Control of UPOs of unknown chaotic systems via ANN

Abstract

In this paper an artificial neural network (ANN) is developed for modeling and controlling unknown chaotic systems to unstable periodic orbits (UPOs). In the modeling phase, the ANN is trained on the unknown chaotic systems using the input-output data obtained from the unknown (or uncertain) underlying chaotic systems, and a specific computational algorithm is employed for the parameter optimization. In the controlling phase, the L 2 -stability criterion is used, which forms the basis of the main design principle. Some simulation results on the chaotic Henon and Duffing systems are given, for both modeling and controlling phases, to illustrate the effectiveness of the proposed chaos control scheme and the proposed neural network. © 2014 Springer International Publishing Switzerland.