Guaranteed Avoidance Control and Holding Control

Abstract

This paper considers the problem of steering the state of a system, in the presence of disturbances, so that it avoids a specified subset of the state space. This subset is called the avoidance set and the problem is called the avoidance control problem. An avoidance control is a control which guarantees that the system does not enter the avoidance set regardless of the disturbance. A necessary condition and a sufficient condition for the existence of an avoidance control are given when the disturbance is subject to magnitude constraints. Closely related to the avoidance problem is the holding problem which is concerned with guaranteeing that the state of the system remains within a specified set. We also reinterpret our conditions for the existence of an avoidance control within the context of the holding problem.