Abstract
We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern neural-network-based control techniques, which are robust to system uncertainties but require a model nonetheless, our technique requires no prior knowledge of the system and is thus model-free. Further, our approach does not require an initial system identification step, resulting in a relatively simple and efficient learning process. Reservoir computers are well-suited to the control problem because they require small training data sets and remarkably low training times. By iteratively training and adding layers of reservoir computers to the controller, a precise and efficient control law is identified quickly. With examples on both numerical and high-speed experimental systems, we demonstrate that our approach is capable of controlling highly complex dynamical systems that display deterministic chaos to nontrivial target trajectories.
Highlights
Controlling dynamical systems is a ubiquitous problem in disciplines ranging from engineering to medicine
Control methods for nonlinear systems include linearizing the dynamics about a typical operating point and applying linear control methods [8], evaluating a model of the system in real time for state estimation [9], or using artificial neural networks (ANNs) to perform the state estimation [10]
We provide motivation for the algorithm, explicitly demonstrate and quantify the ability of a class of reservoir computing (RC) known as an echo state network (ESN) [27] to ‘invert’ a system, and study optimizing the RC parameters that are specific to the control problem
Summary
Controlling dynamical systems is a ubiquitous problem in disciplines ranging from engineering to medicine. The fundamental problem in control engineering is to design control signals that are applied to a system with accessible inputs, referred to as a plant, so that it follows a desired behavior. Recurrent neural networks (RNNs), in which the ANN remains directed but is no longer acyclic, naturally have temporal dynamics that can be used to learn time series, but training the recurrent weights is notoriously difficult and typically fails to converge. This can be addressed by considering restricted RNN topologies.
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