Invariant Sets and Control Synthesis for Switching Systems with Safety Specifications

Abstract

A structural procedure is proposed for solving the problem of maximal safe-set determination based on maximal controlled invari- ant sets. However, the procedure is not guaranteed to converge in a finite number of steps. The procedure is made computationally appealing first by linearizing and discretizing the dynamical systems and, second, by using an inner approximation of these sets that, together with the classical outer approximation, yields tight bounds for an error due to the truncation of the procedure after a finite number of steps. The theory is applied to idle-speed regulation in engine control.