论文标题
连续近似方法的合同性最佳控制方法
Contractivity of the Method of Successive Approximations for Optimal Control
论文作者
论文摘要
强大的收缩动态系统具有许多属性（例如增量ISS），找到广泛的应用程序（例如，在对照和学习中），他们的研究正在受到越来越多的关注。这项工作始于这样一个简单的观察，即鉴于一个强大的收缩系统，其伴随的动力学系统在时间逆转下也以相同的速率与相同的速率签约。作为这种双重合并性的主要意义，我们表明，连续近似的经典方法（MSA）是最佳控制中的间接方法，是用于短暂优化间隔或较大收缩率的收缩映射。因此，我们为MSA算法建立了新的收敛条件，这进一步暗示了Pontryagin在其他假设下的最低最低原理的最佳控制和充分性。
Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple observation that, given a strongly contracting system, its adjoint dynamical system is also strongly contracting, with the same rate, with respect to the dual norm, under time reversal. As main implication of this dual contractivity, we show that the classic Method of Successive Approximations (MSA), an indirect method in optimal control, is a contraction mapping for short optimization intervals or large contraction rates. Consequently, we establish new convergence conditions for the MSA algorithm, which further imply uniqueness of the optimal control and sufficiency of Pontryagin's minimum principle under additional assumptions.
