Two-parameter cooperative intelligent optimal control of chaotic motion for a vibro-impact system with soft constraint

Abstract

For the chaotic motion control of a single-degree-of-freedom vibro-impact system with soft constraint, two-parameter cooperative intelligent optimal control method based on LRS-QPSO (i.e., Local Rotational Search Quantum Particle Swarm Optimization) algorithm optimization SVM (i.e., Support Vector Machines) was proposed. Firstly, in the parameter plane (ω,ζ), the motion distribution of the system and the change of the maximum Lyapunov exponent is obtained by numerical simulation, and the correlation between parameters change and the transition from chaotic motion to periodic motion is analyzed. Secondly, by introducing ω and ζ into the construction of the input variables of the SVM controller, a chaotic motion two-parameter cooperative intelligent optimal control strategy is proposed to meet the requirements of expected control objectives. Therefore, by the virtue of nonlinear mapping characteristics of SVM, the combined effects of ω and ζ on the dynamic state transition of the system can be reflected in the output variables of the controller. Finally, with single parameter ω and single parameter ζ as the research object, the bifurcation diagram, Lyapunov exponential spectrum, and controlled periodic motion orbit diagram are analyzed, and the advantages of two-parameter cooperative intelligent optimal control are compared and analyzed.