一类不确定分段线性系统的优化控制  

Optimal control of one class of uncertain piecewise linear systems

作　　者：张建雄[1] 唐万生[1] 

机构地区：[1]天津大学系统工程研究所,天津300072

出　　处：《吉林大学学报（工学版）》2006年第6期929-933,共5页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家自然科学基金资助项目(70171004)

摘　　要：针对不确定分段线性系统,将最优控制设计问题转化成最优控制性能上界的优化问题及性能下界的求取问题。其中性能上界的优化是一组以反馈增益为寻优参数的双线性矩阵不等式(bilinearmatrix inequalities,BM I)问题,而性能下界是一组基于线性矩阵不等式(linearmatrix inequalities,LM I)的半正定规划问题。对BM I问题,结合混沌优化算法和内点法设计了一种混合算法。最后的算例表明对控制律的设计及其求解算法的有效性。The optimal control design for the uncertain piecewise linear system has been converted to the problem of optimizing upper bound and seeking lower bound of the optimal control performance. Therein the optimizing the upper bound of the performance can be expressed as a problem of bilinear matrix inequalities （BMI） in which the feedback gain is taken as the optimization parameters, and the seeking the lower bound is a semidefinite programming problem based on the linear matrix inequalities （LMI）. A mixed algorithm combining the chaos optimization and the interior-point method was designed to solve the BMI. The effectiveness of the control design and its solving algorithm was demonstrated successfully by a numerical example.

关 键 词：自动控制技术 不确定分段线性系统 最优控制 双线性矩阵不等式 半正定规划 混沌优化 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]