具有对称循环结构的大系统Riccati方程的求解

The Solving of Riccati Equations for Large-Scale Systems with Symmetric Circulant Structure*

中文关键词  大系统  对称循环结构  Riccati方程  二次型最优控制  鲁棒控制

英文关键词  large-scale svstems  symmetric circulant structure  Riccati equation  linear quadratic optimal control  robust control

中文摘要

      本文研究了具有对称循环结构的大系统的代数Riccati方程和Lyapunov矩阵方程的求解问题. 结果表明， 这类系统的代数Riccati方程和Lyapunov矩阵方程的求解问题可以简化为求解N+l个独立的低阶方程， 做为一个应用， 这类系统的二次型最优控制问题和鲁棒二次型最优控制问题也可以简化.

英文摘要

      This paper discusses the solving of the algebraic Riccati equations and the Lyapunov matrix equations for large-scale svstems with symmetric circulant structure. It is shown that the solving of the algebraic Riccati equations and the Lyapunov matrix equations for such a system can be simplified by solving N/2+1 independent equations of dimension N times smaller than the origi-nal equations. As an application,the problems of the linear quadratic optimal control and the robust linear quadratic optimal control for such a system can also be simplified.