Enlarged terminal sets guaranteeing stability of receding horizon control.(English)Zbl 1094.93544

Summary: The purpose of this paper is to relax the terminal conditions typically used to ensure stability in model predictive control, thereby enlarging the domain of attraction for a given prediction horizon. Using some recent results, we present novel conditions that employ, as the terminal cost, the finite-horizon cost resulting from a nonlinear controller $$u=-\text{sat}(Kx)$$ and, as the terminal constraint set, the set in which this controller is optimal for the finite-horizon constrained optimal control problem. It is shown that this solution provides a considerably larger terminal constraint set than is usually employed in stability proofs for model predictive control.

MSC:

 93D21 Adaptive or robust stabilization 49N35 Optimal feedback synthesis
Full Text:

References:

 [1] Chen, C.C.; Shaw, L., On receding horizon feedback control, Automatica, 18, 349-352, (1982) · Zbl 0479.93031 [2] Chmielewsky, D.; Manousiouthakis, V., On constrained infinite-time linear quadratic optimal control, Systems control lett., 29, 121-129, (1996) · Zbl 0867.49025 [3] J.A. De Doná, G.C. Goodwin, Elucidation of the state-space regions wherein model predictive control and anti-windup strategies achieve identical control policies, in: Proceedings of the American Control Conference, Chicago, 2000. [4] J.A. De Doná, G.C. Goodwin, Characterisation of regions in which model predictive control policies have a finite dimensional parameterisation, Technical Report EE99044, School of Electrical Engineering and Computer Science, The University of Newcastle, Australia. [5] Gilbert, E.G.; Tan, K.T., Linear systems with state and control constraints: the theory and applications of maximal output admissible sets, IEEE trans. automat. control, 36, 1008-1020, (1991) · Zbl 0754.93030 [6] Keerthi, S.S.; Gilbert, E.G., Optimal, infinite horizon feedback laws for a general class of constrained discrete time systemsstability and moving-horizon approximations, J. optim. theory appl., 57, 265-293, (1988) · Zbl 0622.93044 [7] D.Q. Mayne, J.A. De Doná, G.C. Goodwin, Improved stabilising conditions for model predictive control, in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, 2000, pp. 172-177. [8] Mayne, D.Q.; Rawlings, J.B.; Rao, C.V.; Scokaert, P.O.M., Constrained model predictive controlstability and optimality, Automatica, 36, 789-814, (2000) · Zbl 0949.93003 [9] Scokaert, P.O.M.; Rawlings, J.B., Constrained linear quadratic regulation, IEEE trans. automat. control, 43, 1163-1169, (1998) · Zbl 0957.93033 [10] M. Sznaier, M.J. Damborg, Suboptimal control of linear systems with state and control inequality constraints, in: Proceedings of the 26th IEEE Conference on Decision and Control, Los Angeles, 1987, pp. 761-762.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.