Invariant manifolds in optimal system synthesis

摘要

A new approach is proposed to deriving the necessary control optimality conditions, which is based on invariant manifolds and a feature of the actual motion of a dynamic system that is determined by an analog of Hamilton's principle for the action integral in the presence of nonpotential forces. Pontryagin variation is applied to that integral to obtain the necessary optimality conditions in the form of a maximum principle without the introduction of a conjugate-variable vector. This simplifies optimal control synthesis.