Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances

Abstract

Piecewise affine (PWA) systems are useful models for describing non-linear and hybrid systems. One of the key problems in designing controllers for these systems is the inherent computational complexity of controller synthesis and analysis. These problems are amplified in the presence of state and input constraints and additive but bounded disturbances. In this paper, we exploit set invariance and parametric programming to devise an efficient robust time optimal control scheme. Specifically, the state is driven into the maximal robust invariant set /spl Omega//sub /spl infin// in minimum time. We show how to compute /spl Omega//spl tilde//sub /spl infin// and derive conditions for finite time computation.