基于混沌优化的一类微分包含系统的最优控制设计  

Optimal Control of a Class of Differential Inclusions Based on Chaos Optimization Algorithm

作　　者：鹿宁[1] 唐英凯[1] 

机构地区：[1]天津大学管理学院,天津市博士研究生300072

出　　处：《中国农机化》2006年第6期70-75,共6页Chinese Agricul Tural Mechanization

摘　　要：根据Hamilton-Jacobi-Bellman(H-J-B)不等式,将一类微分包含系统的最优控制问题转化成最优控制性能上界的优化及性能下界的求取问题。其中性能上界的优化是一组以控制律为寻优参数的双线性矩阵不等式(bilinearmatrixinequalities,BMI)问题,而性能下界是一组半正定规划问题。BMI问题是NP难问题,对此设计了一种基于混沌优化的算法进行求解,所设计的算法更有效地收敛到全局最优解。最后的算例表明对控制律的设计及其求解算法的有效性。By Hamilton-Jacobi-Bellman inequalities method, the optimal control of a class of differential inclusions is cast as the problem of seeking upper and lower bounds on cost function. The design of upper bound is converted to a bilinear matrix inequalities （BMI） problem in which the parameters of control law are to be optimized, and a lower bound can be obtained by semi definite programming. The BMI problem is an NP hard problem, and an algorithm that based on chaos optimization is designed for solving it. The proposed algorithm is validly convergent to optimal solution, and the results from a numerical example illustrate the effectiveness of the design method for the control law .

关 键 词：微分包含系统 最优控制 双线性矩阵不等式 混沌优化 算法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]