CAJ | 학술논문

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。
본문연구재최우공제계통중우도적리산시간대수Riccati구진방정(DTARME)이류약속해적수치계산문제。수선대다변량DTARME중적역구진채용구진급수방법진행등개전화，연후채용우돈산법구다변량DTARME적이류약속해，병채용수정공액제도법구유우돈산법매일보질대계산도출적선성구진방정적이류약속해혹자이류약속최소이승해，건립구다변량DTARME적이류약속해적쌍질대산법。쌍질대산법부요구다변량DTARME유이류약속해，불요구타적이류약속해유일，야불대타적계수구진주부가한정。수치산례표명，쌍질대산법시유효적。
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.