Obtaining Stabilizing Stationary Controls Via Finite Horizon Cost

This paper focus on the stabilizing properties of stationary feedback controls for general nonlinear systems that are obtained by minimizing a finite horizon cost, in a receding horizon control basis. The main result is to establish exponential stability for stationary controls obtained from minimization of sufficiently large but finite time horizon cost. The approach requires a previously defined notion of closed-loop detectability of nonlinear systems, and in the present paper we introduce conditions under which the aforementioned detectability sense is verified from the open-loop system data, as is usual in linear systems. In connection, we verify that stabilizable and detectable linear time-invariant systems satisfy each of the work assumptions. © 2006 IEEE.200642974302Anderson, B.D.O., Moore, J.B., Detectability and stabilizability of time-varying discrete-time linear systems (1981) SIAM Journal on Control and Optimization, 19 (1), pp. 20-32Costa, E.F., do Val, J.B.R., Optimal cost convergence with respect to the time horizon (2003) ECC'03 European Control Conference, pp. 1-6. , Cambridge, United KingdomCosta, E.F., do Val, J.B.R., Stability of receding horizon control of nonlinear systems (2003) 42st IEEE Conference on Decision and Control, pp. 2077-2081. , Maui, Hawaii, USA, IEEECosta, E.F., do Val, J.B.R., A finite-time stability concept and conditions for finite-time and exponential stability of controlled nonlinear systems (2006) Submitted to the ACC'06 American Control ConferenceDe Nicolao, G., Strada, S., On the stability of receding-horizon LQ Control with zero-state terminal contraint (1997) IEEE Transactions on Automatic Control, 42 (2), pp. 257-260Hager, W.W., Horowitz, L.L., Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems (1976) SIAM Journal on Control and Optimization, 14 (2), pp. 295-312Ito, K., Kunisch, K., Asymptotic properties of receding horizon optimal control problems (2002) Siam Journal on Control and Optimization, 40 (5), pp. 1585-1610Jadbabaie, A., Hauser, J., On the stablity of unconstrained receding horizon control with a general terminal cost (2001) Conference on Decicion and Control 2001Kailath, T., (1980) Linear Systems, , Prentice-HallKothare, M.V., Balakrishnan, V., Morari, M., Robust constrained model predictive control using linear matrix inequalities (1996) Automatica, 32 (10), pp. 1361-1379Lee, J.W., Kwon, W.H., Choi, J., On stability of constrained receding horizon control with finite terminal weighting matrix (1998) Automatica, 34 (12), pp. 1607-1612Lee, Y.I., Kouvaritakis, B., Constrained receding horizon predictive control for systems with disturbances (1999) International Journal of Control, 72 (11), pp. 1027-1032Mayne, D.Q., Michalska, H., Receeding horizon control of nonlinear systems (1990) IEEE Transactions on Automatic Control, 35, pp. 814-824Mosca, E., Zhang, J., Stable redesign of predictive control (1992) Automatica, 28 (6), pp. 1229-1233Primbs, J.A., Nevistic, V., A new approach to stability analysis for constrained finite receding horizon control without end constraints (2000) IEEE Transactions on Automatic Control, 45, pp. 1507-1512Rawlings, J.B., Muske, K.R., The stability of constrained receding horizon control (1993) IEEE Transactions on Automatic Control, 38 (10), pp. 1512-151