Second moment constraints and the control problem of Markov jump linear systems

This paper addresses the optimal solution for the regulator control problem of Markov jump linear systems subject to second moment constraints. We can characterize and obtain the solution explicitly using linear matrix inequalities techniques. The constraints are imposed on the second moment of both the system state and control vector, and the optimal solution is obtained in a computable form. To illustrate the usefulness of the approach, specially that for systems subject to abrupt variations and physical limitations, we present an application for one joint of the European Robotic Arm

Constrained Model Predictive Control Of Jump Linear Systems With Noise And Non-observed Markov State

This paper presents a variational method to the solution of the model predictive control (MPC) of discrete-time Markov jump linear systems (MJLS) subject to noisy inputs and a quadratic performance index. Constraints appear on system state and input control variables in terms of the first two moments of the processes. The information available to the controller does not involve observations of the Markov chain state and, to solve the problem a sequence of linear feedback gains that is independent of the Markov state is adopted. The necessary conditions of optimality are provided by an equivalent deterministic form of expressing the stochastic MPC control problem subject to the constraints. A numerical solution that attains the necessary conditions for optimality and provides the feedback gain sequence is proposed. The solution is sought by an iterative method performing a variational search using a LMI formulation that takes the state and input constraints into account. © 2006 IEEE.2006929934Costa, O.L.V., Fragoso, M.D., Marques, R.P., (2005) Discrete-Time Markovian Jump Linear Systems, , New York: Springer-VerlagCosta, O.L.V., Fragoso, M.D., Stability results for discrete-time linear systems with Markovian jumping parameters (1993) Journal of Mathematical Analysis and Aplications, 179, pp. 154-178Costa, O.L.V., Fragoso, M.D., Discrete-time LQ-optimal control problems for finite Markov jump parameters systems (1995) IEEE Transactions on Automatic Control, 40, pp. 2076-2088Ji, Y., Chizeck, H.J., Controllability, stabilizability and continuous-time Markovian jump linear quadratic control (1990) IEEE Transactions on Automatic Control, 35 (7), pp. 777-788Ji, Y., Chizeck, H.J., Jump linear quadratic Gaussian control: Steady-state solution and testable conditions (1990) Control-Theory and Advanced Technology, 6 (3), pp. 289-319. , SeptemberMaciejowski, J.M., (2001) Predictive Control with constraints, , Pearson Education LimitedBitmead, R.R., Gevers, M., Wertz, V., (1990) Adaptive Optimal Control: The thinking man's GPC, , Prentice HallMayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M., (2000) Constrained model predictive control: Stability and optimality, 36 (6), pp. 789-814Costa, O.L.V., Assumpção, E.O., Discrete-time constrained quadratic control of Markovian jump linear systems (1996) 35th IEEE Conference on Decision and Control, pp. 1763-1764. , Kobe, JapanCosta, O.L.V., Assumpção, E.O., Boukas, E.K., Marques, R.P., Constrained quadratic state feedback control for discrete-time Markovian jump linear systems (1999) Automatica, 35 (4), pp. 617-626Vargas, A.N., do Val, J.B.R., Costa, E.F., Receding horizon control of Markov jump linear systems subject to noise and unobservable state chain (2004) 43th IEEE Conference on Decision and Control, pp. 4381-4386. , Paradise Island, The BahamasBoyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAMVanAntwerp, J.G., Braatz, R.D., A tutorial on linear and bilinear matrix inequalities (2000) Journal of Process Control, (10), pp. 363-385Geromel, J.C., Peres, P.L.D., Souza, S.R., 2- guaranteed cost control for uncertain discrete-time linear systems (1993) Int. Journal of Control, 57, pp. 853-864Sturm, J.F., Using SeDuMi, a Matlab Toolbox for optimization over symmetric cones (1999) Optimization Methods and Software, 11-12, pp. 625-653Peaucelle, D., Henrion, D., Labit, Y., Users guide for SeDuMi interface 1.04, , http://www.laas.fr/~peaucell/ software/SeDuMiInt.html, Online, Availabl

Second moment constraints and the control problem of Markov jump linear systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper addresses the optimal solution for the regulator control problem of Markov jump linear systems subject to second moment constraints. We can characterize and obtain the solution explicitly using linear matrix inequalities techniques. The constraints are imposed on the second moment of both the system state and control vector, and the optimal solution is obtained in a computable form. To illustrate the usefulness of the approach, specially that for systems subject to abrupt variations and physical limitations, we present an application for one joint of the European Robotic Arm. Copyright (c) 2012 John Wiley & Sons, Ltd.202SI357368Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Spanish agency Fundacion Carolina ProgramaFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [FAPESP 03/06736-7]CNPq [CNPq 71557/2009-9, 304856/2007-0