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arXiv 2403.08448cs.LGcs.ROcs.SYeess.SY
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Actor-Critic 物理信息神经 Lyapunov 控制

Actor-Critic Physics-informed Neural Lyapunov Control

Johns Hopkins University(约翰斯·霍普金斯大学)

Jiarui Wang, Mahyar Fazlyab

AI总结:

本文提出一种基于 actor-critic 和 Zubov 偏微分方程的神经 Lyapunov 控制方法,交替优化控制策略与 Lyapunov 证书以最大化吸引域,并通过 SMT 求解器计算最大可认证吸引域,实验表明该方法能显著提升吸引域大小。

摘要:

为具有可证明保证的稳定任务设计控制策略是非线性控制中长期存在的问题。一个关键的性能指标是所得吸引域的大小,它本质上充当闭环系统对抗不确定性的鲁棒性“裕度”。在本文中,我们提出了一种新方法来训练一个稳定的神经网络控制器及其相应的 Lyapunov 证书,目标是在尊重执行器约束的同时最大化所得吸引域。我们方法的关键在于使用 Zubov 偏微分方程(PDE),它精确刻画了给定控制策略的真实吸引域。我们的框架遵循 actor-critic 模式,在改进控制策略(actor)和学习 Zubov 函数(critic)之间交替进行。最后,我们在训练过程结束后通过调用 SMT 求解器计算最大的可认证吸引域。我们在多个设计问题上的数值实验表明,所得吸引域的大小得到了一致且显著的改进。

英文摘要:

Designing control policies for stabilization tasks with provable guarantees is a long-standing problem in nonlinear control. A crucial performance metric is the size of the resulting region of attraction, which essentially serves as a robustness "margin" of the closed-loop system against uncertainties. In this paper, we propose a new method to train a stabilizing neural network controller along with its corresponding Lyapunov certificate, aiming to maximize the resulting region of attraction while respecting the actuation constraints. Crucial to our approach is the use of Zubov's Partial Differential Equation (PDE), which precisely characterizes the true region of attraction of a given control policy. Our framework follows an actor-critic pattern where we alternate between improving the control policy (actor) and learning a Zubov function (critic). Finally, we compute the largest certifiable region of attraction by invoking an SMT solver after the training procedure. Our numerical experiments on several design problems show consistent and significant improvements in the size of the resulting region of attraction.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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