扩展约束仿射非线性系统预测控制吸引域  

Enlarging the Domain of Attraction of Predictive Control for Constrained Affine Nonlinear Systems

作　　者：王超[1,2] 张胜修 秦伟伟 郑建飞 

机构地区：[1]第二炮兵工程大学,陕西西安710025 [2]第二炮兵青州士官学校,山东青州262500

出　　处：《信息与控制》2014年第5期551-557,共7页Information and Control

基　　金：国家自然科学基金资助项目(61203354)

摘　　要：针对受约束的仿射型非线性系统,提出了一种采用扩张终端约束集与其容许集来扩大其双模非线性模型预测控制吸引域的新方法.首先,采用反馈线性化控制律和非线性系统的多面体线性微分包含,给出了一种求解仿射非线性系统最大控制不变集的方法,并基于此设计了扩张终端约束集的不变集切换控制策略;其次,引入区间算法,研究了约束非线性系统N步容许集的离线算法,在此基础上以扩张终端约束集的N步容许集作为初始状态吸引域,利用双模单步优化控制策略以实现系统状态渐近稳定,并扩大了预测控制的吸引域;最后,将该算法用于一类典型的非线性过程——连续搅拌反应釜的控制中,仿真结果验证了方法的有效性.A new method for enlarging the domain of attraction of dual-mode nonlinear model predictive control （NMPC） is developed for a constrained affine nonlinear system by adopting the extended terminal constraint set and its admissible set. First, an optimization method for calculating a maximal control invariant set with respect to a feedback linearizing control law and a polytope linear difference inclusion （PLDI） for an affine nonlinear system is presented. Accordingly, a switching control strategy of the control invariant set is designed to extend the terminal constraint set. Second, interval arithmetic is introduced to compute the N step admissible sets of the extended terminal constraint set off-line, and then the resulting dual-mode controller with a one-step predictive horizon can guarantee the stability and enlargement of the domain of attraction of predictive control by considering this sequence as an attraction domain of initial states in the optimization problem. Fi- nally, the method is tested in a typical nonlinear process control system - a continuously stirring tank reactor （CSTR） ; the results show the feasibility of the proposed method.

关 键 词：约束非线性系统 非线性模型预测控制 吸引域 多面体不变集 连续搅拌反应釜 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]