具有对称循环结构的广义大系统最优控制

Optimal Control for Large-scale Descriptor Systems with Symmetric Circulant Structure

考虑具有对称循环结构的广义大系统的最优控制设计问题·基于Riccati方程和Lyapunov方程的解与许多控制问题密切相关,研究了具有对称循环结构的广义复杂大系统的Lyapunov方程与Riccati方程的求解问题;利用具有对称循环结构的广义大系统的特殊结构,提出了对具有对称循环结构复杂大系统Lyapunov方程与Riccati方程的求解问题,可以简化为一些低阶系统Lyapunov方程与Riccati方程求解问题·利用Riccati方程的解解决了这类系统最优控制问题·

?The optimal control for largescale descriptor systems with symmetric circulant structure were studied. Considering that many control problems are related to the solving of the algebraic Riccati equation and Lyapunov matrix equation, a method of solving the equations is suggested for largescale systems with symmetric circulant structure. Exploiting the special structure of symmetric circulant systems, the problem of solving these systems can be simplified to the one of solving lower dimension systems. The quadratic optimal control problem was investigated for largescale descriptor systems with symmetric circulant structure by using the simplified solution of Riccati equation.