A stochastic MPC scheme for distributed systems with multiplicative uncertainty

被引：2
作者：
Mark, Christoph [1 ]
Liu, Steven [1 ]
机构：
[1] Univ Kaiserslautern, Inst Control Syst, Dept Elect & Comp Engn, Erwin Schrodinger Str 12, D-67663 Kaiserslautern, Germany
来源：
AUTOMATICA | 2022年 / 140卷
关键词：
Distributed Model Predictive Control; Stochastic control; Distributed control; Predictive control; MODEL-PREDICTIVE CONTROL; LINEAR-SYSTEMS; STATE;
D O I：
10.1016/j.automatica.2022.110208
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are approximated via Cantelli's inequality by means of expected value and covariance. The cooperative control algorithm is based on the distributed Alternating Direction Method of Multipliers, which renders the controller fully distributedly implementable, recursively feasible and ensures point-wise convergence of the states. The aforementioned properties are guaranteed through a properly selected distributed invariant set and distributed terminal constraints for the mean and covariance. The paper closes with an example highlighting the chance constraint satisfaction, numerical properties and scalability of our approach. (C) 2022 Elsevier Ltd. All rights reserved.
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页数：8
相关论文
共 23 条
[1]  
[Anonymous], 1997, Linear Matrix Inequalities in System and Control Theory
[2]   Scenario-based Model Predictive Control of Stochastic Constrained Linear Systems [J].
Bernardini, Daniele ;
Bemporad, Alberto .
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, :6333-6338
[3]   A Probabilistic Particle-Control Approximation of Chance-Constrained Stochastic Predictive Control [J].
Blackmore, Lars ;
Ono, Masahiro ;
Bektassov, Askar ;
Williams, Brian C. .
IEEE TRANSACTIONS ON ROBOTICS, 2010, 26 (03) :502-517
[4]   Distributed optimization and statistical learning via the alternating direction method of multipliers [J].
Boyd S. ;
Parikh N. ;
Chu E. ;
Peleato B. ;
Eckstein J. .
Foundations and Trends in Machine Learning, 2010, 3 (01) :1-122
[5]   Stochastic Tubes in Model Predictive Control With Probabilistic Constraints [J].
Cannon, Mark ;
Kouvaritakis, Basil ;
Rakovic, Sasa V. ;
Cheng, Qifeng .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (01) :194-200
[6]   Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints [J].
Cannon, Mark ;
Kouvaritakis, Basil ;
Wu, Xingjian .
AUTOMATICA, 2009, 45 (01) :167-172
[7]   Distributed model predictive control: A tutorial review and future research directions [J].
Christofides, Panagiotis D. ;
Scattolini, Riccardo ;
Munoz de la Pena, David ;
Liu, Jinfeng .
COMPUTERS & CHEMICAL ENGINEERING, 2013, 51 :21-41
[8]   Distributed synthesis and stability of cooperative distributed model predictive control for linear systems [J].
Conte, Christian ;
Jones, Colin N. ;
Morari, Manfred ;
Zeilinger, Melanie N. .
AUTOMATICA, 2016, 69 :117-125
[9]   Distributed Stochastic MPC of Linear Systems With Additive Uncertainty and Coupled Probabilistic Constraints [J].
Dai, Li ;
Xia, Yuanqing ;
Gao, Yulong ;
Cannon, Mark .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2017, 62 (07) :3474-3481
[10]  
Dai L, 2016, CHIN CONTR CONF, P4312, DOI 10.1109/ChiCC.2016.7554022
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