Chaos control based on the two-level algorithm
基于两级算法的混沌控制

A two-level algorithm is proposed to solve the minimum-energy control for a continuous chaotic system. A quadratic performance function is first given, and the chaotic system is decomposed into the linear part and the nonlinear part. The upper-level algorithm predicts the nonlinear part and expresses the whole system as a linear system with constant coefficients. The lower-level algorithm solves a typical quadratic-optimal-control problem by using the principle of optimality. The solution thus obtained is fed back to the upper-level algorithm for re-estimating the nonlinear part. By continuously exchanging information between the two levels of the algorithm in this way, the optimal control law for the chaotic system is eventually determined. This method not only realizes the control of the chaotic system, but also minimizes the energy-cost in the whole process. The convergence of the two-level algorithm and the asymptotic stability of the closed-loop system are proved. For a general chaotic system, the simulation results show the effectiveness of the proposed method.