亏损系统模态优化控制Riccati方程的求解方法

讨论亏损重复特征值的Ｒｉｃｃａｔｉ方程的模态控制算法．由于亏损特征值的Ｊｏｒｄａｎ块矩阵的阶数ｍ小于状态方程的阶数ｎ，即ｍ＜＜ｎ；所提出的模态控制算法可极大地减少计算工作量．其中的数值例子说明了该方法的有效性．

MODAL OPTIMAL CONTROL ALGORITHM OF THE RICCATI EQUATIONS FOR DEFECTIVE SYSTEMS

This study presents a modal optimal control algorithm for solving the Riccati equations in the generalized modal subspace corresponding to defective repeated eigenvalues. The discussions on vibration optimal control mainly involve the eigenvectors to span the eigenspace. However, in engineering problems, such as general damping systems, flutter analysis of aeroelasticcity, the sys- tem which is called defective system has not a set of complete eigenvectors to span the eigenspace. This paper focuses on the case of defective systems with repeated eigenvalues. By using modal transformation, the state control equation can be transferred into two sets of modal control equa- nons. The first is in the subspace corresponding to defective repeated eigenvalues. The second is in the subspace corresponding to distinct eigenvalues.The solution based on the modal control equations is simpler than that of the original stage control equations. The Potter's algorithm is extended to deal with the optimal control baized on the modal control equations corresponding to defective repeated eigenvalues. A numerical example is given to illustrate the application of the present procedure. The numerical results show that the present procedure is effective for dealing with the optimal control problem of defective systems.