一类非线性系统最大可控不变集求解  

Maximal Robust Controlled Invariant Set of A Class of Nonlinear System

作　　者：李坚强[1] 裴海龙[1] 

机构地区：[1]华南理工大学自动化学院,广东广州510641

出　　处：《控制工程》2009年第2期188-190,210,共4页Control Engineering of China

基　　金：国家自然科学基金资助项目(60374036;60574004;60736024);高校博士点基金资助项目(20040561031);广东省自然科学基金资助项目(031407)

摘　　要：针对非线性系统线性化在状态约束下最优鲁棒控制求解问题,提出了一种基于混合系统的非线性系统最大鲁棒控制不变集的方法。对于一类非线性系统通过平衡点线性化的方法转化为多模态的混合系统,并进行了混合逻辑动态模型(MLD)的建模,在不变集基本理论的基础上,通过多参数规划的混合整数规划(MIQP)的方法迭代求解最大可控不变集,并求得不变集内的最优控制器,解决系统的状态约束问题。通过一个非线性系统的实例进行建模、仿真,证明了本方法的可行性。To the optimal robust control problem of nonlinear systems with state constraint, a mehtod to obtain the maximal robust controlled invariant set of nonliear systems based on hybrid systems is proposed. The nonlinear system is transformed to a hybrid system by linearization on equilibrium points and modeled in mixed logic dynamic model. Based on the concept of invariant set, the maximal invariant set is obtained by multi-parameter mixed integer programming method. The optimization controller is computed to solve the problem of constraints. As an example, a nonlinear system is modeled and simulated, and the result shows the validity of the method.

关 键 词：混合系统 最大鲁棒控制不变集 混合逻辑动态模型 混合整数二次规划 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置]