摘要
本文针对目前求解Riccati矩阵代数方程时存在鲁棒性差,对高维问题求解结果耗时多,结果差的缺点,提出了一种改进型遗传算法来匹配Riccati矩阵代数方程最佳解阵P*的新方法。改进型遗传算法通过检测种群熵S值的变化可以及时发现早熟现象,并定义基因熵G有导向地对种群进行变异操作,使当前搜索跳出早熟,不断向全局最优解收敛。对单级倒立摆控制系统最优控制问题的求解实例表明,改进型遗传算法比基本遗传算法具有更好的寻优性能,求解结果P对应得最优指标J与Matlab中LQR函数所求结果的误差仅为0.3%,但其耗时更少。这表明改进型遗传算法为Riccati矩阵代数方程的求解提供了一种高效鲁棒的方法,尤其是对高维P*的求解更具有工程意义。
This paper proposes an improved genetic algorithm to match the optimal solution P＂ of the Riccati matrix algebraic equation. This new method overcomes the shortcomings such as lack of robustness, high time-consuming and imprecise, which generally exist in many solution methods at present. The improved genetic algorithm have the ability to discover and handle the premature successfully and converge to the global optimal solution continually through detecting the value change of population entropy S and mutating the population oriented by the new defined gene entropy G. The application to solve the optimal control on single-stage inverted pendulum indicate that the improved genetic algorithm has better optimization performance than the basic genetic algorithm, and the optimal index J deduced from P compared with that given by LQR function in Madab only have O. 3 percent error, but have less tlme-consuruing. This shows that the improved genetic algorithm offers a robust and efficient method to solve Riccati matrix algebraic equation, especially have more engineering significance for solving the high-dimension P.
出处
《现代机械》
2011年第5期36-39,51,共5页
Modern Machinery
