Stability analysis of markovian jump systems with multiple delay components and polytopic uncertainties

This paper investigates the stability problem of Markovian jump systems with multiple delay components and polytopic uncertainties. A new Lyapunov-Krasovskii functional is used for the stability analysis of Markovian jump systems with or without polytopic uncertainties. Two numerical examples are provided to demonstrate the applicability of the proposed approach. © Springer Science+Business Media, LLC 2011.published_or_final_versio

On the Robust Control of Continuous-time Markov Jump Linear Systems Subject to Block-diagonal Uncertainty

Abstract-This paper addresses the robust H 2 2 2 and H ∞ ∞ ∞ control problems for continuous-time Markov jump linear systems subjected to block-diagonal perturbations. The proposed approach features the introduction of more powerful scaling techniques than the ones available in the current Markov jump linear systems literature. We further propose uncertaintydependent LMI design methods to treat the case of polytopic uncertainty on the transition rates of the Markov process. In the end of the paper, an application of the main results is illustrated with a numerical example

Optimal control of DC-DC buck converter via linear systems with inaccessible Markovian jumping modes

The note presents an algorithm for the average cost control problem of continuous-time Markov jump linear systems. The controller assumes a linear state-feedback form and the corresponding control gain does not depend on the Markov chain. In this scenario, the control problem is that of minimizing the long-run average cost. As an attempt to solve the problem, we derive a global convergent algorithm that generates a gain satisfying necessary optimality conditions. Our algorithm has practical implications, as illustrated by the experiments that were carried out to control an electronic dc–dc buck converter. The buck converter supplied a load that suffered abrupt changes driven by a homogeneous Markov chain. Besides, the source of the buck converter also suffered abrupt Markov-driven changes. The experimental results support the usefulness of our algorithm.Peer ReviewedPostprint (author's final draft

Normas e estabilidade para modelos estocásticos cuja variação do controle e do estado aumentam a incerteza

Orientador: João Bosco Ribeiro do ValDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Essa dissertação de mestrado gira em torno da discussão sobre controle de sistemas incertos. Modelos matemáticos utilizados como base para o design de controladores automáticos são naturalmente uma representação aproximada do sistema real, o que, em conjunto com perturbações externas e dinâmica não modelada, gera incertezas a respeito dos sistemas estudados. Na literatura de controle, este tema vêm sendo discutido frequentemente, em particular nas sub-áreas de controle estocástico e controle robusto. Dentre as técnicas desenvolvidas dentro da teoria de controle estocástico, uma proposta recente se diferencia das demais por basear-se na idéia de que variações abruptas na política de controle possam acarretar em maiores incertezas a respeito do sistema. Matematicamente, essa noção é representada pelo uso de um ruído estocástico dependente do módulo da ação de controle, e a técnica foi apelidada de VCAI - acrônimo para variação do controle aumenta a incerteza. A definição da política de controle ótima correspondente, obtida por meio do método de programação dinâmica, mostra a existência de uma região ao redor do ponto de equilíbrio para a qual a política ótima é manter a ação de controle do equilíbrio inalterada, um resultado que parece particular à abordagem VCAI, mas que pode ser relacionado a políticas de gerenciamento cautelosas em áreas como economia e biologia. O problema de controle ótimo VCAI foi anteriormente resolvido ao adotar-se um critério de custo quadrático descontado e um horizonte de otimização infinito, e nessa dissertação nós utilizamos essa solução para atacar o problema de custo médio a longo prazo. Dada certa semelhança entre a estrutura do ruído estocástico na abordavem VCAI e modelos utilizados na teoria de controle robusto, discutimos ainda possíveis relações entre a abordagem proposta e controladores robustos. Discutimos ainda algumas possíveis aplicações do modelo propostoAbstract: This work discusses a new approach to the control of uncertain systems. Uncertain systems and their representation is a recurrent theme in control theory: approximate mathematical models, unmodeled dynamics and external disturbances are all sources of uncertainties in automated systems, and the topic has been extensively studied in the control literature, particularly within the stochastic and robust control research areas. Within the stochastic framework, a recent approach, named CVIU - control variation increases uncertainty, for short -, was recently proposed. The approach differs from previous models for assuming that a control action might actually increase the uncertainty about an unknown system, a notion represented by the use of stochastic noise depending on the absolute value of the control input. Moreover, the solution of the corresponding stochastic optimal control problem shows the existence of a region around the equilibrium point in which the optimal action is to keep the equilibrium control action unchanged. The CVIU control problem was previously solved by adopting a discounted quadratic cost formulation, and in this work we extend this previous result and study the corresponding long run average control problem. We also discuss possible relations between the CVIU approach and models from robust control theory, and present some potential applications of the theory presented hereMestradoAutomaçãoMestre em Engenharia Elétrica2016/02208-6, 2017/10340-4FAPES

On The Observability And Detectability Of Continuous-time Markov Jump Linear Systems

The paper introduces a new detectability concept for continuous-time Markov jump linear systems with finite Markov space that generalizes previous concepts found in the literature. The detectability in the weak sense is characterized as mean square detectability of a certain related stochastic system, making both detectability senses directly comparable. The concept can also ensure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is unique and stabilizing, making other concepts redundant. The paper also obtains a set of matrices that plays the role of the observability matrix for deterministic linear systems, and it allows geometric and qualitative properties. Tests for weak observability and detectability of a system are provided, the first consisting of a simple rank test, similar to the usual observability test for deterministic linear systems. The complete results are presented in [3].219941999Brewer, J.W., Kronecker products and matrix calculus in system theory (1979) IEEE Trans. Circuits Systems I Fund. Theory Appl., 25, pp. 772-781Costa, E.F., Do Val, J.B.R., On the detectability and observability of discrete-time Markov jump linear systems (2001) Systems Control Lett., 44, pp. 135-145Costa, E.F., Do Val, J.B.R., On the detectability and observability of continuous-time Markov jump linear systems (2002) SIAM J. Control Optim., 41 (4), pp. 1295-1314Costa, O.L.V., Do Val, J.B.R., Geromel, J.C., Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis (1999) Automatica J. IFAC, 35, pp. 259-268Costa, O.L.V., Fragoso, M., Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems (1995) IEEE Trans. Automat. Control, 40, pp. 2076-2088Do Val, J.B.R., Geromel, J.C., Costa, O.L.V., Solutions for the linear quadratic control problem of Markov jump linear systems (1999) J. Optim. Theory Appl., 103, pp. 283-311Ji, Y., Chizeck, H.J., Controllability, stabilizability and continuous time Markovian jump linear quadratic control (1990) IEEE Trans. Automat. Control, 35, pp. 777-788Morozan, T., Stability and control for linear systems with jump Markov perturbations (1995) Stochastic Anal. Appl., 13, pp. 91-11

H2 And H∞ State-feedback Control Of Continuous-time Mjls With Uncertain Transition Rates?

This paper addresses the H2 and the H∞ state-feedback control of Markov Jump Linear Systems (MJLS) in continuous-time through LinearMatrix Inequalities (LMIs).We derive new necessary and sufficient LMI conditions for the case with completely known transition rates which are affine with respect to these parameters. Then, we treat the case where transition rates are considered uncertain, but belong to a given convex set. We illustrate the quality of our results through a numerical example.22372241Alsace Region,et al.,Groupement de Recherche - Modeling, Analysis and Control of Dynamical Systems (GdR MACS),MathWorks,Siemens,Strasbourg.euBoukas, E.-K., (2006) Stochastic Switching Systems, , BirkhäuserCosta, O.L.V., Do Val, J.B.R., Geromel, J.C., Continuous time state-feedback h2-control of markovian jump linear systems via convex analysis (1999) Automatica, 35, pp. 259-268Costa, O.V.L., Fragoso, M.D., Todorov, M.G., (2013) Continuous- Time Markov Jump Linear Systems. Probability and its Applications, , SpringerDe Farias, D.P., Geromel, J.C., Do Val, J.B.R., A note on robust control of markov jump linear uncertain systems (2002) Optimal Control Applications and Methods, 23, pp. 105-112De Farias, D.P., Geromel, J.C., Do Val, J.B.R., Costa, O.L.V., Output feedback control of markov jump linear system in continuous-time (2000) IEEE Transaction on Automatic Control, 45, pp. 944-949Fioravanti, A.R., Geromel, J.C., Gonçalves, A.P.C., Dynamic output feedback control of discrete-time markov jump linear systems through linear matrix inequalities (2009) SIAM Journal on Control and Optimization, 48, pp. 573-593Fioravanti, A.R., Geromel;alves, Gonçalves, A.P.C., H1 robust and networked control of discrete-time mjls through lmis (2012) Journal of the Franklin Institute, 349, pp. 2171-2181Ji, Y., Chizeck, H.J., Controlability, stabilizability, and continuoustime markovian jump linear quadratic control (1990) IEEE Transactions on Automatic Control, 35, pp. 777-788Leon-Garcia, A., (2007) Probability, Statistics, and Random Processes for Electrical Engineering, , PearsonShen, M., Yang, G.-H., New analysis and synthesis conditions for continuous markov jump linear systems with partly known transition probabilities (2012) IET Control Theory and Applications, 6, pp. 2318-2325Zhang, L., Boukas, E.K., H1 control of a class of extended markov jump linear systems (2009) IET Control Theory and Applications, 3 (7), pp. 834-842Zhang, L., Boukas, E.K., Stability and stabilization of markovian jump linear systems with partly unknown transition probabilities (2009) Automatica, 45, pp. 463-468Zhang, L., Lam, J., Necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions (2010) IEEE Transactions on Automatic Control, 55 (7), pp. 1695-170