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

cluster hybrid monte carlo simulation algorithms we show that addition of metropolis single spin flips to the wolff cluster flipping monte carlo procedure leads to a dramatic increase in performance for the spin 1 2 ising model we also show that adding wolff cluster flipping to the metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious such as the spin 3 2 ising model can substantially reduce the statistical errors of the simulations a further advantage of these methods is that systematic errors introduced by the use of imperfect random number generation may be largely healed by hybridizing single spin flips with cluster flipping

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

low temperature series expansions for the spin 1 ising model the finite lattice method of series expansion has been used to extend low temperature series for the partition function order parameter and susceptibility of the spin 1 ising model on the square lattice a new formalism is described which uses two distinct transfer matrix approaches in order to significantly reduce computer memory requirements and which permits the derivation of the series to 79th order subsequent analysis of the series clearly confirms that the spin 1 model has the same dominant critical exponents as the spin 1 2 ising model accurate estimates for both the critical temperature and non physical singularities are obtained in addition evidence for a non analytic confluent correction with exponent delta 1 1 1 or 0 1 is found

generalized van der waerden identities the idea of generalized van der waerden identities is introduced to facilitate the polynomial expansion of multi spin functions of the type that are frequently encountered in theoretical studies of ising spin systems

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

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

total blow up versus single point blow up traditional thermal explosion theory is used to describe reaction initiation in condensed explosives and is limited formally to nondeformable materials kassoy and poland 4 significantly extended this theory to develop an ignition model for a reactive gas in a bounded container in order to describe the induction period during this induction period there is a spatially homogeneous pressure rise in the system which causes a com pressive heating effect in the constant volume container mathematically this compressibility of the gas is expressed by means of an integral term in the induction model for the temperature perturbation 0 x t this model is given by e ak 1 j e x t dx y x 2 0 x 0 d x 2 0

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

the spin 3 2 blume capel model with competing short and long range interactions abstract the phase diagrams of the spin 3 2 blume capel model with competing short and long range interactions were studied through the free energy density obtained by analytical methods the competition emerges when positive short range interactions of strength k arranged in a linear chain tend to establish an anti parallel spin order whereas negative long range interactions j tend to align them in parallel thus no ferromagnetic order exists for k j 0 25 so the phase diagrams were scanned by varying the values of k for 0 k j 0 25 as in other similar study done for the spin 1 case the second order frontier separating the ferromagnetic and the paramagnetic phases is transformed gradually into a first order line when k j is greater than a certain critical value accordingly there is a sub interval of k for which two tricritical points appear restricting the length of the second order frontier nevertheless for greater values of k j the ferromagnetic paramagnetic frontier becomes wholly of first order also the typical line of coexistence of the spin 3 2 blume capel model which divides two different ferromagnetic phases of magnetization m 3 2 and m 1 2 becomes more complex by giving rise to another first order line with a reentrant behavior that encloses a third ordered phase in this case the competition is such that there is a region in the phase diagram where for each spin i with s i 3 2 s i 3 2 there is another spin j where j i 1 and s j 1 2 s j 1 2 such that the absolute value of the magnetization per spin is one

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

global existence and asymptotic behavior of solutions to a nonlocal fisher kpp type problem abstract in this work we consider a nonlocal fisher kpp reaction diffusion problem with neumann boundary condition and nonnegative initial data in a bounded domain in r n n 1 with reaction term u 1 m t where m t is the total mass at time t with the help of poho aev s identity the non existence of nontrivial stationary solutions with dirichlet boundary conditions is being shown when 1 and the initial mass is greater than or equal to one the problem has nonnegative classical solutions while if the initial mass is less than one then the problem admits global solutions for n 1 2 with any 1 2 or n 3 with any 1 1 2 n moreover the asymptotic convergence to the solution of the heat equation is proved

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

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

uniform blow up rate for diffusion equations with localized nonlinear source abstract in this short paper we investigate blow up rate of solutions of reaction diffusion equations with localized reactions we prove that the solutions have a global blow up and the rate of blow up is uniform in all compact subsets of the domain

a general theory of spin one ising models in the correlated effective field approximation abstract a new correlated effective field theory of spin one ising systems namely the blume capel and blume emery griffiths models is developed using exact ising spin identities the honmura kaneyoshi differential operator technique and the concept of correlated effective field in particular the general expressions for evaluating the second order phase transition and the tricritical point of both models are obtained the present method can be applied to a wide class of spin one ising systems

statistical mechanics of the spin 3 2 blume capel model on the bethe lattice using the recursion method abstract exact expressions for the magnetization or the dipole moment the quadrupolar moment and the curie temperature of the spin 3 2 blume capel model on the bethe lattice are derived using the recursion method the thermal variations of the magnetization and quadrupolar moment order parameters are studied in depth for a range of the coupling parameter d j and a number of characteristic behaviors for their thermal variations are obtained besides the stable branches of the order parameters we find the unstable branches of them which occur at low temperatures and near the first and second order phase transition temperatures finally the phase diagram and the critical behavior of the model are discussed

probability distribution of the order parameter for the three dimensional ising model universality class a high precision monte carlo study we study the probability distribution p m of the order parameter average magnetization m for the finite size systems at the critical point the systems under consideration are the 3 dimensional ising model on a simple cubic lattice and its 3 state generalization known to have remarkably small corrections to scaling both models are studied in a cubic box with periodic boundary conditions the model with reduced corrections to scaling makes it possible to determine p m with unprecedented precision we also obtain a simple but remarkably accurate approximate formula describing the universal shape of p m

universality class of the two dimensional site diluted ising model in this work we evaluate the probability distribution function of the order parameter for the two dimensional site diluted ising model extensive monte carlo simulations have been performed for different spin concentrations p 0 70 ensuremath le p ensuremath le 1 on square lattices with linear sizes l 20 ensuremath le l ensuremath le 100 the results indicate that the universality class of the diluted ising model seems to be independent of the amount of dilution logarithmic corrections of the finite size critical temperature behavior of the model can also be inferred even for such small lattices

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

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

correlation identities and rigorous upper bounds on the critical temperature for the spin 1 blume capel model on a kagome lattice abstract spin correlation identities for the blume capel model on kagome lattice are derived and combined with rigorous correlation inequalities lead to upper bounds on the critical temperature from the spin correlation identities the mean field approximation and the effective field approximation results for the magnetization the critical frontiers and the tricritical points are obtained the rigorous upper bounds on the critical temperature improve over those effective type theories results

a spin s model on a bethe lattice we present an exact formulation of an ising spin s model on a cayley tree as a 2s dimensional nonlinear discrete map the attractors of the map are associated with the thermodynamic solutions on a bethe lattice we analyse in detail the typical half integer case s 32 with bilinear interactions and the inclusion of a crystal field there is a stable paramagnetic fixed point at high temperatures there is also a low temperature region of stability of two distinct ferromagnetic fixed points in addition to these usual attractors we detect the presence of several unstable fixed points which are however irrelevant to the thermodynamic behavior in the limit of infinite coordination of the tree the problem is simplified and we regain the standard results of a mean field approximation for s 32 with biquadratic interactions but no crystal field we confirm the existence of a ferrimagnetic phase for finite coordinations of the tree and analyse the occurrence of re entrant boundaries inside the ordered region for the typical integer spin case s 2 without biquadratic interactions we show the splitting of the first order paramagnetic boundary in agreement with mean field calculations also we confirm the existence of a ferrimagnetic phase in the s 1 case for negative biquadratic interactions

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

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

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

the two and three dimensional spin 3 2 random blume capel model by the position space renormalization group we use the migdal kadanoff renormalization group technique to study the spin 3 2 blume capel model under a random crystal field in the two and three dimensional cases studying the fixed points and the phase diagrams established we find interesting results allowing us to understand the critical behavior of the system in the two dimensional case the randomness even in small amounts removes completely the first order transition between the two ferromagnetic phases present replacing it by a smooth continuation only the second order phase transitions occur in the three dimensional case the first order phase transition disappears only at a certain threshold of randomness below this threshold we observe the presence of an end point where finishes the first order transition line inside the ferromagnetic phases this end point reaches t 0k at a critical value of probability beyond which only the second order transitions occur

uniform blow up profiles for nonlinear and nonlocal reaction diffusion equations abstract in this paper we investigate the blow up properties of positive solutions to the following integro parabolic equations u t u e u 1 e u d x where 0 and 1 and x r n x r for the radially symmetric and non increasing initial data we give a complete classification in terms of global and single point blow up according to the parameters and moreover the blow up rates are also determined in each case particularly for the special case and n 2 it will be proved that the blow up rate at x 0 is faster than that at the other point x 0 this seems to be a new phenomenon for this kind of problem

new effective field theory for the blume capel model abstract a new type of effective field theory that has recently been used with success for many applications concerning the usual two state ising model is herein extended to the blume capel model the method which can explicitly and systematically include correlation effects is illustrated in several lattice structures by employing its simplest approximate version in which spin spin correlations are neglected it is shown that this approximative procedure although analytically simple provides in particular a vanishing critical temperature for one dimensional systems and leads to results quite superior to those currently obtained within the molecular field approximation for higher dimensional systems within this framework we discuss as functions of temperature and for any values of the anisotropy parameter d the order parameter the thermal average of the square of the single site spin variable the internal energy and the specific heat as well as the ferromagnetic phase stability limit whenever comparison is possible a satisfactory qualitative and to a certain extent quantitative agreement is observed with results available in the literature in which more sophisticated treatments are used in particular our result for the tricritical point at which the system exhibits a first order phase transition is in quite good agreement with those obtained by using series expansion methods

total versus single point blow up of solutions of a semilinear parabolic equation with localized reaction abstract in this paper we study the initial boundary value problem of a semilinear parabolic equation with localized reaction p u t u u p u q x t x t b 0 t u x t 0 x t b 0 t u x 0 u 0 x x b where b is a unit ball in r n x b and p q 0 for the case x 0 we completely classify blow up solutions of p into total blow up cases and single point blow up cases according to the values p and q moreover we give the blow up rates of solutions near the blow up time for the other case x 0 we show total blow up and single point blow up of solutions of p in some cases depending on p and q

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

a nonlocal reaction diffusion equation and its relation with fujita exponent abstract this paper is concerned with a type of nonlinear reaction diffusion equation which arises from the population dynamics the equation includes a certain type reaction term u 1 r n u d x of dimension n 1 and 0 an energy methods based proof on the existence of global solutions is presented and the qualitative behavior of solution which is decided by the choice of is exhibited more precisely for 1 1 1 2 p where p is the exponent appears in sobolev s embedding theorem defined in 3 the equation admits global solution for any nonnegative initial data especially in the case of n 2 and 1 the exponent 1 2 n is exactly the well known fujita exponent the global existence result obtained in this paper shows that by switching on the nonlocal effect i e from 0 to 0 the solution s behavior differs distinctly that s from finite time blow up to global existence

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

blow up behavior for a nonlinear heat equation with a localized source in a ball in this paper we consider the initial boundary value problem of a semilinear parabolic equation with local and non local localized reactions in a ball ut u up uq x t in b r where p q 0 b r x rn x 1 there exist blow up solutions of this problem for large initial data we treat the radially symmetric and one peak non negative solution u x t u r t r x of this problem we give the complete classification of total blow up phenomena and single point blow up phenomena according to p and q i if q 1 or p q 2 then single point blow up occurs whenever solutions blow up ii if 1 p q both phenomena total blow up and single point blow up occur depending on the initial data iii if p 1 q total blow up occurs whenever solutions blow up iv if max p q 1 every solution exists globally in time

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

critical behavior of the two dimensional spin diluted ising model via the equilibrium ensemble approach the equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two dimensional ising model in the presence of quenched random site dilution the numerical transfer matrix technique in semi infinite strips of finite width together with phenomenological renormalization and conformal invariance is particularly suited to putting the equilibrium ensemble approach to work a method by which to extract with great precision the critical temperature of the model is proposed and applied a more systematic finite size scaling analysis than in previous numerical studies has been performed a parallel investigation along the lines of the two main scenarios currently under discussion namely the logarithmic corrections scenario with critical exponents fixed in the ising universality class versus the weak universality scenario critical exponents varying with the degree of disorder is carried out in interpreting our data maximum care is constantly taken to be open to both possibilities a critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite size data s1063 651x 99 16110 5

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

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

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

universality and double critical end points a double critical end point in the two dimensional spin 3 2 blume capel model is studied via extensive monte carlo simulations the resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points

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

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

the general spin blume capel model a study of the multicritical behavior using effective field theory abstract the general spin blume capel model is studied by using an effective field theory with correlation an expression for the free energy within the effective field theory is proposed and the complete phase diagram is constructed in the temperature and single ion anisotropy plane the first order transition lines are obtained by maxwell construction comparison between free energies beyond first order transitions at low temperatures the results show second order transitions and tricritical points as well as a variety of double critical endpoints the existence of the tricritical point and the number of critical endpoints strongly depend on the value of the spin

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