The study of finite-time stability active control method for Lorenz-Haken laser chaotic system

Abstract

In this paper, the problem of finite-time stability for Lorenz-Haken laser chaotic system is studied by active control method. On the basis of the study for terminal attractor, and the consideration fo the uncertainties, an active control method with dynamic active compensation based on terminal attractor is proposed, which makes the controlled Lorenz-Haken laser chaotic system achieve the finite-time stability approximately. Meantime, in order to solve the uncertainties, a new observer is designed, which makes the estimate value follow the real value of uncertainties in a very short time. The approximate finite-time stability of the closed-loop system is analyzed in detail by introducing a singular perturbation theory. Simulation results show the effectiveness of the active control method and observer.