摘要
本文研究在最优控制系统中遇到的离散时间代数Riccati矩阵方程(DTARME)异类约束解的数值计算问题.首先对多变量DTARME中的逆矩阵采用矩阵级数方法进行等价转化,然后采用牛顿算法求多变量DTARME的异类约束解,并采用修正共轭梯度法求由牛顿算法每一步迭代计算导出的线性矩阵方程的异类约束解或者异类约束最小二乘解,建立求多变量DTARME的异类约束解的双迭代算法.双迭代算法仅要求多变量DTARME有异类约束解,不要求它的异类约束解唯一,也不对它的系数矩阵做附加限定.数值算例表明,双迭代算法是有效的.
An iterative method is studied to compute the heterogeneous constrained solution of the discrete time algebraic Riccati matrix equation （DTARME） in optimal control system. Firstly, the multivariable DTARME is processed by matrix series. Secondly, Newton’s method is applied to find the heterogeneous constrained solution of multivariable DTARME and then we find the heterogeneous constrained solution or heterogeneous constrained least-square solu-tion of the linear matrix equation derived from each step of Newton’s method by the modified conjugate gradient method. Finally, a double iterative method is established to find the het-erogeneous constrained solution of multivariable DTARME. Multivariable DTARME is only required to have heterogeneous constrained solutions by our double iterative algorithm, and the solution may not be unique.Besides, there are not additional limits to the coe？cient matrices of multivariable DTARME. Numerical experiments confirm that the double iterative algorithm is effective.
出处
《工程数学学报》
CSCD
北大核心
2014年第6期847-856,共10页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(11071196)~~
关键词
异类约束解
牛顿算法
修正共轭梯度法
双迭代算法
multivariable DTARME
heterogeneous constrained solution
Newton’s method
modified conjugate gradient method
double iterative algorithm
