Sufficient Conditions for Optimal Control with State and Control Constraints

摘要

A monotonicity result is used to derive sufficient optimality conditions of considerable generality for an individual trajectory in control theory. The sufficiency theorem embodying these conditions generalizes those of Boltyanskii and Leitmann and is applied to a simple control system to which their sufficiency theorems are not applicable. Conditions on the state equations and state space are completely relaxed. The set of admissible controls is extended to the set of measurable controls and the integrand of the performance index has its membership extended to the class of bounded Borel measurable functions. The decomposition of the state space is required to be only 'plain' denumerable. (Author)