奇异控制系统控制律的精细计算

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，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。最后通过数值例题说明了本方法有效性。

Precise Computation for Control Law of Singular Control System

We aim to provide a different and precise way of solving singular control problems in engineering. We worked many years to introduce mature methods of structural analysis into control problems and now go further to precise computation of control law for singular control system. We start from our previous research results on substructural condensation algorithm in structural analysis and on time precise integration method 1]. Based on the elimination of singularity for control system, we use the definition of time-interval mix-energy and generalized variational principle to give the condensation formulas of time-interval, and then, by introducing the 2N precise computational algorithm, obtain the solution method for the algebraic Riccati equation of singular control system. For showing the characteristics of singular control system better, we give the above algebraic Riccati equation in subspace and divide the control law into the first control law and the second one. Finally the effectiveness of the method in this paper is shown by the numerical example.