Singular controls in a given stepwise control problem

摘要

The Goursat-Darboux stepwise problem of systems control, i.e., the multi-stage problem of control of systems with distributed parameters, is considered. Second-order formulas for the increment in the quality functional are constructed. In investigating these formulas on needle variations in the control, a number of necessary Pontryagin maximum principle-type optimality conditions is obtained and a singular case is studied.