Aiming at discrete-time chaotic systems, the neural network sliding mode equivalent control method based on
a hybrid algorithm which combines the particle swarm optimization algorithm and the Powell search method(Powell-PSO
algorithm) is proposed. When taking the output of BP neural network as the coefficient of the switch part of sliding mode
equivalent control, the method effectively overcomes the chattering phenomenon of conventional sliding mode equivalent
control. The Powell-PSO algorithm is applied to globally optimize the parameters of neural network sliding mode controller
and then to control discrete-time chaotic systems more effectively. Simulation results show that the method requires no
knowledge about the precise mathematical model of discrete-time chaotic systems with fast response speed, high control
precision and strong anti-interference ability.