基于粒子群的状态反馈控制特征向量的配置

Eigenvector Assignment Based on Particle Swarm Optimization in State Feedback Control

状态反馈控制特征结构的配置分为特征值的配置和特征向量的配置,在特征值已经确定的情况下,特征向量矩阵的条件数对于系统鲁棒稳定性有着直接的影响。因此以减小特征向量矩阵的条件数为直接目的对特征向量进行配置,是提高系统鲁棒稳定性的最直接的办法。由于在状态反馈控制中特征向量的配置存在自由度,因此以特征向量矩阵的条件数为适应度函数,采用粒子群算法进行优化。同时针对粒子群算法中存在的后期收敛速度慢,搜索精度不高,并可能陷入局部极值的缺陷,对粒子浓度进行调节以保持粒子的多样性,防止算法陷入局部极值。同时建立优秀粒子记忆库,克服粒子群算法后期收敛速度慢的缺点。最后通过实例将改进后的粒子群算法与其它算法进行了比较,验证了本算法对于减小特征向量矩阵的条件数和提高系统鲁棒稳定性的优越性。

Eigenstructure assignment of state feedback control is divided into two parts： eigenvalue assignment and eigenvector assignment. When the eigenvalue is determined, the condition number of eigenvector matrix has the directly effect on the robust stability of the system. In order to improve the robust stability of the system, the most direct way is deducing the condition number of eigenvector matrix. Because of the freedom of eigenvector assignment, the particle swarm arithmetic has been used to deduce the condition number. But this method has a slow search speed at the last period, and it may converge to local optima easily. In order to avoid these disadvantages, density regulation mechanism has been used to maintain the diversity of particles and the excellent particle database has been established to accelerate the search speed. It is proved by experiments that the improved particle swarm arithmetic has great superiority to deduce the condition number of eigenvector matrix and to improve the robust stability of the system.