lower bounds for both the state and the markovian interruption variables fault indicators of the system are derived using the recently presented sequential version of the crame spl acute r rao lower bound crlb for general nonlinear systems because of the hybrid nature of the systems addressed the crlb cannot be directly applied due to violation of its associated regularity conditions to facilitate the calculation of the lower bound the hybrid system is first approximated by a system in which the discrete distribution of the fault indicators is replaced by an approximating continuous one the lower bound is then obtained via a limiting process applied to the approximating system the results presented herein facilitate a relatively simple calculation of a nontrivial lower bound for the state vector of systems with fault prone measurements the crlb type lower bound for the interruption process variables turns out to be trivially zero however a nontrivial non crlb type bound for these variables has been recently presented elsewhere by the authors the utility and applicability of the proposed lower bound are demonstrated via a numerical example involving a simple global positioning system gps aided navigation system where the gps measurements are fault prone due to their sensitivity to multipath errors

haagerup property for c algebras and rigidity of c algebras with property t abstract we study the haagerup property for c algebras we first give new examples of c algebras with the haagerup property a nuclear c algebra with a faithful tracial state always has the haagerup property and the permanence of the haagerup property for c algebras is established as a consequence the class of all c algebras with the haagerup property turns out to be quite large we then apply popa s results and show the c algebras with property t have a certain rigidity property unlike the case of von neumann algebras for the reduced group c algebras of groups with relative property t the rigidity property strongly fails in general nevertheless for some groups without nontrivial property t subgroups we show a rigidity property in some cases as examples we prove the reduced group c algebras of the non amenable affine groups of the affine planes have a rigidity property

outranking under uncertainty using scenarios abstract this paper considers the use of scenarios to treat uncertain attribute evaluations in the outranking methods the scenario based approach allows the decision maker to think deterministically about the problem by attaching causal links to a small number of potential outcomes instead of using probability distributions the scenario approach can be expressed as a simplified version of the comprehensive but practically complex distributive outranking method of d avignon and vincke using a scenario approach has distinct practical advantages but also presents the inherent danger that meaningful information is ignored the extent of this danger is assessed using a simulation experiment where it is found to be of a magnitude that is non trivial but still potentially acceptable for certain decision contexts

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

singularly perturbed ordinary differential equations with dynamic limits coupled slow and fast motions generated by ordinary differential equations are examined the qualitative limit behaviour of the trajectories as the small parameter tends to zero is sought after invariant measures of the parametrised fast flow are employed to describe the limit behaviour rather than algebraic equations which are used in the standard reduced order approach in the case of a unique invariant measure for each parameter the limit of the slow motion is governed by a chattering type equation without the uniqueness the limit of the slow motion solves a differential inclusion the fast flow in turn converges in a statistical sense to the direct integral respectively the set valued direct integral of the invariant measures

property t c algebras with amenable tracial states abstract as a non unital analogue of the main result in 6 we show in this article that if a is a separable quasi central c algebra with property t and is nuclear then there is a sequence of positive integers n k k n such that the c 0 direct sum of the family m n k k n of matrix algebras is an ideal j a of a and that a j a has no tracial state in particular a separable c algebra a is a c 0 direct sum of matrix algebras if and only if a is quasi central is nuclear has property t and every unital simple quotient of a has a tracial state we also show that a separable property t c algebra a is residually finite dimensional if and only if a admits an amenable faithful tracial state and every ideal of a has non zero center

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

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 controlability of linear systems with stochastic jump parameters this note studies the notion of stochastic e controllability in probability for linear systems subject to sudden jumps in parameter values by using a lyapunov like approach sufficient conditions are obtained in terms of a set of coupled bernoulli equations the potential use of the results is illustrated by an example

on the construction of asymptoticallly optimal controls for singularly perturbed systems we construct asymptotically optimal controls for singularly perturbed nonlinear systems where both the slow and the fast motions are controlled for this purpose we give necessary optimality conditions for an averaged system for the slow motion

controlled wear process modeling optimal control models for wear in which wear is a continuous increasing stochastic process are set up optimal control problems for these models are posed and explicitly solved in one case

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

property t and strong property t for unital c algebras in this paper we will give a thorough study of the notion of property t for c algebras as introduced by m b bekka as well as a slightly stronger version of it called strong property t which is also an analogue of the corresponding concept in the case of discrete groups and type ii1 factors more precisely we will give some interesting equivalent formulations as well as some permanence properties for both property t and strong property t we will also relate them to certain t type properties of the unitary group of the underlying c algebra

operator algebraic superridigity for sl n ℤ n 3 for n 3 let sln we prove the following superridigity result for in the context of operator algebras let l be the von neumann algebra generated by the left regular representation of let m be a finite factor and let u m be its unitary group let u m be a group homomorphism such that m then either

a full description of property t of unital c crossed products abstract let be a discrete group that acts on a unital c algebra a through an action we study property t as well as its stronger variant of the full and the reduced crossed products we show that if a has a invariant tracial state then the reduced crossed product a r has strong property t if and only if has property t and a r a has strong property t if has the haagerup property the strong property t of a r a in the above statement can be replaced by that of a furthermore the strong property t of the full crossed product is shown to coincide with that of the reduced one in the case of property t we obtain the corresponding result when the group is either icc or abelian as an application a non compact locally compact group g is amenable if and only if c b g lt r g d does not have strong property t where g d is the group g equipped with the discrete topology and lt is the left translation action

paper optimal control of markov chains admitting strong and weak interactions this paper is devoted to the study of an optimal control problem for a markov chain with generator b ea where e is a small parameter it is shown that an approximate solution can be calculated by a policy improvement algorithm involving computations relative to an aggregated problem the dimension of which is given by n the number of ergodic sets for the b matrix together with a family of decentralized problems the dimensions of which are given by the number of elements in each ergodic set for the b matrix

haagerup property for c algebras abstract we define the haagerup property for c algebras a and extend this to a notion of relative haagerup property for the inclusion b a where b is a c subalgebra of a let be a discrete group and a normal subgroup of we show that the inclusion a r a r has the relative haagerup property if and only if the quotient group has the haagerup property in particular the inclusion c r c r has the relative haagerup property if and only if has the haagerup property c r has the haagerup property if and only if has the haagerup property we also characterize the haagerup property for in terms of its fourier algebra a

asymptotic optimization of a nonlinear hybrid system governed by a markov decision process we consider in this paper a continuous time stochastic hybrid control system with finite time horizon the objective is to minimize a nonlinear function of the state trajectory the state evolves according to a nonlinear dynamics the parameters of the dynamics of the system may change at discrete times l epsilon l 0 1 according to a controlled markov chain which has finite state and action spaces under the assumption that epsilon is a small parameter we justify an averaging procedure allowing us to establish that our problem can be approximated by the solution of some deterministic optimal control problem

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

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

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

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

improved multiplex control systems dynamic reliability and stochastic optimality redundant control systems are considered in the modelling context of stochastic jump linear processes optimal control problems are formulated for a quadratic performance index and solved for different classes of feedback laws and on line information structures the resulting control algorithms provide stochastic optimality together with dynamic reliability thus improving previous conservative solutions based on a notion of stochastic stability

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

singular perturbations in manufacturing an asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing is presented a typical example of the problems considered in this paper is a production planning problem with random capacity and demand in this example it is assumed that the capacity of the system fluctuates faster than the other quantities the general model considered here also has a fast controlled markov process in its state description by using the difference in the time scales of different quantities the problem is simplified by averaging out the fast process then asymptotically optimal strategies are constructed from the optimal solutions of the limiting problems the proofs of these results use the theory of viscosity solutions to dynamic programming equations however the formal construction of the asymptotically optimal strategies does not require knowledge of this theory

perturbation and stability theory for markov control problems a unified approach to the asymptotic analysis of a markov decision process disturbed by an epsilon additive perturbation is proposed irrespective of whether the perturbation is regular or singular the underlying control problem that needs to be understood is the limit markov control problem the properties of this problem are studied

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

production control of a manufacturing system with multiple machine states the production control of a single product manufacturing system with arbitrary number of machine states failure modes is discussed the objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost the optimal production policy has a special structure and is called a hedging point policy if the hedging points are known the optimal production rate is readily specified assuming a set of tentative hedging points the simple structure of the optimal policy is utilized to find the steady state probability distribution of the surplus inventory or backlog once this function is determined the average surplus cost is easily calculated in terms of the values of the hedging points the average cost is then minimized to find the optimum hedging points

ds ahp method a mathematical analysis including an understanding of uncertainty abstract the analytic hierarchy process ahp was developed to aid decision makers to rank or sort information based on a number of criteria a recent advance is the ds ahp method which incorporates the dempster shafer theory of evidence with ahp this method allows judgements on groups of decision alternatives da to be made it also offers a measure of uncertainty in the final results in this paper a mathematical analysis of ds ahp is included constructing the functional form of the preference weightings given to groups of da these functions allow an understanding of the appropriateness of the rating scale values used in the ds ahp method through evaluating the range of uncertainty able to be expressed by the decision maker

a renewal theoretic analysis of a class of manufacturing systems the authors present the partial differential equations pdes describing the transients of the probability density functions pdfs characterizing the statistical evolution of a manufacturing system producing a single product under hedging point control policies the authors demonstrate the markov renewal nature of the dynamics of the controlled process and use the system of pdes to compute the transition kernel of that renewal process this markov renewal viewpoint is particularly useful in discussing ergodicity in view of the abundant literature on the asymptotic behavior of markov renewal processes moreover besides allowing direct determination of system steady state when it exists it permits the computation of various statistics as well as in some cases the derivation of bounds on the speed of convergence to steady state

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

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

practical stability controllability and optimal control of stochastic markovian jump systems with time delays the notions of the practical stability in probability and in the pth mean and the practical controllability in probability and in the pth mean are introduced for some stochastic systems with markovian jump parameters and time varying delays sufficient conditions on such practical properties are obtained by using the comparison principle and the lyapunov function methods besides for a class of stochastic nonlinear systems with markovian jump parameters and time varying delays existence conditions of optimal control are discussed particularly for linear systems optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters

on the adaptive control for jump parameter systems vianonlinear filtering in this paper we first present an error analysis for the process of estimates generated by the wonham filter when it is used for the estimation of the finite set valued jump markov parameters of a random parameter linear stochastic system and further give bounds on certain functions of these estimates we then consider a certainty equivalence adaptive linear quadratic gaussian feedback control law using the estimates generated by the nonlinear filter and demonstrate the global existence of solutions to the resulting closed loop system a stochastic lyapunov analysis establishes that the certainty equivalence law stabilizes the markov jump parameter linear system in the mean square average sense the conditions for this result are that certain products of i the parameter process jump rate and ii the solution of the control riccati equation and its second derivatives should be less than certain given bounds an example is given where the controlled linear system has state dimension 2 finally the stabilizing properties of certainty equivalence laws which depend on i the maximum likelihood estimate of the parameter value and ii a modified version of this estimate are established under certain conditions

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

an optimal stochastic production planning problem with randomly fluctuating dem and this paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous time markov chain the problems with control production and state inventory constraints are treated it is shown that a unique optimal feedback solution exists after first showing that convex viscosity solutions to the associated dynamic programming equation are continuously differentiable

algorithms for singularly perturbed limiting average markov control problems a singularly perturbed markov decision process with the limiting average reward criterion is considered it is assumed that the underlying process is composed of n separate irreducible processes and that the small perturbation is such that it unites these processes into a single irreducible process two algorithms for the solution of the underlying limit markov control problem are presented the first of these is a linear program possessing the wolfe dantzig structure inherited from the ergodic nearly decomposable assumption in the model the second is an aggregation disaggregation policy improvement algorithm

limits of singularly perturbed control problems with statistical dynamics of fast motions we describe the limit behavior of admissible trajectories in a singularly perturbed control system as the small parameter tends to zero a general case is considered where in the limit the fast motion may infinitely rapidly oscillate in time invariant measures of the parameterized fast flow are employed to describe the limit behavior and construct the limit control problem the notion of relatively slow controls is introduced approximating properties of the limit problem within the families of relatively slow controls are verified the results are illustrated by examples

suboptimization of singularly perturbed control systems a technique different from the boundary layer method is developed to deal with singularly perturbed optimal control problems the technique is applicable in particular in the case when the optima

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

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

output feedback for a class of linear systems with stochastic jump parameters a class of linear systems subject to sudden jumps in parameter values is studied for a quadratic performance index the optimal controller has already been proposed it consists of a full state feedback that requires the synthesis of an observer for the plant state and mode to avoid this difficulty the present note develops new results that lead to the selection of the best feedback control law depending only on measurable outputs necessary optimality conditions are derived and two computationnal algorithms proposed an example is included

on the exponential stability of switching diffusion processes in this note we investigate almost sure exponential stability for a class of switching diffusion processes lyapunov type sufficient conditions to ensure this type of stability for nonlinear switching diffusions are derived the conditions are an improvement over related results in the literature since they do not rely on the moment stability of the system these conditions are then specialized to case of linear switching diffusion processes to provide easily checkable sufficient criteria for exponential stabilization and robust stability

value of additional information in multicriterion analysis under uncertainty abstract the expected value of information in classical monocriterion decision analysis has been well covered in the literature one cannot say the same thing about the multicriterion analysis particularly when one is in the presence of multicriterion aggregation procedures based on outranking relations for a ranking problematic the objective of this paper is to try to extend the bayesian approach to a multicriterion analysis in the context of uncertainty after illustrating the a posteriori analysis we shall mention some difficulties associated with the pre a posteriori analysis and the concepts of the expected value of perfect or imperfect information

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

suboptimal control of singularly perturbed systems and periodic optimization a traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by reduced problems which are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls it is shown that such an approximation is valid if and only if certain families of periodic optimization problems admit steady state solutions it is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when approximation by reduced problems is not possible

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

kazhdan s property t and c algebras abstract kazhdan s property t has recently been imported to the c world by bekka our objective is to extend a well known fact to this realm we show that a nuclear c algebra with property t is finite dimensional for all intents and purposes though the result is not surprising the proof is a bit more complicated than the group case