Constructive Theory of Positional Differential Games and Generalized Solutions to Hamilton—Jacobi Equations

Abstract

This chapter first presents the basic notions of the theory of positional differential games, including the notions of feedback strategy and stable bridge, and of the theory of minimax solutions for Hamilton—Jacobi equations. In this framework constructive and numerical methods are developed for time-optimal as well as fixed-horizon games by the procedure of extremal aiming. Mixed feedback strategies and counterstrategies are also studied. Finally the numerical algorithms are tested on some examples.