非线性预测控制终端约束集的优化

于树友; 冯阳阳; KIMJung-Su; 陈虹

doi:10.16383/j.aas.c200911

非线性预测控制终端约束集的优化

doi: 10.16383/j.aas.c200911

于树友^{1, 2,},
冯阳阳^2,,
KIMJung-Su^3,,
陈虹^{1, 4,}

1.
吉林大学汽车仿真与控制国家重点实验室长春 130025 中国
2.
吉林大学控制科学与工程系长春 130025 中国
3.
首尔国立科技大学电子与信息工程系首尔 139-743 韩国
4.
同济大学新能源汽车工程中心上海 200092 中国

基金项目: 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

详细信息

作者简介:
于树友：吉林大学控制科学与工程系教授. 2011年获得德国斯图加特大学工学博士学位. 主要研究方向为预测控制, 鲁棒控制及其在机电系统中的应用. 本文通信作者. E-mail: shuyou@jlu.edu.cn

冯阳阳：吉林大学控制科学与工程系博士研究生. 主要研究方向为预测控制, 分布式预测控制和车辆队列控制. E-mail: yyfeng19@mails.jlu.edu.cn

KIMJung-Su：首尔国立科技大学电子与信息工程系教授. 主要研究方向为模型预测控制, 鲁棒控制和多智能体系统. E-mail: jungsu@seoultech.ac.kr

陈虹：同济大学特聘教授、吉林大学唐敖庆讲座教授. 1997 年获得德国斯图加特大学工学博士学位. 主要研究方向为预测控制, 鲁棒控制, 非线性控制和汽车控制. E-mail: chenhong2019@tongji.edu.cn

计量
- 文章访问数: 1610
- HTML全文浏览量: 380
- PDF下载量: 369
- 被引次数: 0
出版历程
- 收稿日期: 2020-11-02
- 录用日期: 2021-04-02
- 网络出版日期: 2021-05-25
- 刊出日期: 2022-01-25

Computation of Terminal Set for Nonlinear Model Predictive Control

YU Shu-You^{1, 2
,},
FENG Yang-Yang^2
,,
KIM Jung-Su^3
,,
CHEN Hong^{1, 4
,}

1.
State Key Laboratory of Automotives Simulation and Control, Jilin University, Changchun 130025, China
2.
Department of Control Science and Engineering, Jilin University, Changchun 130025, China
3.
Department of Electrical and Information Engineering, Seoul National University of Science and Technology, Seoul 139-743, South Korea
4.
New Energy Automotive Engineering Center, Tongji University, Shanghai 200092, China

Funds: Supported by National Natural Science Foundation of China (U1964202), the Foundation of Key Laboratory of Industrial Internet of Things and Networked Control (2019FF01), and the New Energy Vehicle Power System Key Laboratory in Jiangsu Province (JKLNEVPS201901)

More Information

Author Bio:
YU Shu-You　Professor in Department of Control Science and Engineering, Jilin University. He received his Ph. D. degree in engineering from the University of Stuttgart, Germany in 2011. His research interest covers model predictive control, robust control and its applications in mechatronic systems. Corresponding author of this paper

FENG Yang-Yang　Ph. D. candidate in Department of Control Science and Engineering, Jilin University. His research interest covers model predictive control, distributed model predictive control, and control of vehicle platoons

KIM Jung-Su　Professor in Department of Electrical and Information Engineering, Seoul National University of Science and Technology. His research interest covers model predictive control, robust control, and multi-agent systems

CHEN Hong　Professor at Tongji University, and Tangaoqing joint professor at Jilin University. She received her Ph. D. degree in engineering from the University of Stuttgart, Germany in 1997. Her research interest covers model predictive control, robust control, nonlinear control, and automotive control

摘要

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.
- 预测控制 /
- 稳定性 /
- 终端约束集 /
- 非线性系统
Abstract: 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.
- Model predictive control /
- stability /
- terminal set /
- nonlinear systems

HTML全文

图 1 终端约束集

Fig. 1 Terminal constraint set

下载: 全尺寸图片幻灯片

图 2 系统的动态响应: x₁

Fig. 2 Dynamic response of the system: x₁

下载: 全尺寸图片幻灯片

图 3 系统的动态响应: x₂

Fig. 3 Dynamic response of the system: x₂

下载: 全尺寸图片幻灯片

图 4 系统的动态响应: u

Fig. 4 Dynamic response of the system: u

下载: 全尺寸图片幻灯片

参考文献(30)

[1]	Maciejowski J M. Predictive Control With Constraints. London: Prentice Hall, 2001.
[2]	Qin S J, Badgwell T A. A survey of industrial model predictive control technology. Control Engineering Practice, 2003, 11(7):733-764. doi: 10.1016/S0967-0661(02)00186-7
[3]	Grüne L, Pannek J. Nonlinear Model Predictive Control: Theory and Algorithms. New York: Springer, 2011.
[4]	席玉庚. 预测控制. 北京: 国防工业出版社, 2013. Xi Yu-Geng. Predictive Control. Beijing: National Defense Industry Press, 2013.
[5]	陈虹. 模型预测控制. 北京: 科学出版社, 2013. Chen Hong. Model Predictive Control. Beijing: China Science Press, 2013.
[6]	Rawlings J B, Mayne D Q, Diehl M. Model Predictive Control: Theory, Computation, and Design (2nd Edition). Madison, Wisconsin: Nob Hill Publishing, LLC, 2017.
[7]	Yu S, Reble M, Chen H, Allgower F. Inherent robustness properties of quasi-infinite horizon nonlinear model predictive control. Automatica, 2014, 50(9):2269-2280. doi: 10.1016/j.automatica.2014.07.014
[8]	Allan D A, Bates C N, Risbeck M J, Rawlings J B. On the inherent robustness of optimal and suboptimal nonlinear MPC. Systems & Control Letters, 2017, 106:68–78.
[9]	Grüne L. Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. SIAM Journal on Control and Optimization, 2010, 48: 1206–1228
[10]	Chen H, Allgower F. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 1998, 34(10):1205–1217. doi: 10.1016/S0005-1098(98)00073-9
[11]	Mayne D Q, Rawlings J B. Constrained model predictive control: stability and optimality.Automatica, 2000, 36(6):789–814. doi: 10.1016/S0005-1098(99)00214-9
[12]	Mayne D Q. An apologia for stabilising terminal conditions in model predictive control. International Journal of Control, 2013, 86(11):2090–2095. doi: 10.1080/00207179.2013.813647
[13]	Yu S, Qu T, Xu F, Chen H. Stability of finite horizon model predictive control with incremental input constraints. Automatica, 2017, 79:265–272. doi: 10.1016/j.automatica.2017.01.040
[14]	Rajhans C, Patwardhan S C, Pillai H K. Discrete time formulation of quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability. In IFAC-Papers OnLine, 2017, 50(1):7181–7186. doi: 10.1016/j.ifacol.2017.08.602
[15]	于树友, 陈虹, 张鹏, 李学军. 一种基于LMI的非线性模型预测控制终端域优化方法.自动化学报, 2008, 34(7):798-804. Yu S, Chen H, Zhang P, Li X J. An LMI optimization approach for enlarging the terminal region of NMPC, Acta Automatica Sinca, 2008, 34, (7):798–804.
[16]	Cannon M, Deshmukh V, Kouvaritakis B. Nonlinear model predictive control with polytopic invariant sets. Automatica, 2003, 39:1487–1494. doi: 10.1016/S0005-1098(03)00128-6
[17]	Pluymers B, Roobrouck L, Buijs J, Suykens J, Moor B. Constrianed linear MPC with time-varying terminal cost unsing convex combinations. Automatica, 2005, 41(5):831-837. doi: 10.1016/j.automatica.2004.11.023
[18]	Fitri I R, Kim J S, Yu S, Lee Y I. Computation of feasible and invariant sets for interpolationbased MPC. International Journal of Control, Automation, and Systems,
[19]	Mircea L, Spinu V. Finite-step terminal ingredients for stabilizing model predictive control. In IFAC-Papers OnLine, 2015, 48(23):9-15. doi: 10.1016/j.ifacol.2015.11.256
[20]	Lazar M, Tetteroo M. Computataion of terminal sets and sets for discrete time nonlinear mpc. IFAC-Papers OnLine 2018, 51(20):141–146. doi: 10.1016/j.ifacol.2018.11.006
[21]	Rajhans C, Griffith D, Patwardhan S C, Biegler L T, Pillai H K. Two approaches for terminal region characterization in discrete time quasi-infinite horizon NMPC. In: Proceedings of the 6th IFAC Conference on Nonlinear Model Predictive Control. Madison, WL, USA: IFAC, 2018. 19−22
[22]	Rajhans C, Griffith D, Patwardhan S C, Biegler L T, Pillai H K. Terminal region characterization and stability anslysis of discrete time quasi-infinite horizon nonlinear model predictive control.Journal of Process Control, 2019, 83:30–52. doi: 10.1016/j.jprocont.2019.08.002
[23]	Boyd S, Ghaoui L E, Feron E, Balakishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
[24]	Kothare M V, Balakrishnan V, Morari M. Robust constrained model predictive control using linear matrix inequalities. Automatica, 1996, 32(10):1361–1379. doi: 10.1016/0005-1098(96)00063-5
[25]	Oliveira M, Bernussou J, Geromel J C. A new discrete-time robust stability condition. Systems & Control Letters, 1999, 37(4):261-265.
[26]	Cuzzola F, Geromel J C, Morari M. An improved approach for constrained robust model predictive control. Automatica, 2002, 38(7):1183–1189. doi: 10.1016/S0005-1098(02)00012-2
[27]	Vandenberghe L, Boyd S, Wu S P. Determinant Maximization with Linear Matrix Inequality Constraints. Siam Journal on Matrix Analysis & Applications, 1998, 19(2):499-533.
[28]	Nesterov Y, Nemirovsky A. Interior Point Polynomial Methods in Convex Programming. Philadelphia, USA: SIAM Publications, 1994.
[29]	Bohm C, Raff T, Findeisen R, Allgower F. Calculating the terminal region of NMPC for Lure systems via LMIs. In: Proceedings of the 2008 American Control Conference. Seattle, WA, USA: IEEE, 2008. 1127−1132
[30]	Bohm C, Yu S, Allgower F. Predictive control for constrained discrete-time periodic systems using a time-varying terminal region. IFAC Proceedings Volumes, 2009, 42(13):537-542. doi: 10.3182/20090819-3-PL-3002.00093