Deterministic Near-Optimal Control, Part 1: Necessary and Sufficient Conditions for Near-Optimality

摘要

Near-optimization is as sensible ind important as optimization for both theory and applications. This paper concerns dynamic near-optimization, or near-optimal control, for systems governed by deterministic ordinary differential equations. Necessary and sufficient conditions for near-optimal control are studied. It is shown that any near-optimal control nearly maximizes the Hamiltonian in some integral sense, and vice versa, if some additional concavity conditions are imposed. Error estimates for both the near-optimality of the controls and the near-maximality of the Hamiltonian are obtained. A number of, examples are presented to. illustrate these results.