Control of 1-D and 2-D coupled map lattices through reinforcement learning

Abstract

In this paper we show that coupled 1-D and 2-D logistic map lattices can be controlled to different types of behaviour through a recently introduced control algorithm (S. Gadaleta and G. Dangelmayr, Chaos 9, 775-788 (1999)) which is based on reinforcement learning. The control policy is established through information from the local neighborhood of a subsytem and does not require any explicit knowledge on system dynamics or location of desired patterns. The algorithm is applicable in noisy and nonstationary environments. We demonstrate that the control policies established from interaction with small systems can be applied to larger systems and combined to trigger the formation of new states.

Chaos synchronization of two coupled map lattice systems using safe reinforcement learning

“…where the mapping function f is the logistic map ( ) (1 ) f x ax x =− and 4 a = , the number of dimensions 100 N = and the coupled strength  is selected as 0.1 [43].…”

Control of chaos in Frenkel–Kontorova model using reinforcement learning*

“…In their further study, they showed that the method was robust against noise and capable of controlling high-dimensional discrete systems, one-dimensional (1D) and two-dimensional (2D) coupled logistic map lattices, by controlling each site. [21] The control policy established from interaction with a local lattice can successfully suppress the chaos in the whole system, and thus forming a new pattern. Their findings might open promising directions for smart matter applications, but future research needs to focus on controlling continuous coupled oscillators as they pointed out.…”

“…In the present work, we use the model-free reinforce-ment learning-based method to control spatiotemporal chaos in the FK model because the method provides a possibility of "intelligent black-box controller", which can be more directly compatible with the actual system, making the controller very suitable for controlling experiment systems. [21] The control of the FK model has drawn much attention in pursuing friction and wear reduction. [12] Surprisingly, Braiman et al showed that the introduction of disorder in pendulum lengths can be used as a means to control the spatiotemporal chaos in the FK model.…”

Control and anti-control of chaos based on the moving largest Lyapunov exponent using reinforcement learning

“…Based on reinforcement learning with Q-learning, Gadaleta and Dangelmayr introduced a general method for optimal chaos control [13]. They showed that this method not only can control high-dimensional discrete systems, 1-D and 2-D coupled logistic map lattices [14], but also can attack the targeting problem in a complex multi-stable system through guiding its trajectory to a metastable state [15]. Lei and Han successfully applied the method with Q-learning to the control of chaos in the Frenkel-Kontorova model [16].…”