Chaos control of a bounded 4D chaotic system

This paper is concerned with the problem of optimal and adaptive control for controlling chaos in a novel bounded four-dimensional (4D) chaotic system. This system can display hyperchaos, chaos, quasiperiodic and periodic behaviors, and may have a unique equilibrium, three equilibria and five equilibria for the different system parameters. An optimal control law is designed for the novel bounded chaotic system, based on the Pontryagin minimum principle. Furthermore, we propose Lyapunov stability conditions to control the new bounded 4D chaotic system with unknown parameters by a feedback control approach. Numerical simulations are presented to show the effectiveness of the proposed chaos control scheme.