行为批判物理信息神经 Lyapunov 控制

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2024-06-18 DOI:10.1109/LCSYS.2024.3416235
Jiarui Wang;Mahyar Fazlyab
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引用次数: 0

摘要

为稳定任务设计具有可证明保证的控制策略是非线性控制领域的一个长期问题。一个重要的性能指标是所产生的吸引区域的大小,它实质上是闭环系统对不确定性的鲁棒性 "裕量"。在这封信中,我们提出了一种训练稳定神经网络控制器及其相应 Lyapunov 证书的新方法,目的是在尊重执行约束的同时,最大化所产生的吸引区域。祖博夫偏微分方程(PDE)的使用对我们的方法至关重要,它能精确描述给定控制策略的真正吸引区域。我们的框架遵循 "行动者-批评者 "模式,在改进控制策略(行动者)和学习祖博夫函数(批评者)之间交替进行。最后,我们通过在训练过程后调用 SMT 求解器来计算最大的可证明吸引力区域。我们在多个设计问题上进行的数值实验表明,所得出的吸引力区域的大小得到了一致且显著的改善。
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Actor–Critic Physics-Informed Neural Lyapunov Control
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 letter, 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.
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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