Constrained piecewise linear systems with disturbances: Controller design via convex invariant sets

Abstract

This paper presents two control strategies under the time optimal control and model predictive control frameworks for constrained piecewise linear systems with bounded disturbances (PWLBD systems). Each of the proposed approaches uses an inner convex polytopal approximation of the non-convex domains of attraction and results in simplified control laws that can be determined off-line via multi-parametric programming. These control strategies rely on invariant sets of PWLBD systems. Thereby, approaches for the computation of the disturbance invariant outer bounds of the minimal disturbance invariant set, F ∞, and convex polytopal disturbance invariant sets are presented. The effectiveness of the approaches is assessed through numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.