Please wait a minute...
J4  2009, Vol. 43 Issue (11): 2012-2016    DOI: 10.3785/j.issn.1008-973X.2009.11.012
自动化技术、计算机技术     
扩大约束分段仿射系统鲁棒预测控制的吸引域
陈孚,赵光宙
(浙江大学 系统科学与工程学系,浙江 杭州 310027)
Enlarging domain of attraction of robust predictive control for constrained piecewise affine systems
CHEN Fu, ZHAO Guang-zhou
(Department of System Science and Engineering, Zhejiang University, Hangzhou 310027, China)
 全文: PDF(521 KB)  
摘要:

针对一类具有附加有界扰动的约束离散时间分段仿射(PWA)系统,提出一种扩大其鲁棒模型预测控制吸引域的新方法.计算系统的最大鲁棒正不变集以及相关的局部稳定控制律.基于最大鲁棒正不变集,通过多参数规划,采用一步预测时域来离线计算一序列具有收缩性质的鲁棒可稳定集,构成收缩序列集,并将它们作为优化问题的预测状态终端约束集.得到的预测控制器可以鲁棒调节收缩序列集内的状态到鲁棒正不变集,从而确保系统的鲁棒稳定,并扩大了鲁棒预测控制的吸引域.通过数值实例验证了方法的有效性.

关键词: 分段仿射系统模型预测控制多参数规划鲁棒不变集吸引域    
Abstract:

Aimed at a class of constrained discrete-time piecewise affine (PWA) systems with addictive bounded disturbances, a new method for enlarging the domain of attraction of robust model predictive control (MPC) was presented. The maximal robust positively invariant set and the associated local stable control law were computed. Based on the maximal robust positively invariant set, a contractive sequence of robust stabilizable sets were computed off-line using multi-parametric programming with one-step predictive horizon. By considering this sequence as terminal constraint of predictive states in the optimization problem, the resulting controller can robustly steer the states in the contractive sequence of sets to the maximal robust positively invariant set. Hence the stability and the enlargement of domain of attraction of robust predictive control were guaranteed. A numerical example showed the validity of the proposed method.

Key words: piecewise affine system    model predictive control    multi-parametric programming    robust invariant set    domain of attraction
出版日期: 2009-12-01
:  TP 273  
基金资助:

浙江省科技计划攻关资助项目(2006C21010).

通讯作者: 赵光宙,男,教授,博导.     E-mail: zhaogz@cee.zju.edu.cn
作者简介: 陈孚(1980-),男,河南南阳人,博士生,从事混杂系统鲁棒预测控制研究.
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  
陈孚
赵光宙

引用本文:

陈孚, 赵光宙. 扩大约束分段仿射系统鲁棒预测控制的吸引域[J]. J4, 2009, 43(11): 2012-2016.

CHEN Fu, DIAO Guang-Zhou. Enlarging domain of attraction of robust predictive control for constrained piecewise affine systems. J4, 2009, 43(11): 2012-2016.

链接本文:

http://www.zjujournals.com/xueshu/eng/CN/10.3785/j.issn.1008-973X.2009.11.012        http://www.zjujournals.com/xueshu/eng/CN/Y2009/V43/I11/2012

[1] HEEMELS W P M H, DE SCHUTTER B, BEMPORAD A. Equivalence of hybrid dynamical models [J]. Automatica, 2001, 37(4): 1085-1091.
[2] 邹媛媛,邹涛,李少远. 混杂系统的预测控制[J]. 控制与决策, 2007, 22(4): 361-366.
ZOU Yuan-yuan, ZOU Tao, LI Shao-yuan. Predictive control for hybrid systems [J]. Control and Decision, 2007, 22(4): 361-366.
[3] MORARI M, BARIC M. Recent developments in the control of constrained hybrid systems [J]. Computers and Chemical Engineering, 2006, 30(10): 1619-1631.
[4] DE DONA J A, SERON M M, MAYNE D Q, et al. Enlarged terminal sets guaranteeing stability of receding horizon control [J]. Systems and Control Letters, 2002, 47(1): 57-63.
[5] LIMON D, GOMES DA SILVA J, ALAMO T, et al. Improved MPC design based on saturating control laws [C]∥ European Control Conference. Cambridge: European Union Control Association, 2003: 104-110.
[6] CHEN W, BALANCE D, OREILLY J. Optimization of attraction domains of nonlinear MPC via LMI methods [C]∥ Proceedings of the ACC. New York: IEEE, 2001: 1024-1027.
[7] CANNON M, DESHMUKKH V, KOUVARITAKIS B. Nonlinear model predictive control with polytopic invariant sets [J]. Automatica, 2003, 39(8): 1487-1494.
[8] LIMON D, ALAMO T, CAMACHO E F. Enlarging the domain of attraction of MPC controllers [J]. Automatica, 2005, 41(4): 629-635.
[9] ONG C J, SUI D, GILBERT E G. Enlarging the terminal region of nonlinear model predictive control using the support vector machine method [J]. Automatica, 2006, 42(6): 1011-1016.
[10] LIMON D, ALAMO T, CAMACHO E F. Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties [C]∥ Proceedings of the CDC. Las Vegas: IEEE, 2002: 1420-1425.
[11] KERRIGAN E C. Robust constraint satisfaction: invariant sets and predictive control [D]. Cambridge: University of Cambridge, 2000: 44-59.
[12] KERRIGAN E C, MACIEJOWSKI J M. Invariant sets for constrained discrete-time systems with application to feasibility in model predictive control [C]∥ Proceedings of the CDC. Sydney: IEEE, 2000: 896-901.
[13] RAKOVIC S V, GRIEDER P, KVASNICA M, et al. Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances [C]∥ Proceedings of the CDC. Atlantis: IEEE, 2004: 841-846.
[14] BLANCHINI F. Set invariance in control [J]. Automatica, 1999, 35(11): 1747-1767.
[15] MAYNE D Q, RAWLINGS J B, RAO C V, et al. Constrained model predictive control: stability and optimality [J]. Automatic, 2000, 36(6): 789-814.
[16] GRIEDER P. Efficient computation of feedback controllers for constrained systems [D]. Zurich: Swiss Federal Institute of Technology, 2004: 179-182.

[1] 杨庆芳, 赵小辉, 郑黎黎, 张伟. 基于模型预测控制的环形交叉口信号配时方法[J]. 浙江大学学报(工学版), 2018, 52(1): 117-124.
[2] 初亮, 李天骄, 孙成伟. 面向再生制动优化的电动车自适应巡航控制策略[J]. 浙江大学学报(工学版), 2017, 51(8): 1596-1602.
[3] 李国飞, 滕青芳, 王传鲁, 张雅琴. 应用滑模控制的四开关逆变器PMSM系统FCS-MPC策略[J]. 浙江大学学报(工学版), 2017, 51(3): 620-627.
[4] 金鑫, 梁军. 基于动态PLS框架的多变量无静差预测控制[J]. 浙江大学学报(工学版), 2016, 50(4): 750-758.
[5] 王玄, 陶建峰, 张峰榕, 吴亚瑾, 刘成良. 泵控非对称液压缸系统高精度位置控制方法[J]. 浙江大学学报(工学版), 2016, 50(4): 597-602.
[6] 李丽娟, 熊路, 刘君, 徐欧官. 基于AP-LSSVM的多模型预测控制[J]. J4, 2013, 47(10): 1741-1746.
[7] 刘志鹏, 颜文俊. 预粉磨系统的智能建模与复合控制[J]. J4, 2012, 46(8): 1506-1511.
[8] 符晓,戴鹏,伍小杰,刘向超. 电励磁同步电动机模型预测控制[J]. J4, 2011, 45(5): 815-817.
[9] 罗莉华, 龚李龙, 李平, 王慧. 考虑驾驶员行驶特性的双模式自适应
巡航控制设计
[J]. J4, 2011, 45(12): 2073-2078.
[10] 王跃宣 苏宏业 胡昔祥 褚健. 多层分布式先进控制软件及其应用[J]. J4, 2004, 38(3): 262-266.