Yu. I. Berdyshev
The problem of consecutive touring in prescribed order of a system of smooth manifolds moving in phase space by nonlinear controlled object is considered. The quality of the process is valuated by the sum of terminal criterions calculated on these manifolds. The necessary conditions of optimality of control and of time moments of convergence in the form of Pontryagin's maximum principle are obtained, which do not exploit the time decomposition. Here the touring problem does not split into a number of consecutively solved "two-point"problems, and choosing a control which realizes the transition from one "target" to another, we take into account an information about all subsequent "targets" remaining to visit.