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