Optimality Condition For The Receding Horizon Control Of Markov Jump Linear Systems With Non-observed Chain And Linear Feedback Controls

We demonstrate here that a necessary condition of optimality studied in a previous paper is in fact a necessary and sufficient condition of optimality for the receding horizon control problem of discrete-time Markov jump linear systems subject to noisy inputs. The performance index is quadratic and the information available to the controller does not involve observations of Markov chain states. Sequences of linear feedback gains that are independent of the Markov state is adopted, in accordance with the information available to the controller. We make use of an equivalent deterministic form of expressing the stochastic problem, and the complete solution given in feedback form, is obtained by dynamic programming arguments and by the benefit of some quadratic convex relations. © 2005 IEEE.200573087313Vargas, 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 BahamasCosta, O.L.V., Fragoso, M.D., Marques, R.P., (2004) 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. , SeptemberBitmead, R.R., Gevers, M., Wertz, V., (1990) Adaptive Optimal Control:the thinking man's GPC, , Sydney, Australia: Prentice HallMosca, E., (1994) Optimal, Predictive and Adaptive Control, , 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. 789-814Magni, L., Scattolini, R., Stabilizing model predictive control of nonlinear continuous time systems (2004) Annual Reviews in Control, 28, pp. 1-11Costa, E.F., do Val, J.B.R., Stability of receding horizon control of Markov jump linear systems without jump observations (2000) American Control Conference, pp. 4289-4293. , Chicago, USAdo Val, J.B.R., Başar, T., Receding horizon control of jump linear systems and a macroeconomic policy problem (1999) Journal of Economics Dynamics and Control, 23, pp. 1099-1131Park, B.-G., Kwon, W.H., Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems (2002) Automatica, 38 (7), pp. 1229-1235Park, B.-G., Kwon, W.H., Lee, J.-W., Robust receding horizon control of discrete-time Markovian jump uncertain systems (2001) IEICE Trans. on Fundamentals, 9, pp. 2272-2279Davis, M.H.A., Vinter, R.B., (1984) Stochastic Modelling and Control, , Chapman and HallLutkepohl, H., (1996) Handbook of Matrices, , Chichester: John Wiley & SonsNeudecker, H., Some theorems on matrix differentiation with special reference to Kronecker matrix products (1969) American Statistical Association Journal, pp. 953-963Brewer, J.W., Kronecker products and matrix calculus in system theory (1978) IEEE Transactions on Circuits and Systems, 25 (9), pp. 772-78