摘要：AbstractThe optimal control problem of connecting any two trajectories with typical behavior, such that this behavior maximally persists during the transient, is put forth and a compact solution is obtained for a general class of behaviors. The behavior is understood in the context of Willems’s theory and is characterized as the kernel of some operator. As a solution exhibiting the same behavior cannot exist, a maximally persistent solution is defined as one that will be as close as possible in a precise sense to the behavior. The problem is linked to the idea of controllability as presented by Willems and draws its roots from quasi-static transitions in thermodynamics, and the embedding problem of Whitney. It is shown that the important class of periodic behaviors, applicable to gaits in locomotion, amounts to modeling by functional difference and differential equations.
关键词：KeywordsODE-modelingfunctional differential equationsoptimal control
