Dynamic optimization is one of the model-based adaptive reinforcement learning methods, which has been widely used in industrial systems with switching mechanisms. This article presents an efficient dynamic optimization strategy to locate an optimal input and switch times for switched systems with guaranteed satisfaction for path constraints during the whole time period. In this article, we propose a single-level algorithm where, at each iteration, gradients of the objective function with respect to switch times and the system input are evaluated by solving adjoint systems and sensitivity equations, respectively. Then the optimization of the input is performed at the same iteration with that of the switch time vector, which greatly reduces the number of nonlinear programs (NLPs) and computational burden compared with multistage algorithms. The feasibility of the optimal solution is guaranteed by adapting a new policy iteration method proposed to switched systems. It is proven that the proposed algorithm terminates finitely, and converges to a solution which satisfies the Karush–Kuhn–Tucker (KKT) conditions to specified tolerances. Numerical case studies are provided to illustrate that the proposed algorithm has less expensive computational time than the bi-level algorithm.

中文翻译：

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路径约束切换系统的高效动态优化算法


动态优化是基于模型的自适应强化学习方法之一，已广泛应用于具有切换机制的工业系统中。本文提出了一种有效的动态优化策略，以找到切换系统的最佳输入和切换时间，并保证在整个时间段内满足路径约束。在本文中，我们提出了一种单级算法，其中在每次迭代时，分别通过求解伴随系统和灵敏度方程来评估目标函数相对于切换时间和系统输入的梯度。然后，输入的优化与切换时间向量的迭代同时进行，与多级算法相比，这大大减少了非线性程序（NLP）的数量和计算负担。通过采用针对切换系统提出的新策略迭代方法，保证了最优解的可行性。事实证明，所提出的算法有限终止，并收敛到满足指定容差的 Karush-Kuhn-Tucker (KKT) 条件的解。提供了数值案例研究来说明所提出的算法比双层算法具有更少的计算时间。