机械系统最优控制问题中速度公路的耗散性特征
A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems
摘要：
收费公路最近获得了显着的研究兴趣，在最优控制，因为它们允许关键的见解结构的解决方案，以最优控制问题。到目前为止，主要是作为最佳操作点的稳态解进行了研究。这是在对比的时变收费公路，这是本文的重点。更具体地说，我们分析了高速公路，即受控的相对平衡，称为修剪原语，这是最佳的操作点，关于给定的成本标准。我们通过耗散性不等式来刻画速度收费公路。此外，我们还通过相应的最优性必要条件研究了最优控制问题与稳态问题之间的等价性。最后给出了一个学术实例。
英文摘要：
Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this paper. More concretely, we analyze symmetry-induced velocity turnpikes, i.e. controlled relative equilibria, called trim primitives, which are optimal operation points regarding the given cost criterion. We characterize velocity turnpikes by means of dissipativity inequalities. Moreover, we study the equivalence between optimal control problems and steady-state problems via the corresponding necessary optimality conditions. An academic example is given for illustration.
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