Adaptive Control of a Four-Dimensional Hyperchaotic System

This paper concerns the application of adaptive control method in a four-dimensional hyperchaotic
system. Firstly, we carry out a systematic dynamic analysis including the properties of equilibrium
point, stability, dissipation, Lyapunov exponent spectrum, and bifurcation. Both the existence
of two positive Lyapunov exponents and the Lyapunov dimension value show the hyperchaotic property of the system. Based on Lyapunov stability theorem, we then construct an adaptive controller and the adaptive law to suppress hyperchaos to the origin, which is an unstable equilibrium point under a certain parameter set. The effectiveness of the adaptive control is veried by theoretical analysis and numerical simulation. We nally brie y demonstrate the control eciency of self-linear feedback control and misaligned feedback control. For the fourdimensional hyperchaotic system, the adaptive control outperforms them from the view of control speed.