论文标题
线性收费定理
Linear turnpike theorem
论文作者
论文摘要
收费公路现象规定，最佳控制问题的解决方案基本上仍然接近动力学的稳态，这本身就是相关静态最佳控制问题的最佳解决方案。在一般的假设下，众所周知，不仅最佳状态和最佳控制，而且还来自pontryagin最大原理的应用所带来的伴随状态，除了在时间范围的开始和结束时，呈指数级接近稳态。在这种结果中，收费公路套装是单身人士，这是一个稳定状态。在本文中，我们为有限维的最佳控制问题建立了收费公路结果，其中一些坐标以单调的方式发展，而另一些坐标是动态的部分稳态。我们证明，最佳轨迹和收费公路集之间的差异是线性的，但不是指数：因此，我们谈到了线性收费定理。
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control problem. Under general assumptions, it is known that not only the optimal state and the optimal control, but also the adjoint state coming from the application of the Pontryagin maximum principle, are exponentially close to a steady-state, except at the beginning and at the end of the time frame. In such results, the turnpike set is a singleton, which is a steady-state. In this paper, we establish a turnpike result for finite-dimensional optimal control problems in which some of the coordinates evolve in a monotone way, and some others are partial steady-states of the dynamics. We prove that the discrepancy between the optimal trajectory and the turnpike set is then linear, but not exponential: we thus speak of a linear turnpike theorem.
