Successive Pursuit

Abstract

In this Chapter we apply the Method of Resolving Functions to the solution of the problem of successive capture of several evaders by a single pursuer. The schemes with both fixed and nonfixed time of capture of each of the evaders are treated. Suggested construction proves to be very efficient in the case of “simple motions” with the preassigned order of captures. In this case the pursuer employs the strategy of “Parallel Pursuit” and, hence, the payoff functional, namely the total time of pursuit, depends only on the evaders’ controls. On the other hand, an extremum of the functional is furnished by the constant controls of the evaders and, thus, an infinite-dimensional problem of maximization of the total time of pursuit reduces to a finite-dimensional problem of constraint optimization.