标题： 离散时间最优控制中价值函数的次梯度演化 显示英文标题

标题： Subgradient evolution of value functions in discrete-time optimal control

摘要： 在本文中，我们研究离散时间凸 Bolza 问题的值函数的次梯度如何随时间演变。 特别是，我们通过证明值函数的次梯度的时间演化可以与离散时间哈密顿系统的轨迹相关联，从而开发了 Rockafellar 和 Wolenski 在 20 世纪 20 年代引入的特征方法的离散时间版本。 为此，我们首先证明值函数有一个对偶对应物，这对应于适当对偶问题的值函数的共轭。 最后，我们讨论了我们结果所需的资格条件，特别地，展示了如线性二次调节器等经典问题满足这些假设。 显示英文摘要

摘要： In this paper we investigate how the subgradients of the value function of a discrete-time convex Bolza problem evolve over time. In particular, we develop a discrete-time version of the characteristic method introduced by Rockafellar and Wolenski in the 2000s, by showing that the time-evolution of the subgradients of the value functions can be associated with trajectories of a discrete-time Hamiltonian system. To do so, we first prove that the value function has a dual counterpart, which corresponds to the conjugate of the value function of a suitable dual problem. We finally make a discussion about the qualification conditions we require for our results, showing in particular that classical problems, such as the Liner-Quadratic regulator, satisfy these hypotheses.