Control strategy and application of hysteretic chaotic neuron and neural network

Abstract

In order to remain the structure of the neural network in the process of the optimization unchanged, taking the hysteretic chaotic neuron and the hysteretic chaotic neural network as controlled plants, a novel control strategy based on the filtered tracking error is proposed to perform the stability control for the single hysteretic chaotic neuron or the hysteretic chaotic neural network. Especially, the hysteretic chaotic neuron and the hysteretic chaotic neural network can be used to solve the optimization problem through using the control strategy on condition that the generation mechanisms of the nonlinear characteristics, hysteresis and chaos, are unchanged. The control law is composed of two terms: one is the equivalent control term in the ideal filtered tracking error surface, and the other is the control term which can make the system reach the filtered tracking error surface quickly. Lyapunov stability method is used to prove the stability of the control strategy for the single hysteretic chaotic neuron and hysteretic chaotic neural network. The control laws of hysteretic chaotic neurons can be obtained according to the optimization function. The state of the single hysteretic chaotic neuron or the hysteretic chaotic neural network can converge to an extreme point of the optimization function gradually by the control law. In this way, the optimization problem can be solved effectively. Simulation results prove the feasibility and validity of the control strategy for optimization problem.