Chaos control using least-squares support vector machines

In this paper we apply a recently proposed technique of optimal control by support vector machines (SVMs) to chaos control. Vapnik's support vector method, which is based on the structural risk minimization principle and has been very successful in classification and function estimation problems, is embedded within the context of the N-stage optimal control problem. State vector tracking is considered by a state feedback controller which is parameterized by SVMs. Mercer's condition, an essential feature in SVMs, is applicable within the optimal control problem formulation. Simulation examples are given for chaos control of the Henon map to a period-1 orbit by means of a SVM controller with radial basis function kernel.