非线性H_∞控制的SOS设计  

SOS design for nonlinear H_∞ control

作　　者：何朕[1] 王广雄[1] 孟范伟[2] 

机构地区：[1]哈尔滨工业大学航天学院,黑龙江哈尔滨150001 [2]东北大学秦皇岛分校控制工程学院,河北秦皇岛066004

出　　处：《电机与控制学报》2015年第1期82-89,共8页Electric Machines and Control

基　　金：国家自然科学基金重点资助项目(61034001);国家自然科学基金资助项目(61174203;60374027)

摘　　要：提出了一种新的非线性H∞控制的设计方法。虽然平方和(简称SOS)方法可用来求解不易用解析法求解的非线性问题,但还是不能直接来求解HJI不等式或非线性的有界实不等式。详细分析了SOS法在求解中的这些局限性。给出了求解非线性H∞控制的一种迭代设计的方法。每一次迭代分为两步。第一步是先用SOS法设计系统的非线性状态反馈,其增益阵是可调整的。第二步是求系统L2增益,用图解解析法求解计算中的优化问题。还给出了一个卫星大姿态机动的非线性H∞控制设计作为应用本方法的实例。A new design method for nonlinear H∞control was proposed. Though sum of squares （ SOS） method can be used to solve analytically unsolvable nonlinear problems, but it still cannot be used direct-ly to solve the Hamilton-Jacobi-Issacs（ HJI） inequality or the nonlinear bounded-real inequality. The re-strictions of the SOS method were discussed in detail. An iterative design procedure for nonlinear H∞ con-trol problems was presented. There are two steps in each round of iteration. The first step is to design the nonlinear state feedback with adjustable gain matrix by using the SOS method. The second step is to solve an optimal problem in computation of the L2-gain by using a graphical-analytical method. A nonlinear H∞control design for large attitude maneuvers of statellites was presented as an application example of the proposed method.

关 键 词：非线性H∞控制 平方和 HJI不等式 有界实引理 姿态控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]