非线性预测控制终端约束集的优化  

Computation of Terminal Set for Nonlinear Model Predictive Control

作　　者：于树友[1,2] 冯阳阳 KIM Jung-Su 陈虹[1,4] YU Shu-You;FENG Yang-Yang;KIM Jung-Su;CHEN Hong(State Key Laboratory of Automotives Simulation and Control,Jilin University,Changchun 130025,China;Department of Control Science and Engineering,Jilin University,Changchun 130025,China;Department of Electrical and Information Engineering,Seoul National University of Science and Technology,Seoul 139-743,South Korea;New Energy Automotive Engineering Center,Tongji University,Shanghai 200092,China)

机构地区：[1]吉林大学汽车仿真与控制国家重点实验室,中国长春130025 [2]吉林大学控制科学与工程系,中国长春130025 [3]首尔国立科技大学电子与信息工程系,韩国首尔139-743 [4]同济大学新能源汽车工程中心,中国上海200092

出　　处：《自动化学报》2022年第1期144-151,共8页Acta Automatica Sinica

基　　金：国家自然科学基金(U1964202);工业物联网与网络化控制教育部重点实验室开放基金(2019FF01);江苏省新能源汽车动力系统重点实验室开放课题(JKLNEVPS201901)资助~~。

摘　　要：为保证预测控制的稳定性,经典的策略是在预测控制的优化问题中加入终端约束集和终端惩罚函数,并保证终端约束集是一个在终端控制律作用下的正不变集,终端惩罚函数是受控系统的局部控制Lyapunov函数.本文提供了一种求解非线性系统终端约束集、终端控制律和终端惩罚函数的新策略.通过在优化问题中引入新的变量来降低求解终端约束条件的保守性,并且可以从理论上保证求解得到的终端约束集更大.通常情况下,较大的终端约束集将允许选取的预测时域较小,因而可以降低预测控制的在线计算负担.从形式上看,新的变量的引入使得终端约束集和终端惩罚项实现了某种程度的解耦,即终端约束集不再是终端惩罚函数的水平截集.最后通过仿真算例验证了所提策略的有效性.In order to guarantee stability in model predictive control,one classic strategy is to add in the involved model predictive control optimization problem a terminal set and a terminal penalty,where the terminal set is an invariant set with the so-called terminal control law,and the terminal penalty is a local control Lyapunov function of the considered systems.In this paper,a novel scheme is proposed to obtain the terminal set,terminal control law and terminal penalty of nonlinear systems.Extra degrees are added to reduce the conservativeness of the offline optimization problem.Thus,it can guarantee theoretically the obtained terminal set is large.Since a large terminal set in principle implies a small prediction horizon in the online optimization problem,it can reduce the online computational burden accordingly.The extra degrees decouple the terminal set and terminal penalty to some extent,i.e.,differently with the existing method,the terminal set is no longer a sub-level set of the terminal penalty anymore.A simulation example shows the effectiveness of the proposed scheme.

关 键 词：预测控制 稳定性 终端约束集 非线性系统 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]