基于鲁棒一步集的Tube不变集鲁棒模型预测控制

秦伟伟; 刘刚; 王剑; 郑志强

doi:10.3724/SP.J.1004.2014.01404

基于鲁棒一步集的Tube不变集鲁棒模型预测控制

doi: 10.3724/SP.J.1004.2014.01404

1.
第二炮兵工程大学自动控制系西安 710025;
2.
第二炮兵工程大学空间工程系西安 710025;
3.
国防科技大学机电工程与自动化学院长沙 410073

基金项目:

国家自然科学基金（61203007）资助

详细信息

作者简介:
刘刚第二炮兵工程大学空间工程系教授. 1998 年获得西北工业大学博士学位. 主要研究方向为精确制导与控制.E-mail：hb830513@126.com

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出版历程
- 收稿日期: 2012-02-29
- 修回日期: 2012-11-26
- 刊出日期: 2014-07-20

Robust MPC with Tube Invariant Set Based on Robust One-step Set

1.
Department of Automatic Control, The Second Artillery Engineering University, Xi'an 710025;
2.
Department of Space Engineering, The Second Artillery Engineering University, Xi'an 710025;
3.
College of Machtronics and Automation, National University of Defense Technology, Changsha 410073

Funds:

Supported by National Natural Science Foundation of China (61203007)

摘要

摘要: 针对一类干扰有界的输入和状态受约束线性离散系统，提出了一种基于鲁棒一步集的Tube不变集鲁棒模型预测控制方法.首先采用多面体不变集离线设计方法得到基于多面体不变集序列的扩展终端约束集;然后为了扩大鲁棒模型预测控制的初始状态允许区域，并提高系统的鲁棒性，在扩展终端约束集的基础上，通过引入鲁棒一步集并借助Tube不变集控制策略，设计了基于鲁棒一步集的鲁棒模型预测控制方法，并给出了算法的存在性和稳定性证明. 该方法不仅极大地扩大了初始状态允许区域，而且对有界干扰具有有效的抑制作用，使得受扰系统收敛到以原点为中心的最小鲁棒正不变集内.最后仿真验证了算法的有效性.
- 鲁棒模型预测控制 /
- 鲁棒一步集 /
- Tube不变集 /
- 最小鲁棒正不变集
Abstract: A robust MPC with Tube invariant set based on robust one-step set is proposed for a constrained discrete-time uncertain linear system with bounded unknown state disturbance. Firstly, the enlarged terminal constraint region is obtained offline by a continuum of polytopic invariant sets. In order to enlarge the region of initial state admissible set and improve the robustness of this method, robust one-step set and Tube invariant set are used for designing the robust model predictive controller. The stability and the theorem of existence of this method are also proved. This algorithm not only enlarges the region of initial state admissible set greatly, but also restrains the state disturbance effectively. And the system states could be drived into the minimal robust positively invariant set around the origin. The simulation results prove the availability of the proposed method.
- Robust MPC /
- robust one-step set /
- Tube invariant set /
- minimal robust positively invariant set

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参考文献(20)

[1]	Mayne D Q, Rawlings J B, Rao C V, Scokaert P O M. Constrained model predictive control: stability and optimality. Automatica, 2000, 36(4): 789-814
[2]	Artsteina Z, Raković S V. Feedback and invariance under uncertainty via set-iterates. Automatica, 2008, 44(2): 520-525
[3]	Xi Yu-Geng, Li De-Wei. Fundamental philosophy and status of qualitative synthesis of model predictive control. Acta Automatica Sinica, 2008, 34(10): 1225-1234(席裕庚, 李德伟. 预测控制定性综合理论的基本思路和研究现状. 自动化学报, 2008, 34(10): 1225-1234)
[4]	Cannon M, Deshmukh V, Kouvaritakis B. Nonlinear model predictive control with polytopic invariant sets. Automatica, 2003, 39(8): 1487-1494
[5]	Cannon M, Kouvaritakis B, Desshmukh V. Enlargement of polytopic terminal region in NMPC by interpolation and partial invariance. Automatica, 2004, 40(2): 311-317
[6]	Pluymers B, Kothare M V, Suykens J A K, De Moor B. Robust synthesis of constrained linear state feedback using LMIs and polyhedral invariant sets. In: Proceedings of the American Control Conference. Minneapolis, MN: IEEE, 2006. 881-886
[7]	Xi Yu-Geng, Zhu Hong-Lin, Li De-Wei. Synthesis off-line robust model predictive control based on polyhedron invariant set. Control and Decision, 2009, 24(2): 302-307(席裕庚, 朱红林, 李德伟. 基于多面体不变集的离线鲁棒预测控制器综合. 控制与决策, 2009, 24(2): 302-307)
[8]	Wan Z Y, Kothare M V. Efficient robust constrained model predictive control with a time varying terminal constraint set. System & Control Letters, 2003, 48(5): 375-383
[9]	Wan Z Y, Pluymers B, Kothare M V, De Moor B. Comments on: "Efficient robust constrained model predictive control with a time varying terminal constraint set" by Wan and Kothare. System & Control Letters, 2006, 55(7): 618-621
[10]	Mayne D Q, Seron M M, Raković S V. Robust model predictive control of constrained linear systems with bounded disturbances. Automatica, 2005, 41(2): 219-224
[11]	Mayne D Q, Langson W. Robustifying model predictive control of constrained linear systems. Electronics Letters, 2001, 37(23): 1422-1423
[12]	Wang C, Ong C J, Sim M. Constrained linear system with disturbance: convergence under disturbance feedback. Automatica, 2008, 44(10): 2583-2587
[13]	Wang C, Ong C J, Sim M. Model predictive control using segregated disturbance feedback. IEEE Transactions on Automatic Control, 2010, 55(4): 831-840
[14]	Wang C, Ong C J. Constraint-admissible sets for systems with soft constraints and their application in model predictive control. International Journal of Robust, Nonlinear Control, 2011, 22(11): 1229-1243
[15]	Limon D, Alvarado I, Alamo T, Camacho E F. Robust Tube-based MPC for tracking of constrained linear systems with additive disturbances. Journal of Process Control, 2010, 20(3): 248-260
[16]	Gilbert E G, Ong C J. Constrained linear systems with hard constraints and disturbances: an extended command governor with large domain of attraction. Automatica, 2011, 47(2): 334-340
[17]	Qin Wei-Wei, Ma Jian-Jun, Zheng Zhi-Qiang, Liu Gang. Off-line RMPC based on Tube invariant set for a discrete-time uncertain system. Information and Control, 2011, 40(3): 307-312(秦伟伟, 马建军, 郑志强, 刘刚. 一类离散不确定系统的Tube 不变集离线RMPC. 信息与控制, 2011, 40(3): 307-312)
[18]	Kerrigan E C. Robust Constraint Satisfaction: Invariant Sets and Predictive Control [Ph.D. dissertation], University of Cambridge, UK, 2000
[19]	Zou Tao. Analysis and Design for Constrained Model Predictive Control System [Ph.D. dissertation], Shanghai Jiaotong University, China, 2004. 83-85(邹涛. 约束模型预测控制系统的分析与设计 [博士学位论文], 上海交通大学, 中国, 2004. 83-85)
[20]	Rakovic S V, Kerrigan E C, Kouramas K I, Mayne D Q. Invariant approximations of the minimal robust positively invariant set. IEEE Transactions on Automatic Control, 2005, 50(3): 406-410