Abstract--We consider a class of controllers which assure that, for a specific class of uncertain dynamical systems, the system state avoids a prescribed region. Each controller is a combination of a memoryless controller and an adaptive controller. The utilization of these controllers is demonstrated by application to two examples, a linear system with a bounded avoidance set and a planar pursuit-evasion problem. Numerical simulations illustrate the results. 1. INTRODUCTION For a given class of uncertain dynamical systems we consider the problem of obtaining controllers which assure that the state of the system avoids a prescribed region of the state space; that is, every state motion which starts outside the region remains outside. The uncertain elements may be due to the imperfectly known actions of other agents (e.g. pursuers) or an uncertain environment, or both. A class of such problems is treated in Refs [1] and [2] employing memoryless controllers. With these controllers, the present control depends only on the present time and state. Here, we follow Ref. [3] in which each of the controllers considered is a combination of a memoryless controller and an adaptive controller. The adaptive controllers generate controls which depend on the previous history of the state; they are dynamic controllers. By considering adaptive controllers, we assure avoidance for a larger class of systems than that considered in Ref. [1]. Sufficient conditions are given for the existence of these avoidance controllers. An explicit characterization of the adaptive controllers in terms of appropriate Lyapunov-type functions is also presented. These conditions are utilized to obtain avoidance controllers for a general class of uncertain linear systems. We also apply the results to obtain evasion strategies for planar pursuit-evasion problems in which the only knowledge available on the pursuer's speed is that it is bounded; not even the bound is known. The above applications are illustrated with numerical simulations. 2. GENERAL PROBLEM STATEMENT Consider an uncertain system described by
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