The inverse optimal control of a chaotic system with multiple attractors

摘要

This paper studies the dynamical behavior of the Newton-Leipnik system and its trajectory-transformation control problem to multiple attractors. A simple linear state feedback controller for the Newton-Leipnik system based on the Lynapunov stability theory and applying the inverse optimal control method is designed. We stabilize asymptotically the chaotic attractors to unstable equilibriums of the system, so that the transformation of one attractor to another for the trajectory of the Newton-Leipnik system is realized. Theoretical analyses and numerical simulations both indicate the effectiveness of the controller. At last, the inverse optimal control method is proven effective for the chaotic systems with multiple attractors by the example on the unified chaotic system.