The turnpike property in nonlinear optimal control --- A geometric approach
The turnpike property in nonlinear optimal control --- A geometric approach
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非线性最优控制中的收费公路特性——几何方法
DOI：
10.1109/cdc40024.2019.9028863
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
E. Zuazua
中科院分区：
文献类型：
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作者：
N. Sakamoto;D. Pighin;E. Zuazua
本文利用动力系统理论，提出了一个研究收费公路性质的非线性最优控制框架。首先，它表明，收费公路般的财产出现在一般的动力系统双曲平衡，然后，将其应用到最优控制问题，以获得收费公路行为发生的充分条件。所采取的方法是几何的，并提供了见解的行为控制轨迹以及收费公路属性和稳定性和/或稳定性之间的联系，在非线性控制理论。它也使我们能够找到更简单的证明现有的结果收费公路的性质。试图消除小的限制，初始和目标状态的基础上（不）稳定流形的几何形状和最近的一个结果的非线性控制系统的指数稳定性的作者之一。
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic equilibrium and then, apply it to optimal control problems to obtain sufficient conditions for the turnpike behavior to occur. The approach taken is geometric and gives insights for the behaviors of controlled trajectories as well as links between the turnpike property and stability and/or stabilizability in nonlinear control theory. It also allows us to find simpler proofs for existing results on the turnpike properties. Attempts to remove smallness restrictions for initial and target states are also discussed based on the geometry of (un)stable manifolds and a recent result on exponential stabilizability of nonlinear control systems obtained by one of the authors.