Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431, USA.
Chaos. 2020 Mar;30(3):031102. doi: 10.1063/5.0002047.
A catastrophic bifurcation in non-linear dynamical systems, called crisis, often leads to their convergence to an undesirable non-chaotic state after some initial chaotic transients. Preventing such behavior has been quite challenging. We demonstrate that deep Reinforcement Learning (RL) is able to restore chaos in a transiently chaotic regime of the Lorenz system of equations. Without requiring any a priori knowledge of the underlying dynamics of the governing equations, the RL agent discovers an effective strategy for perturbing the parameters of the Lorenz system such that the chaotic trajectory is sustained. We analyze the agent's autonomous control-decisions and identify and implement a simple control-law that successfully restores chaos in the Lorenz system. Our results demonstrate the utility of using deep RL for controlling the occurrence of catastrophes in non-linear dynamical systems.
非线性动力系统中的灾难性分岔，称为危机，通常会导致它们在经过一些初始混沌瞬态后收敛到不理想的非混沌状态。防止这种行为一直是相当具有挑战性的。我们证明，深度强化学习（RL）能够恢复洛伦兹方程组的暂态混沌区域中的混沌。在不需要任何关于控制方程基本动力学的先验知识的情况下，RL 代理发现了一种有效的策略来扰动洛伦兹系统的参数，从而维持混沌轨迹。我们分析了代理的自主控制决策，并确定并实施了一个简单的控制律，成功地恢复了洛伦兹系统中的混沌。我们的结果证明了使用深度 RL 控制非线性动力系统中灾难发生的效用。
