持续扰动下多耦合非线性系统分布式经济模型预测控制

王定超; 何德峰; 谢永芳

doi:10.16383/j.aas.c240295

持续扰动下多耦合非线性系统分布式经济模型预测控制

doi: 10.16383/j.aas.c240295

1.
浙江工业大学信息工程学院杭州 310023
2.
中南大学自动化学院长沙 410083

基金项目: 国家自然科学基金 (62173303), 中央引导地方科技发展资金项目 (2023ZY1045) 资助

详细信息

作者简介:
王定超：浙江工业大学信息工程学院博士研究生. 2019 年获得浙江师范大学硕士学位. 主要研究方向为非线性系统分布式经济模型预测控制. E-mail: 1112103015@zjut.edu.cn

何德峰：浙江工业大学信息工程学院教授. 2001 年和 2008 年分别获得中南大学学士学位和中国科学技术大学博士学位. 主要研究方向为智能预测与最优控制和网络系统运行优化控制. 本文通信作者. E-mail: hdfzj@zjut.edu.cn

谢永芳：中南大学自动化学院教授. 1999 年获得中南工业大学博士学位. 主要研究方向为分散控制与鲁棒控制, 过程控制, 工业大数据和知识自动化. E-mail: yfxie@csu.edu.cn

计量
- 文章访问数: 106
- HTML全文浏览量: 45
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-27
- 录用日期: 2024-08-05
- 网络出版日期: 2024-09-02

Distributed EMPC of Multi-Coupled Nonlinear Systems with Persistent Disturbances

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023
2.
School of Automation, Central South University, Changsha 410083

Funds: Supported by National Natural Science Foundation of China (62173303) and the Central Guidance Project for Local Scientific and Technological Development (2023ZY1045)

More Information

Author Bio:
WANG Ding-Chao Ph.D. candidate at the College of Information Engineering, Zhejiang University of Technology. He received his Master degree from Zhejiang Normal University in 2019. His research interest covers distributed economic model predictive control for nonlinear system

HE De-Feng Professor at the College of Information Engineering, Zhejiang University of Technology. He received his bachelor degree from Central South University in 2001 and Ph.D. degree from University of Science and Technology of China in 2008. His research interest covers intelligent prediction and optimal control, optimization control of network systems. Corresponding author of this paper

XIE Yong-Fang Professor at the School of Automation, Central South University. He received his Ph.D. degree from Central South University in 1999. His research interest covers decentralized control and robust control, process control, industrial big data and knowledge automation

摘要

摘要: 针对持续扰动下的分布式状态耦合非线性系统, 提出一种新的多耦合分布式经济模型预测控制 (Economic model predictive control, EMPC) 策略. 由于耦合非线性系统的经济性能函数的非凸性和非正定性, 首先引入关于经济最优平衡点的正定辅助函数和相应的辅助优化问题. 接着, 利用辅助函数的最优值函数构造原始分布式 EMPC 的一类隐式收缩约束. 然后建立状态耦合分布式 EMPC 的递推可行性和闭环系统关于最优经济平衡点的输入到状态稳定性结论. 最后, 以耦合的四个连续搅拌釜反应器为例, 验证本文所提策略的有效性.
- 模型预测控制 /
- 分布式控制 /
- 非线性系统 /
- 经济优化 /
- 耦合系统
Abstract: This paper presents a novel multi-coupled distributed economic model predictive control (EMPC) strategy for distributed state-coupled nonlinear systems with persistent disturbances. Due to the non-convex and non-positive-definite of the economic performance functions for coupled nonlinear systems, a positive definite auxiliary function related to the optimal economic equilibrium point and the corresponding auxiliary optimization problem are introduced. Then, the optimal value function of the auxiliary function is used to formulate a class of implicit contractive constraints for the original distributed EMPC. Subsequently, the recursive feasibility of the state coupled distributed EMPC and the input-state stability of the closed-loop system with respect to the optimal economic equilibrium point are established. Finally, the effectiveness of the proposed strategy is demonstrated by a simulation example of four coupled continuous stirred-tank reactors.
- Model predictive control (MPC) /
- distributed control /
- nonlinear systems /
- economic optimization /
- coupled systems

HTML全文

图 1 子系统i的上游和下游邻居集合示意图

Fig. 1 Schematic diagram of the upstream and downstream neighbor sets of subsystem i

下载: 全尺寸图片幻灯片

图 2 子系统1的状态x1轨迹

Fig. 2 State x1 trajectories of subsystem 1

下载: 全尺寸图片幻灯片

图 3 子系统1的状态x2轨迹

Fig. 3 State x2 trajectories of subsystem 1

下载: 全尺寸图片幻灯片

图 4 子系统1的控制输入

Fig. 4 Control input of subsystem 1

下载: 全尺寸图片幻灯片

图 5 子系统1的性能函数

Fig. 5 Performance function of subsystem 1

下载: 全尺寸图片幻灯片

图 6 子系统2的状态x1轨迹

Fig. 6 State x1 trajectories of subsystem 2

下载: 全尺寸图片幻灯片

图 7 子系统2的状态x2轨迹

Fig. 7 State x2 trajectories of subsystem 2

下载: 全尺寸图片幻灯片

图 8 子系统2的控制输入

Fig. 8 Control input of subsystem 2

下载: 全尺寸图片幻灯片

图 9 子系统2的性能函数

Fig. 9 Performance function of subsystem 2

下载: 全尺寸图片幻灯片

图 10 子系统3的状态x1轨迹

Fig. 10 State x1 trajectories of subsystem 3

下载: 全尺寸图片幻灯片

图 11 子系统3的状态x2轨迹

Fig. 11 State x2 trajectories of subsystem 3

下载: 全尺寸图片幻灯片

图 12 子系统3的控制输入

Fig. 12 Control input of subsystem 3

下载: 全尺寸图片幻灯片

图 13 子系统3的性能函数

Fig. 13 Performance function of subsystem 3

下载: 全尺寸图片幻灯片

图 14 子系统4的状态x1轨迹

Fig. 14 State x1 trajectories of subsystem 4

下载: 全尺寸图片幻灯片

图 15 子系统4的状态x2轨迹

Fig. 15 State x2 trajectories of subsystem 4

下载: 全尺寸图片幻灯片

图 16 子系统4的控制输入

Fig. 16 Control input of subsystem 4

下载: 全尺寸图片幻灯片

图 17 子系统4的性能函数

Fig. 17 Performance function of subsystem 4

下载: 全尺寸图片幻灯片

参考文献(35)

[1]	Liu M, Shi Y, Liu X. Distributed MPC of aggregated heterogeneous thermostatically controlled loads in smart grid. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1120−1129 doi: 10.1109/TIE.2015.2492946
[2]	Chilin D, Liu J, Chen X, Christofides P. Fault detection and isolation and fault tolerant control of a catalytic alkylation of benzene process. Chemical Engineering Science, 2012, 78: 155−166 doi: 10.1016/j.ces.2012.05.015
[3]	Zhang A, Yin X, Liu S, Zeng J, Liu J. Distributed economic model predictive control of wastewater treatment plants. Chemical Engineering Research and Design, 2019, 141: 144−155 doi: 10.1016/j.cherd.2018.10.039
[4]	Leirens S, Zamora C, Negenborn R, De S. Coordination in urban water supply networks using distributed model predictive control. In: Proceedings of the 29st American Control Conference. Baltimore, Maryland, USA: IEEE, 2010. 3957-3962
[5]	Ma S, Zou Y, Li S. Distributed model predictive control with priority coordination for limited supply multi-zone HVAC systems. Journal of Process Control, 2022, 117: 157−168 doi: 10.1016/j.jprocont.2022.07.013
[6]	Kang Y, Wang T, Li P, Xu Z, Zhao Y. Compound event-triggered distributed MPC for coupled nonlinear systems. IEEE Transactions on Cybernetics, 2023, 53(9): 5572−5584 doi: 10.1109/TCYB.2022.3159343
[7]	Wang T, Kang Y, Li P, Zhao Y, Tang H. Rolling self-triggered distributed MPC for dynamically coupled nonlinear systems. Automatica, 2024, 160: Article No. 111444 doi: 10.1016/j.automatica.2023.111444
[8]	Ma A, Liu K, Zhang Q, Xia Y. Distributed MPC for linear discrete-time systems with disturbances and coupled states. Systems and Control Letters, 2020, 135: Article No. 104578 doi: 10.1016/j.sysconle.2019.104578
[9]	Farina M, Scattolini R. Distributed predictive control: A non-cooperative algorithm with neighbor-to-neighbor communic-ation for linear systems. Automatica, 2012, 48(6): 1088−1096 doi: 10.1016/j.automatica.2012.03.020
[10]	Liu C, Li H, Shi Y, Xu D. Distributed event-triggered model predictive control of coupled nonlinear systems. SIAM Journal on Control and Optimization, 2020, 58(2): 714−734 doi: 10.1137/18M1176671
[11]	Riverso S, Farina M, Ferrari G. Plug-and-play decentralized model predictive control for linear systems. IEEE Transactions on Automatic Control, 2013, 58(10): 2608−2614 doi: 10.1109/TAC.2013.2254641
[12]	Long Y, Liu S, Xie L, Johansson K. Distributed nonlinear model predictive control based on contraction theory. International Journal of Robust and Nonlinear Control, 2018, 28(2): 492−503 doi: 10.1002/rnc.3881
[13]	Gao Y, Dai L, Xia Y, Liu Y. Distributed model predictive control for consensus of nonlinear second-order multi-agent systems. International Journal of Robust and Nonlinear Control, 2017, 27(5): 830−842 doi: 10.1002/rnc.3603
[14]	Wang Q, Duan Z, Lv Y, Wang Q, Chen G. Distributed model predictive control for linear-quadratic performance and consensus state optimization of multiagent systems. IEEE Transactions on Cybernetics, 2021, 51(6): 2905−2915 doi: 10.1109/TCYB.2020.3001347
[15]	Müller M, Reble M, Allgöwer F. Cooperative control of dynamically decoupled systems via distributed model predictive control. International Journal of Robust and Nonlinear Control, 2012, 22(12): 1376−1397 doi: 10.1002/rnc.2826
[16]	Dai L, Cao Q, Xia Y, Gao Y. Distributed MPC for formation of multi-agent systems with collision avoidance and obstacle avoidance. Journal of the Franklin Institute, 2017, 354(4): 2068−2085 doi: 10.1016/j.jfranklin.2016.12.021
[17]	Chen X, Heidarinejad M, Liu J, Christofides P. Distributed economic MPC: Application to a nonlinear chemical process network. Journal of Process Control, 2012, 22: 689−699 doi: 10.1016/j.jprocont.2012.01.016
[18]	Jia Y, Dong ZY, Sun C, Chen G. Distributed economic model predictive control for a wind-photovoltaic-battery microgrid power system. IEEE Transactions on Sustainable Energy, 2020, 11(2): 1089−1099 doi: 10.1109/TSTE.2019.2919499
[19]	Albalawi F, Durand H, Christofides P. Distributed economic model predictive control with safeness-index based constraints for nonlinear systems. Systems and Control Letters, 2017, 110: 21−28 doi: 10.1016/j.sysconle.2017.10.002
[20]	Huang M, Zheng Y, Li S. Distributed economic model predictive control for an industrial fluid catalytic cracking unit ensuring safe operation. Control Engineering Practice, 2022, 126: Article No. 105263 doi: 10.1016/j.conengprac.2022.105263
[21]	Jia Y, Meng K, Wu K, Sun C, Dong Z. Optimal load frequency control for networked power systems based on distributed economic MPC. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(4): 2123−2133 doi: 10.1109/TSMC.2020.3019444
[22]	Bian Y, Du C, Hu M, Li S, Liu H, Li C. Fuel economy optimization for platooning vehicle swarms via distributed economic model predictive control. IEEE Transactions on Automation Science and Engineering, 2022, 19(4): 2711−2723 doi: 10.1109/TASE.2021.3128920
[23]	Köhler P, Müller M, Allgöwer F. A distributed economic MPC framework for cooperative control under conflicting objectives. Automatica, 2018, 96: 368−379 doi: 10.1016/j.automatica.2018.07.001
[24]	Luo J, He D, Zhu W, Du H. Multiobjective platooning of connected and automated vehicles using distributed economic model predictive control. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(10): 19121−19135 doi: 10.1109/TITS.2022.3170977
[25]	He D, Qiu T, Luo R. Fuel efficiency-oriented platooning control of connected nonlinear vehicles: A distributed economic MPC approach. Asian Journal of Control, 2020, 22(4): 1628−1638 doi: 10.1002/asjc.2049
[26]	Li A, Sun J. Stability of nonlinear system under distributed Lyapunov-based economic model predictive control with time-delay. ISA Transactions, 2020, 99: 148−153 doi: 10.1016/j.isatra.2019.10.004
[27]	Dai L, Qiang Z, Sun Z, Zhou T, Xia Y. Distributed economic MPC for dynamically coupled linear systems with uncertainties. IEEE Transactions on Cybernetics, 2022, 52(6): 5301−5310 doi: 10.1109/TCYB.2020.3030021
[28]	何德峰. 约束非线性系统稳定经济模型预测控制. 自动化学报, 2016, 42(11): 1680−1690 He De-Feng. Stabilizing economic model predictive control of constrained nonlinear systems. Acta Automatica Sinica, 2016, 42(11): 1680−1690
[29]	Ellis M, Durand H, Christofides P. A tutorial review of economic model predictive control methods. Journal of Process Control, 2014, 24(8): 1156−1178 doi: 10.1016/j.jprocont.2014.03.010
[30]	Zhou T, Dai L, Li Q, Xia Y. Distributed economic MPC for dynamically coupled systems with stochastic disturbances. IEEE Transactions on Circuits and Systems. I, Regular Papers, 2023, 70(12): 5442−5455 doi: 10.1109/TCSI.2023.3321682
[31]	Darivianakis G, Eichler A, Lygeros J. Distributed model predictive control for linear systems with adaptive terminal sets. IEEE Transactions on Automatic Control, 2020, 65(137): 1044−1056
[32]	Dai L, Zhou T, Qiang Z, Sun Z, Xia Y. Distributed economic MPC for dynamically coupled linear systems: A Lyapunov-based approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(3): 1408−1419 doi: 10.1109/TSMC.2022.3201701
[33]	Angeli D, Amrit R, Rawlings J. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control, 2012, 57(7): 1615−1626 doi: 10.1109/TAC.2011.2179349
[34]	何德峰, 韩平, 王青松. 有界扰动下约束非线性系统鲁棒经济模型预测控制. 自动化学报, 2022, 48(2): 572−581 He De-Feng, Han Ping, Wang Qing-Song. Robust economic MPC of constrained nonlinear systems with bounded disturbances. Acta Automatica Sinica, 2022, 48(2): 572−581
[35]	Yin X, Qin Y, Liu J, Huang B. Data-driven moving horizon state estimation of nonlinear processes using Koopman operator. Chemical Engineering Research and Design, 2023, 200: 481−492 doi: 10.1016/j.cherd.2023.10.033