奇异控制系统控制律的精细计算

Precise Computation for Control Law of Singular Control System

利用结构力学中的子结构消元算法对奇异控制系统的控制律进行精细计算研究。在消去控制系统奇异性的基础上 ,通过给出时段混合能的定义 ,并利用广义变分原理 ,可得出一套时段消元公式 ,进而引入 2 N 类精细计算方法可求解奇异控制系统的 Riccati代数方程。为了更好地体现奇异控制系统的特性 ,在子空间内给出了上述 Riccati代数方程 ,从而将控制律分为第一控制律和第二控制律。

The singular control is a hot problem in control region, especially for complex control system. A discreted linear quadratic control problem was considered, in which the singularity of weighting matrix R appears. Based on the substructural condensation algorithm in computational structural mechanics and precise integration method, the precise computational method for control law of the singular control system was given. On the basis of the elimination of singularity for the system, the condensation formulas of time-interval were given by using the definition of time-interval mixed energy and generalized variational principle. By introducing the 2N precise computational algorithm, the solved method for the algebraic Riccati equation of the singular control system was obtained. For showing the characteristics of the singular control system better, the control law was divided into first and second control laws. The effectiveness of the method is shown in a numerical example.