On the Existence of an Evasion Strategy in a Linear Differential Game with Integral Constraints

We construct an evasion strategy in a general evasion differential game, played on the Euclidean space, with one evader and any finite number of pursuers where the dynamics of the objects are given by a system of linear differential equations. Our construction of the evasion strategy is based on the ai-tau i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_i - \tau _i$$\end{document} method. We show that if the evader can successfully implement this strategy, then it can win the game against all possible strategy choices of the pursuers.