基于高斯伪谱方法的混沌系统最优控制

针对混沌系统最优控制问题，提出一种基于高斯伪谱方法的数值求解新算法. 首先在勒让德-高斯点上构造Lagrange插值多项式并近似表示混沌系统最优控制中的状态变量和控制变量；接着将连续空间的最优控制问题转化为非线性规划问题；然后通过序列二次规划（SQP）算法获得最优解；最后对三个典型混沌系统的仿真实验结果表明，新方法能有效和快速地实现混沌系统的最优控制. 关键词： 混沌系统 最优控制 高斯伪谱法 非线性规划

Optimal control for a chaotic system by means of Gauss pseudospectral method

A new numerical method is presented to solve optimal control problem of a chaotic system based on Gauss pseudospectral method (GPM). Firstly, the Lagrange interpolation polynomials are constructed on Legendre-Gauss nodes and used to parameterize the state and control the trajectories in optimal control of the chaotic system. Then, the chaotic optimal control problem in the continuous space is transformed into a nonlinear programming (NLP) problem through GPM. Furthermore, the NLP problem is solved by the sequential quadratic programming algorithm. Finally, the proposed method is applied to the optimal control of the typical Lorenz, Chen, and Liu chaotic systems respectively. The simulation processes indicate that the GPM is effective, fast and feasible for solving optimal control problems of chaotic systems.
Keywords： chaotic system optimal control Gauss pseudospectral method nonlinear programming