Staticization, its dynamic program and solution propagation
Staticization, its dynamic program and solution propagation
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静态化、动态规划和解传播
DOI：
10.1016/j.automatica.2017.03.004
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
P. Dower
中科院分区：
文献类型：
--
作者：
W. McEneaney;P. Dower
考虑动力系统的定态作用公式。利用静止作用公式可以生成一类两点边值问题（TPBVP）的基本解。一个解决固定点的收益作为一个函数的输入，而不是最小化/最大化，这是一个任务，这是显着不同的最优控制问题。对于包含定常作用形式的一类问题，得到了一个动态规划原理（DPP）和一个Hamilton Jacobi偏微分方程（HJ PDE）。虽然收益的凸性（或凸性）可能会随着时间的推移而消失，但稳定点仍然存在，并且必须能够使用DPP和/或HJ PDE来向前求解这样的时间范围。在线性/二次模型中，这导致需要传播微分Riccati方程的解经过有限的逃逸时间。这种传播也需要在（非线性）n体问题的配方，其中潜在的是通过双凸对偶表示。这里开发的动态规划工具是适用的。
Stationary-action formulations of dynamical systems are considered. Use of stationary-action formulations allows one to generate fundamental solutions for classes of two-point boundary-value problems (TPBVPs). One solves for stationary points of the payoff as a function of inputs rather than minimization/maximization, a task which is significantly different from that in optimal control problems. Both a dynamic programming principle (DPP) and a Hamilton–Jacobi partial differential equation (HJ PDE) are obtained for a class of problems subsuming the stationary-action formulation. Although convexity (or concavity) of the payoff may be lost as one propagates forward, stationary points continue to exist, and one must be able to use the DPP and/or HJ PDE to solve forward to such time horizons. In linear/quadratic models, this leads to a requirement for propagation of solutions of differential Riccati equations past finite escape times. Such propagation is also required in (nonlinear) n-body problem formulations where the potential is represented via semiconvex duality. The dynamic programming tools developed here are applicable.