论文标题
最佳控制问题的有限时间收费公路现象：通过非平滑跟踪术语稳定
The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms
论文作者
论文摘要
在本文中，除了控制成本外，还考虑了最佳控制问题的位置，还有一个跟踪术语可以测量与所需的固定状态的距离。跟踪术语由某些规范给出，因此通常不是可区分的。在最佳控制问题中，规定了初始状态。我们假设该系统在经典意义上是可以完全控制的，或者可以控制系统配置文件。 我们表明，对于由普通微分方程和无限二维系统控制的系统，例如，对于由波方程支配的边界控制系统，在某些假设下，最佳系统状态在有限的时间后准确地转向所需的状态。
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some norm and therefore it is in general not differentiable. In the optimal control problem, the initial state is prescribed. We assume that the system is either exactly controllable in the classical sense or nodal profile controllable. We show that both for systems that are governed by ordinary differential equations and for infinite-dimensional systems, for example for boundary control systems governed by the wave equation, under certain assumptions the optimal system state is steered exactly to the desired state after finite time.
