Backstepping-based Chaotic System Control Applications

Chaos is a kind of quasi-stochastic behaviors of determinate nonlinear system. As one of the most important achievements of nonlinear science, chaos attracted common attention and had been extensively studied in the last four decades. Recently, how to apply chaos have become the researching focus, chaos control and anti-control is the basic problem of the application of chaos. To deal with this problem, the history of chaos research is retrospect, several tendencies of chaos research are pointed out, some basic concepts about chaos control is given, some existing methods are reviewed and their features are analyzed, and then, this paper places emphasis on chaos control.The tracking control method based on Backstepping is proposed for nonlinear systems demonstrating chaos. Firstly, we introduced the base thought of the backstepping method with continuous and discrete form. Based former method, we also introduced the improved method and its application. Secondly, the paper mainly researched the application of backstepping in the continuous autonomy chaos system, such as Lüchaos system. In the system, we mainly thought about the feedback chaos control and chaos track with certain parameters. When some parameters were not certain, we designed different feedback controllers which can control chaos system and identified parameter of the uncertain Lüchaos system. Numerical simulations show the effectiveness and feasibility of the chaos control and parameter identification.Chaos in permanent magnet synchronous motor (PMSM) is studied. To overcome the drawbacks of some existing methods, backstepping method is proposed to control chaos in PMSM. We stabilized and leaded the chaos using backstepping. Simulation results show that the method is simple, feasible and effective.Thought about the chaos presented in many practical engineering backgrounds, we would study the environment disturb in controlled chaos system with backstepping method. So we studied thoroughly the environment disturb in Lüchaos system and PMSM, through simulation showed the method was effective, feasible and robust.