Neural network control of chaos in a class of impact vibration systems

This study examines the challenge of regulating chaotic motion within a specific category of single-degree-of-freedom impact vibration systems. By utilizing principles of mechanics and system dynamics theory, the authors developed a mathematical model for the system’s dynamics. To facilitate chaos control, a double-hidden-layer radial basis function neural network (DRBFNN) chaos controller, characterized by its robust nonlinear properties, is proposed. This controller demonstrates enhanced nonlinear fitting capabilities, thereby effectively accommodating the system’s pronounced nonlinear and non-smooth characteristics. Furthermore, the Harris Hawks Optimization (HHO) algorithm is employed to optimize the parameters of the controller. The chaotic behavior of the system is investigated through bifurcation diagrams and Lyapunov exponent spectra. A fitness function is formulated based on the distances between adjacent points on the Poincaré section, which guides the parameter optimization process of the HHO algorithm, thereby validating the efficacy of the control strategy and ensuring the efficiency and precision of the parameter search for the controller. Simulation results indicate that the HHO-DRBFNN control approach is successful in transforming chaotic motion into periodic motion, exhibiting commendable dynamic response performance.