THE SYNTHESIS OF UNIVERSAL FEEDBACK PURSUIT STRATEGIES IN DIFFERENTIAL-GAMES

We show how any (generalized) supersolution of the Hamilton-Jacobi equ ation can be used to construct a feedback pursuit strategy which guara ntees (to any given tolerance) a capture time not exceeding the soluti on's value. If the supersolution is the value function, then a near-op timal pursuit strategy is obtained in this way. An important feature o f the construction is its ''universal'' nature, i.e., the fact that th e feedback law is uniformly effective on compact sets of initial condi tions. This implies in particular that the feedback construction is on e that exploits nonoptimal behavior on the part of the evader.