Evasion with weak superiority (Q1115826)

Consider a differential game governed by \(\dot z=Az+f(u,v)\), where A is an (n\(\times n)\)-matrix and f is a given map. The terminal set is a subspace of \(R^ n\). By analysing the minimal polynomial of A, the author gives a set of conditions under which the game is evadable, i.e., for any \(z_ 0\in R^ n\setminus M\) and pursuit control u(\(\cdot)\), there exists an evasion control v(\(\cdot)\), the value of which at time t only depends on \(\{\) z(s), u(s) \(|\) \(0\leq s\leq t\}\), such that \(d(M,z(t))>0\), for all \(t\geq 0\). It turns out that the conditions imposed may contain the case that the evader is ``less'' powerful than the pursuer, which demonstrates the title of the paper.