Nonlinear differential game with on-line identified opposition (Q1076626)

The Lyapunov design technique and the theory of adaptive identifiers are used to provide the deterministic on-line state (feedback) information and the information on the opponent's control to each of the players in a competitive two-person zero-sum non-linearizable differential game. To this aim the identifier theory is extended to the case of time-varying parameters, and a new approach without the standard ''error-equation'' is adopted to handle the non-linearity. The information provided is of prescribed accuracy and obtainable in prescribed time. The identifiers constructed allow to obtain the standard objectives: playability for collision with a target, possibly (permanent) capture there, avoidance of an anti-target and min-max of a given cost functional. The Luenberger type observers for a linear game follow as a particular case. The method is also illustrated by an example.