Receding–Horizon Control of LTI Systems with Quantized Inputs∗

This paper deals with the stabilization problem for a particular class of hybrid systems, namely discrete– time linear systems subject to a uniform (a priori fixed) quantization of the control set. Results of our previous work on the subject provided a description of minimal (in a specific sense) invariant sets that could be rendered maximally attractive under any quantized feedback strategy. In this paper, we consider the design of stabilizing laws that optimize a given cost index on the state and input evolution on a finite, receding horizon. Application of Model Predictive Control techniques for the solution of similar hybrid control problems through Mixed Logical Dynamical reformulations can provide a stabilizing control law, provided that the feasibility hypotheses are met. In this paper, we discuss precisely what are the shortest horizon length and the minimal invariant terminal set for which it can be guaranteed a stabilizing MPC scheme. The final paper will provide an example and simulations of the application of the control scheme to a practical quantized control problem. ∗Support from “European Project Recsys–Ist–2001–37170” and from “Progetto coordinato Agenzia 2000 CNR C00E714” †Centro “E. Piaggio”, Università di Pisa; e–mail: [email protected] ‡Centro “E. Piaggio”, Università di Pisa; e–mail: [email protected] §Dip. di Ingegneria dell’Informazione, Università di Siena; e–mail: [email protected] ¶Corresponding Author: Centro “E. Piaggio”, Università di Pisa, Via Diotisalvi 2 – 56126 Pisa . Tel: +39–050554134 ; Fax: +39–050550650 ; e–mail: [email protected]