一种基于优化的参数化鲁棒极点配置方法

An optimization based parametric robust pole assignment method

研究时不变线性系统状态反馈鲁棒极点配置问题,首先提出了一种新的衡量系统鲁棒性的目标函数,该目标函数定量考虑了不确定性对闭环系统特征值的影响.然后通过对某些矩阵进行奇异值分解得到闭环特征向量和状态反馈矩阵的参数表达式.基于提出的目标函数和闭环特征向量矩阵的参数解,给出了目标函数梯度的显式表达式,从而可以用成熟的基于给出梯度信息的优化方法对目标函数进行优化而得到最优解.通过实际例子和现有方法的比较,结果显示了本方法的有效性.

The robust pole assignment for linear time - invariant system by state feedback is considered. A new object function concerning the robustness of the closed - loop is firstly given. Such objective function takes quantificationally the affection of uncertainties to the closed - loop into consideration. Then the parametric expressions for the eigenvector matrix of the closed - loop system and the feedback gain matrix are obtained by a series of singular value decompositions on some matrices. Based on the objective function and parametric expressions to the eigenvector matrix and feedback gain matrix, the explicit gradient to the objective function is given and thus standard optimization algorithm can be applied to obtain an optimal solution. The numerical example comparing with existing results shows the effectiveness of the orooosed aooroach.