lyapunov iterations for optimal control of jump linear systems at steady state in this paper we construct a sequence of lyapunov algebraic equations whose solutions converge to the solutions of the coupled algebraic riccati equations of the optimal control problem for jump linear systems the obtained solutions are positive semidefinite stabilizing and unique the proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced order decoupled lyapunov equations several examples are included to demonstrate the procedure

some remarks about stochastic controllability for linear composite systems sufficient conditions of e controllability for a class of continuous parameter stochastic linear composite systems are established in this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure an example is given to illustrate the criterion

mice multiple peak identification characterization and estimation summary mice multiple peak identification characterization and estimation is a procedure for estimating a lower bound of the number of frequency peaks and for estimating the frequency peak parameters the leading application is protein structure determination using nuclear magnetic resonance nmr experiments nmr frequency data are multiple peak data where each frequency peak corresponds to two connected atoms in the three dimensional protein structure we analyze the nmr frequency data through a series of steps a preliminary step for separating the signal from the background followed by identification of local maxima up to a noise level dependent threshold estimation of the frequency peak parameters using an iterative algorithm and detection of mixtures of peaks using hypothesis testing

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

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

implicit method for incompressible flow calculations in three dimensional ducts and cascades a method is presented for the numerical solution of the incompressible navier stokes equations in three dimensional ducts and cascades both laminar and turbulentows are resolved the latter through the k turbu lence model the method is based on an elliptic formulation which consists of the sequential solution of the mean ow and the turbulence equations through an approximate factorization technique the cost of factorization is minimized through the formation and inversion of a single matrix for all but the continuity equations the conti nuity constraint is enforced by means of thepressure correction technique forwhich a moreef cient variant of the approximate factorization scheme is employed the method exhibitsgood convergence characteristics asdepicted from the analyzed three dimensional problems the prediction capabilities of this method are demonstrated by analyzing thelaminarowin a three dimensional bend and theturbulentowin a linearcompressorcascade with zero and nonzero tip clearance for cascadeow problems with nonzero tip clearances a variant of the present method accommodating multiple patched subdomains is devised

testing in normal mixture models when the proportions are known summary the aim of this paper is to study the behaviour of the likelihood ratio test statistic in mixture models when the proportions of the distributions are known a priori the results depend on the value of the proportion the dimensionality of the problem and whether or not the variance of the distributions is known

the modified operator strongly implicit scheme mosi as a fast elliptic solver a new fast elliptic solver is introduced that is suited for systems of finite difference equations associated with five point molecules this modified operator strongly implicit scheme mosi is a further development of the modified strongly implicit scheme msi which is an approximate lu decomposition sparse matrix solver comparisons are made between mosi and some other commonly used equation solvers which indicate that it is faster than these solvers including the msi scheme

properties of solutions of stochastic differential equations with continuous state dependent switching abstract this work is concerned with several properties of solutions of stochastic differential equations arising from hybrid switching diffusions the word hybrid highlights the coexistence of continuous dynamics and discrete events the underlying process has two components one component describes the continuous dynamics whereas the other is a switching process representing discrete events one of the main features is the switching component depending on the continuous dynamics in this paper weak continuity is proved first then continuous and smooth dependence on initial data are demonstrated in addition it is shown that certain functions of the solutions verify a system of kolmogorov s backward differential equations moreover rates of convergence of numerical approximation algorithms are dealt with

conjugate mixture models for clustering multimodal data the problem of multimodal clustering arises whenever the data are gathered with several physically different sensors observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space a solution may consist in considering multiple clustering tasks independently for each modality the main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent in this letter we show that multimodal clustering can be addressed within a novel framework conjugate mixture models these models exploit the explicit transformations that are often available between an unobserved parameter space objects and each of the observation spaces sensors we formulate the problem as a likelihood maximization task and derive the associated conjugate expectation maximization algorithm the convergence properties of the proposed algorithm are thoroughly investigated several local and global optimization techniques are proposed in order to increase its convergence speed two initialization strategies are proposed and compared a consistent model selection criterion is proposed the algorithm and its variants are tested and evaluated within the task of 3d localization of several speakers using both auditory and visual data

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

robust stability of a class of uncertain markov jump nonlinear systems this note addresses the problem of robust stability analysis for a class of markov jump nonlinear systems subject to polytopic type parameter uncertainty a condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed an estimate of a robust domain of attraction of the origin is also provided the approach is based on a stochastic lyapunov function with polynomial dependence on the system state and uncertain parameters a numerical example illustrates the proposed result

comments on robust jump linear quadratic control a mode stabilizing solution in the above paper an optimal control problem with discounting was proposed to achieve closed loop mode stabilization for linear systems with jump parameters the paper used the unstated hypothesis that the diagonal entries of the generator of the jump process are equal this correspondence discusses the situation in the general case

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

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

brief paper backstepping controller design for a class of stochastic nonlinear systems with markovian switching a more general class of stochastic nonlinear systems with irreducible homogenous markovian switching are considered in this paper as preliminaries the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a lyapunov function the state feedback controller is designed by regarding markovian switching as constant such that the closed loop system has a unique solution and the equilibrium is asymptotically stable in probability in the large the output feedback controller is designed based on a quadratic plus quartic form lyapunov function such that the closed loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded in probability solution in the biased case

compressible flow airfoil design using natural coordinates abstract an irrotational inviscid compressible inverse design method for two dimensional airfoil profiles is described the potential and streamfunction are used as the independent natural coordinates the physical space on which the boundaries of the airfoil are sought is mapped onto the space via a body fitted coordinate transformation a novel procedure based on differential geometry arguments is employed to derive the governing equations for the inverse problem by requiring the curvature of the flat 2 d euclidean space to be zero an auxiliary coordinate transformation permits the definition of c type computational grids on the plane resulting in a more accurate description of the leading edge region geometry is determined by integrating frenet equations along the grid lines a two parameter iterative scheme has been incorporated in the design procedure in order to assure closure of the trailing edge to validate the method inverse calculation results are compared with direct reproduction calculation results the design procedure of a new airfoil shape is also presented

a note on the aitkin rubin approach to hypothesis testing in mixture models on montre que les conditions de regularite habituellement utilisees pour obtenir des resultats asymptotiques standards ne conviennent pas meme en utilisant une distribution a priori sur le vecteur des proportions de melange

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

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

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

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

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

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

filtering based robust fault detection of fuzzy jump systems this paper studies the robust fault detection filter rfdf design problems for uncertain nonlinear markov jump systems with state delays and parameter uncertainties by means of takagi sugeno fuzzy models the dynamics of filtering error generator and the fuzzy rfdf system are constructed with the aid of the selected weighting matrix function the design objective is to find an optimal rfdf which results in a minimal difference between the reference model ideal solution and the rfdf real solution to be designed a sufficient condition is firstly established on the stochastic stability by using stochastic lyapunov krasovskii functional approach then in terms of linear matrix inequalities techniques sufficient conditions on the existence of fuzzy rfdf are presented and proved finally the design problem is formulated as an optimization algorithm simulation results illustrate that the proposed rfdf can detect the faults shortly after the occurrences

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

stability of hybrid stochastic delay systems whose discrete components have a large state space a two time scale approach abstract this work is concerned with stability of stochastic differential delay equations with markovian switching where the modulating markov chain has a large state space and is subject to both fast and slow movements under simple conditions we demonstrate that if the limit systems are p th moment exponentially stable then the original systems are p th moment exponentially stable in an appropriate sense in addition the exponential stability is also investigated moreover stability in distribution is obtained for such hybrid systems

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

uniqueness of constrained viscosity solutions in hybrid control systems we study constrained viscosity solutions with an unbounded growth for a class of first order hamilton jacobi bellman equations arising in hybrid control systems to deal with the boundary constraint and rapid growth of the solutions we construct a particular set of test functions and under very mild conditions establish a comparison theorem which gives the estimate of distance between the subsolution and the supersolution the comparison theorem implies uniqueness of the constrained viscosity solution if its existence is ensured and under some additional assumptions we give an existence result by showing that the value function is a constrained viscosity solution we then apply the obtained uniqueness results to an optimal scheduling problem and finally to stochastic manufacturing systems

a three dimensional modified strongly implicit procedure for heat conduction the application of discretizatio n techniques frequently leads to a system of algebraic equations having a welldefined coefficient structure a modified strongly implicit procedure for solving the system resulting from the modeling of heat conduction in three dimensions is presented in this work the method is derived for a 19 point scheme with the more common 7 point scheme emerging as a special case of the procedure in this way the asymmetric influence of the additional terms in the lu matrix product is weakened as a consequence the method is less sensitive to the iteration parameter and mesh aspect ratio and in addition provides considerably more rapid convergence than does the strongly implicit procedure the increased convergence is exhibited by a significant reduction in the computational cost the characteristics of the method are examined through application to several model problems and application is made to a more complex three dimensional problem comparisons with the sip strongly implicit and adi alternating direction implicit methods are provided

brief paper stochastically exponential stability and stabilization of uncertain linear hyperbolic pde systems with markov jumping parameters this paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear first order hyperbolic partial differential equations fohpdes with markov jumping parameters for which the manipulated input is distributed in space based on an integral type stochastic lyapunov functional islf the sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of spatial differential linear matrix inequalities sdlmis then an sdlmi approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition furthermore using the finite difference method and the standard linear matrix inequality lmi optimization techniques recursive lmi algorithms for solving the sdlmis in the analysis and synthesis are provided finally a simulation example is given to demonstrate the effectiveness of the developed design method

a graphical technique for determining the number of components in a mixture of normals abstract when a population is assumed to be composed of a finite number of subpopulations a natural model to choose is the finite mixture model it will often be the case however that the number of component distributions is unknown and must be estimated this problem can be difficult for instance the density of two mixed normals is not bimodal unless the means are separated by at least 2 standard deviations hence modality of the data per se can be an insensitive approach to component estimation we demonstrate that a mixture of two normals divided by a normal density having the same mean and variance as the mixed density is always bimodal this analytic result and other related results form the basis for a diagnostic and a test for the number of components in a mixture of normals the density is estimated using a kernel density estimator under the null hypothesis the proposed diagnostic can be approximated by a stationary gaussian process under the alternative hypothesis components in the mixtu

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

a note on stability of hybrid stochastic differential equations the method is different from those usual methods used in previous literature some harsh restrictions imposed on diffusion operators have been removed the differentiability of delays has been removed we studied the robustness of exponential stability respect to delays in this paper the pth moment stability of hybrid stochastic differential equations is investigated several new sufficient conditions are derived by constructing an auxiliary delayed differential equation and using the comparison principle the proposed criteria remove some harsh restrictions imposed on the diffusion operators and improve some previous related works numerical examples and simulations are given to illustrate the effectiveness of theoretical results

stability for a random evolution equation with gaussian perturbation in this paper we consider a random evolution equation which is perturbed by gaussian type noise and show how to construct its coupled solutions on the basis of the coupling results we discuss the asymptotic flatness and the stability in total variation norm for the solutions of the equation in addition we also prove the feller continuity and the existence and uniqueness of invariant measures of the solutions

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

continuity of the solution of the riccati equations for continuous time jlqp in this paper the continuity of the solution of the differential and algebraic riccati equations for a continuous time markovian jump linear quadratic control problem as a function of coefficients is verified the assumptions for this are stochastic stabilizability and observability

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

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

perturbation of multivariable linear quadratic systems with jump parameters considers the problem of the perturbation of a class of linear quadratic systems where the change from one structure for the dynamics and costs to another is governed by a finite state markov process the problem above leads to the analysis of some perturbed linearly coupled sets of riccati equations we show that the matrix obtained as the solution of the equations which determines the optimal value and control has a taylor expansion in the perturbation parameter we compute explicitly the terms of this expansion

acceleration of a two dimensional combustion code using mosi to find the pressure and pressure correction fields for a simpler based algorithm an easily implemented method for achieving modest savings in cpu time in modeling two dimensional combustor geometries is presented this method achieves its savings through the substitution of an mosi method for the more conventional adi method used to solve the pressure and pressure correction fluid flow equations of a simpler based algorithm typical cpu savings of from 10 to 20 are to be expected based on the several test cases examined in this study

stochastic stabilization of a class of nonhomogeneous markovian jump linear systems this paper deals with the problem of stochastic stability analysis and control synthesis of a class of markovian jump linear systems mjls with time varying transition probabilities tps in the discrete time domain the time varying character is considered to be in a polytopic sense the approach followed in this note is based on the use of a parameter dependent stochastic lyapunov function we give a stability condition in terms of a linear matrix inequality lmi feasibility problem the obtained results are illustrated in a numerical example

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

on eigenvalue sets and convergence rate of ito stochastic systems with markovian switching this technical note is concerned with stability analysis and stabilization of ito stochastic systems with markovian switching a couple of eigenvalue sets for some positive operator associated with the stochastic system under study are defined to characterize its stability in the mean square sense properties for these eigenvalue sets are established based on which we show that the spectral abscissa of these eigenvalues sets are the same and thus these eigenvalue sets are equivalent in the sense of characterizing the stability of the system also it is shown that the guaranteed convergence rate of the markovian jump ito stochastic systems can be determined by some eigenvalue set finally a linear matrix inequality based approach is proposed to design controllers such that the closed loop system has guaranteed convergence rate some numerical examples are carried out to illustrate the effectiveness of the proposed approach the research in this technical note opens several perspectives for future work stated as some open problems

stochastic stability analysis of fault tolerant control systems in the presence of noise the stochastic stability of fault tolerant control systems ftcss in the presence of noise are analyzed using the lyapunov function approach in particular the ftcs with a markovian fault detection and isolation process having transition probabilities conditioned on the state of another markovian process representing component failures is considered the almost sure asymptotic stability in probability and the exponential stability in the mean square are considered specifically a testable necessary and sufficient condition for the exponential stability in the mean square is derived a numerical example is presented to illustrate the theoretical analysis

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

robust stability and boundedness of nonlinear hybrid stochastic differential delay equations one of the important issues in the study of hybrid stochastic differential delay equations sddes is the automatic control with consequent emphasis being placed on the asymptotic analysis of stability and boundedness in the study of asymptotic properties the robust stability has received a great deal of attention the theory of robust stability shows how much perturbation a given stable hybrid sdde can tolerate so that its perturbed system remains stable almost all results so far on the robust stability require that the underlying sddes be either linear or nonlinear with linear growth condition however little is known on the robust stability of nonlinear hybrid sddes without the linear growth condition which is one of the key topics in this paper the other key topic is the robust boundedness the aim here is to answer the question how much perturbation can a given asymptotically bounded hybrid sdde tolerate so that its perturbed system remains asymptotically bounded

estimation and hypothesis testing in finite mixture models summary finite mixture models are a useful class of models for application to data when sample sizes are not large and the number of underlying densities is in question likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter x and the parameter of the underlying densities 0 are problematical our approach places a prior distribution on x and estimates 0 by maximizing the likelihood of the data given 0 with x integrated out advantages of this approach computational issues using the em algorithm and directions for further work are discussed the technique is applied to two examples

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

synchronization of markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time varying delays the paper investigates the synchronization stability problem for a class of complex dynamical networks with markovian jumping parameters and mixed time delays the complex networks consist of m modes and the networks switch from one mode to another according to a markovian chain with known transition probability the mixed time delays are composed of discrete and distributed delays the discrete time delay is assumed to be random and its probability distribution is known a priori in terms of the probability distribution of the delays the new type of system model with probability distribution dependent parameter matrices is proposed based on the stochastic analysis techniques and the properties of the kronecker product delay dependent synchronization stability criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

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

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

almost sure stabilization for feedback controls of regime switching linear systems with a hidden markov chain this work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown markov chain the control system displays continuous dynamics represented by differential equations and discrete events given by a hidden markov chain in the previous investigation on this class of problems averaging criteria were used which provides only the system behavior in some expectation sense a closer scrutiny of the system behavior necessarily requires the consideration of sample path properties different from previous work on stabilization of adaptive controlled systems with a hidden markov chain where average criteria were considered this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes under simple conditions it is shown that as long as the feedback controls have linear growth in the continuous component the resulting process is regular moreover by appropriate choice of the lyapunov functions it is shown that the adaptive system is stabilizable almost surely as a by product it is also established that the controlled process is positive recurrent

a note on mgr methods by mgr we denote a class of special highly efficient multigrid methods for solving h discrete elliptic differential equations unlike standard multigrid methods 4 9 18 mgr methods are characterized by intermediate grids between the given h grid and the 2h grid and by special fine to coarse and coarse to fine grid transfer techniques the mgr idea has been conceived 13 7 by the second author in trying to extend the range of applicability of the total reduction method 15 16 to more general problems described in a somewhat different way methods of mgr type have in the meantime also been considered by braess 1 3 and meis 11 the convergence properties of the simplest mgr method mgr 0 are essentially improved if it is combined with one step of checkered gauss seidel iteration mgr ch for the model problem of poisson s equation in the unit square for example the spectral radius decreases from 12 to 227 by such a modification whereas the computational effort is not essentially enlarged for poisson like equations mgr ch yields the fastest iterative solver known so far other mgr variants are particularly suitable for anisotropic operators

parallel computation of the solutions of coupled algebraic lyapunov equations a parallel algorithm for solving systems of coupled lyapunov equations associated with linear jump parameter systems is introduced the recursive scheme is based on solving independent reduced order lyapunov equations monotonicity of convergence is established

delay dependent robust stabilization for uncertain discrete time fuzzy markovian jump systems with mode dependent time delays this paper deals with the problem of delay dependent robust stabilization for uncertain discrete time fuzzy markovian jump systems with mode dependent time varying delays a delay dependent stochastic stability condition for a fuzzy markovian jump system with two levels of structure is obtained based on a new lyapunov functional the lyapunov functional depends not only on the fuzzy basis functions but also on the system modes furthermore a delay dependent sufficient condition for the solvability of the robust stabilization problem is proposed in terms of linear matrix inequalities finally a simulation example is given to show the effectiveness of the proposed design method

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

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

rotational compressible inverse design method for two dimensional internal flow configurations the development of a rotational inviscid compressible inverse design method for two dimensional internal flow configurations is described rotationality is due to incoming entropy gradient whereas total enthalpy is considered to be constant throughout the flowfield the method is based on the potential function stream function formulation the clebsch formulation is adopted to decompose the velocity vector into a potential and a rotational part the physical space on which the boundaries of the flowfield are sought is mapped onto the 0 v7 space via a body fitted coordinate transformation a novel procedure based on differential geometry arguments is employed to derive the governing equation for the velocity the velocity equation solved in conjunction with a transport equation for a thermal drift function provide the flowfield without any geometry feedback an auxiliary orthogonal computational grid adapted to the solution is employed geometry is determined by integrating frenet equations of the grid lines inverse calculation results are compared with results of direct reproduction calculations

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

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

transportation cost inequalities for diffusions with jumps and its application to regime switching processes abstract by using the malliavin calculus we establish the t 1 transportation cost inequalities for stochastic differential equations with jumps which generalizes the results in 14 as an application we establish the t 1 transportation cost inequalities for regime switching diffusion processes

on a logistic mixture autoregressive model summary we generalise the mixture autoregressive mar model to the logistic mixture autoregressive with exogenous variables lmarx model for the modelling of nonlinear time series the models consist of a mixture of two gaussian transfer function models with the mixing proportions changing over time the model can also be considered as a generalisation of the self exciting threshold autoregressive setar model and the open loop threshold autoregressive tarso model the advantages of the lmarx model over other nonlinear time series models include a wider range of shape changing predictive distributions the ability to handle cycles and conditional heteroscedasticity in the time series and better point prediction estimation is easily done via a simple em algorithm and the model selection problem is addressed the models are applied to two real datasets and compared with other competing models

a note on an lqg regulator with markovian switching and pathwise average cost we study a linear system with a markovian switching parameter perturbed by white noise the cost function is quadratic under certain conditions we find a linear feedback control which is almost surely optimal for the pathwise average cost over the infinite planning horizon

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

algebraic riccati equation and symplectic algebra questions of existence uniqueness and the parametric dependence of solutions of the algebraic riccati equation are considered the different criteria for the solubility of this equation are obtained with the help of symplectic algebra

on the iterative refinement of matrix upper bounds for the solution of continuous coupled algebraic riccati equations abstract in this paper we develop a new approach for the iterative refinement algorithm along with fully mathematical justifications which sharpens matrix solution upper bounds for the well known continuous coupled algebraic riccati equation ccare our methodology is studied within a broader framework recently proposed in xu in press several desirable properties of the algorithm are then established which include the strict monotonicity and convergence of the sequences generated by the algorithm thus strengthening the existing results in the literature for computing tighter matrix upper solution bounds for the ccare in addition new admissibility conditions within the general framework are proposed which guarantee tighter matrix upper solution bounds to be computed from the algorithm

comparison principle and stability of ito stochastic differential delay equations with poisson jump and markovian switching abstract in this paper the comparison principle for the nonlinear ito stochastic differential delay equations with poisson jump and markovian switching is established later using this comparison principle we obtain some stability criteria including stability in probability asymptotic stability in probability stability in the p th mean asymptotic stability in the p th mean and the p th moment exponential stability of such equations some known results are generalized and improved

mixtures of experts of autoregressive time series asymptotic normality and model specification we consider a class of nonlinear models based on mixtures of local autoregressive time series at any given time point we have a certain number of linear models denoted as experts where the vector of covariates may include lags of the dependent variable additionally we assume the existence of a latent multinomial variable whose distribution depends on the same covariates as the experts that determines which linear process is observed this structure denoted as mixture of experts me is considerably flexible in modeling the conditional mean function as shown by jiang and tanner we present a formal treatment of conditions to guarantee the asymptotic normality of the maximum likelihood estimator mle under stationarity and nonstationarity and under correct model specification and model misspecification the performance of common model selection criteria in selecting the number of experts is explored via monte carlo simulations finally we present applications to simulated and real data sets to illustrate the ability of the proposed structure to model not only the conditional mean but also the whole conditional density

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching