Wu Jenq-Lang, Lee Tsu-Tian
Electronic Engineering Department, Hwa Hsia Institute of Technology, Taipei, Taiwan.
IEEE Trans Syst Man Cybern B Cybern. 2005 Oct;35(5):881-93. doi: 10.1109/tsmcb.2005.846650.
The problem of optimal simultaneous regional pole placement for a collection of linear time-invariant systems via a single static output feedback controller is considered. The cost function to be minimized is a weighted sum of quadratic performance indices of the systems. The constrained region for each system can be the intersection of several open half-planes and/or open disks. This problem cannot be solved by the linear matrix inequality (LMI) approach since it is a nonconvex optimization problem. Based on the barrier method, we instead solve an auxiliary minimization problem to obtain an approximate solution to the original constrained optimization problem. Moreover, solution algorithms are provided for finding the optimal solution. Furthermore, a necessary and sufficient condition for the existence of admissible solutions to the simultaneous regional pole placement problem is derived. Finally, two examples are given for illustration.
考虑通过单个静态输出反馈控制器对一组线性时不变系统进行最优同时区域极点配置的问题。要最小化的成本函数是系统二次性能指标的加权和。每个系统的约束区域可以是几个开半平面和/或开圆盘的交集。由于这是一个非凸优化问题，所以不能用线性矩阵不等式（LMI）方法来解决。基于障碍法，我们转而求解一个辅助最小化问题，以获得原始约束优化问题的近似解。此外，还提供了寻找最优解的求解算法。此外，推导了同时区域极点配置问题存在容许解的充要条件。最后，给出两个例子进行说明。
