歧管收费公路，修剪和对称性
Manifold Turnpikes, Trims and Symmetries
摘要：
经典的收费公路对应于最优稳态，这是最优控制问题的吸引子。在本文中，动力学系统的对称性，我们推广这一概念的流形turnpikes。具体地说，在一定条件下，一个非线性诱导流形上的必要最优性条件与降阶问题的必要条件一致。我们还提出了充分条件存在的歧管收费公路的基础上定制的概念耗散方面的流形。我们展示了如何经典的勒让德变换之间的欧拉-拉格朗日和汉密尔顿形式主义可以扩展到伴随变量。最后，我们利用开普勒问题来说明我们的发现。
英文摘要：
Classical turnpikes correspond to optimal steady states which are attractors of optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions on a symmetry-induced manifold coincide with those of a reduced-order problem under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. We show how the classical Legendre transformation between Euler-Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.
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