Identification and control of unknown chaotic systems via dynamic neural networks

Identification and control problems for unknown chaotic dynamical systems are considered. Our aim is to regulate the unknown chaos to a fixed point or a stable periodic orbit. This is realized by following two contributions. First, a dynamic neural network is used as identifier. The weights of the neural networks are adjusted by the sliding mode technique. Second, we derive a local optimal controller via the neuroidentifier to remove the chaos in a system. The identification error and trajectory error are guaranteed to be bounded. The controller proposed in this paper is effective for many chaotic systems, including the Lorenz system, Duffing equation, and Chua's circuit.