Adaptive control for avoidance or evasion in an uncertain environment (Q1096557)

A class of controlled systems with uncertain dynamics is considered. The problem is to obtain two controls which guarantee that the system avoids a prescribed region. Admissible controls are a pure positional strategy (memoryless controller) and a positional strategy with a parameter which integrates the information of the previous history of the state (adaptive controller). Sufficient conditions for solving this avoidance problem are given in terms of appropriate Lyapunov-type functions. The ideas are illustrated by examples of linear systems and pursuit-evasion problems.