Optimal chaos control through reinforcement learning

Abstract

A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics.

Modelling and control of chaotic processes through their bifurcation diagrams generated with the help of recurrent neural network models. Part 2: An industrial study

“…While controlling chaotic systems through stabilisation of an unstable periodic orbit remains important method of chaos control [14], but as studied in [10] the method requires that each orbit be observed while waiting for particular type of orbit to occur. This further requires modification in input parameters through which the operating point on the attractor of the system can be shifted to a stable region to meet the desirable objective.…”

“…While this approach leads to successful classification of slightly differing periodic data, its use in developing any controller has not been demonstrated. In [14] it has been shown that using reinforcement learning techniques, control of chaotic systems can be achieved from observed data based methods without formal models, but the approach has been limited to stabilising an unstable fixed orbit. Therefore, the proposition brought out in [10], where modelling the system through multiinput and multi-output recurrent neural networks, training it to very low MSE levels using back-propagation algorithm, to achieve a capability to predict number of subsequent steps, has been adopted here, for the study of real-world systems.…”

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

“…In [8] we showed how a single logistic map can be controlled through a method based on reinforcement learning. Here we extend this method to the control of 1-D and 2-D LCML.…”

“…The use of reinforcement learning to control chaotic systems was first suggested by Der and Herrmann [7] who applied it to the logisitic map. In [8] we generalized the method and applied it to the control of several discrete and continous lowdimensional chaotic and hyperchaotic systems. Lin and Jou [9] proposed a reinforcement learning neural network for the control of chaos and applied it to the logistic and the Hénon map.…”

“…In this work we present a control method for spatiotemporal systems which relies on the recently introduced chaos control method [8] and uses reinforcement learning to establish control of a coupled map system in an optimal manner with respect to a certain optimality criterion. The control policy is established through interaction with a local neighborhood of a controlling unit and is able to find a global control as will be demonstrated through stabilization of different unstable patterns in a 1-D and 2-D LCML.…”