基于两级算法的混沌控制

Chaos control based on the two-level algorithm

提出了一种两级算法,可以解决连续混沌系统的最小能量控制问题,首先,给出一个二次目标函数,同时把混沌系统分解为线性部分和非线性部分.上级算法对混沌系统中的非线性部分进行预估,并把整个原系统表为带有常系数的线性系统;下级算法用极小值原理解决这个典型线性二次最优控制问题,并把解返回到上级算法,上级算法根据下级的解对非线性部分重新预估.这样通过两级间不断的信息交换,最终得到混沌系统的最优控制律.该方法不仅实现了对混沌系统的控制,而且在整个控制过程中保证控制能耗为最小.证明了算法的收敛性和闭环系统的稳定性.对统一混沌系统的仿真结果表明了控制策略的有效性.

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.