/spl epsiv/-feasible approximation of the state reachable set for discrete-time systems

This paper considers an approximation problem of the state reachable set for linear discrete-time systems with unknown but bounded exogenous inputs. A simple recursive procedure provides a sequence of enlarging convex polyhedral sets which successively approximates the state reachable set. The main contribution of this paper is to clarify a stopping criterion for the recursive procedure. The notion of positive invariance is utilized to derive the stopping criterion. The procedure makes it possible, as it is contrast to those of other existing methods, to estimate the state reachable set within a required accuracy.

[1]  W. J. Grantham.  Estimating Reachable Sets , 1981 .

[2]  E. Gilbert,et al.  Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints , 1987 .

[3]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[4]  J. E. Gayek.  A survey of techniques for approximating reachable and controllable sets , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[5]  J. Shamma.  Optimization of the l∞-induced norm under full state feedback , 1996, IEEE Trans. Autom. Control..

[6]  Masayuki Fujita,et al.  Analysis of conditions for non-violation of constraints on linear discrete-time systems with exogenous inputs , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[8]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[9]  R. Watanabe,et al.  Behavioral inclusion , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10]  K. Hirata,et al.  Systems with state and control constraints , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).