多模型自適應控制理論及應用

張玉振; 李擎; 張維存; 楊宇航

doi:10.13374/j.issn2095-9389.2019.02.25.006

多模型自適應控制理論及應用

doi: 10.13374/j.issn2095-9389.2019.02.25.006

北京科技大學自動化學院，北京 100083

基金項目: 國家自然科學基金資助項目（61673098，61603034）；北京市自然科學基金資助項目（3182027）；中央高校基本科研業務費（FRF-GF-17-B44）

詳細信息

通訊作者:
E-mail：liqing@ies.ustb.edu.cn

中圖分類號: TP273
計量
- 文章訪問數: 2694
- HTML全文瀏覽量: 1538
- PDF下載量: 206
- 被引次數: 0
出版歷程
- 收稿日期: 2019-02-25
- 刊出日期: 2020-02-01

Survey of multi-model adaptive control theory and its applications

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

More Information

Corresponding author: E-mail: liqing@ies.ustb.edu.cn

摘要

摘要: 作為對經典自適應控制改進的控制方法，多模型自適應控制是解決復雜的大范圍參數不確定系統的一種有效途徑，并在理論和實踐中取得了豐富成果。依據控制器集的不同綜合策略，其被分為多種類型，本文旨在對加權型的多模型自適應控制進行綜述。加權多模型自適應控制的基本思路是采用“分而治之”的辦法，離線建立多個局部模型和對應的多個局部控制器，在線加權融合各個局部控制器的控制輸出，從而形成全局控制，是實現魯棒自適應控制的一類重要方法。首先比較詳細地介紹了加權多模型自適應控制研究的歷史及現狀，然后給出相關研究的新進展和一些觀點，包括新的加權算法和相應的加權多模型自適應控制系統的穩定性結果等，最后指出未來的幾個研究方向。
- 加權算法 /
- 多模型自適應控制 /
- 穩定性 /
- 收斂性 /
- 虛擬等價系統
Abstract: Multi-model adaptive control, as an improved method of classical adaptive control, can effectively solve the control performance issues for the complex systems with large parameter uncertainties. It has attracted increasing attention from scholars, and a vast array of research results have been achieved in theory and practice. According to the different synthesis methods of multiple local controllers corresponding to the multiple local models, the multi-model adaptive control scheme can be divided into different categories. This paper provides a survey of weighted multi-model adaptive control (WMMAC). The basic idea of the WMMAC is to adopt the method of “divide and conquer”; multiple local models and corresponding multiple local controllers are established offline, and the control outputs of local controllers are integrated online, such that the global control law can be formed. The WMMAC is a promising method to achieve strong robustness and a self-adaptive ability for control systems. First, we presented the development process and the main problems of the WMMAC. Then, the research status of control systems and the latest progress were shown, including model set construction and weighting algorithm design. To improve the rationality of model set construction, WMMACs with self-tuning model and even a dynamic model set have been developed. Meanwhile, to reduce the calculation burden, a new weighting algorithm has been designed, which is based on the model output errors of the multi-model adaptive control system. Especially for system stability analysis, which has always been a recognized problem in the WMMAC system, some research results have been obtained. The proof of system stability in the general sense has been given preliminarily by introducing the theory of virtual equivalent system. This paper gave a review of WMMAC in the order of the variation on the structure, the development of algorithms and its applications. Furthermore, the main problems in the control system were analyzed, and some potential research directions, which are the difficulties and emphases of future research including model set, weight calculation, disturbance rejection, stability, were pointed out.
- weighting algorithm /
- multi-model adaptive control /
- stability /
- convergence /
- virtual equivalent system

HTML全文

圖 1 經典加權多模型自適應控制系統框圖

Figure 1. Block diagram for CMMAC

下載: 全尺寸圖片幻燈片

圖 2 魯棒多模型自適應控制系統框圖

Figure 2. Block diagram for RMMAC

下載: 全尺寸圖片幻燈片

圖 3 采用模糊融合的多模型自適應控制系統框圖

Figure 3. Block diagram for MMAC using fuzzy fusion

下載: 全尺寸圖片幻燈片

圖 4 加權多模型自適應控制系統框圖

Figure 4. Block diagram for WMMAC

下載: 全尺寸圖片幻燈片

259luxu-164

參考文獻(78)

[1]	Fekri S, Athans M, Pascoal A. Issues, progress and new results in robust adaptive control. Int J Adapt Control Signal Process, 2006, 20(10): 519 doi: 10.1002/acs.912
[2]	Ioannou P A. CDC semi-plenary: “Robust adaptive control: The search for the Holy Grail” // Proceedings of 2018 47th IEEE Conference on Decision and Control. Cancun, 2008: 12
[3]	Sun Z D, Ge S S. Switched Linear Systems: Control and Design. London: Springer, 2005
[4]	Sun Z D, Ge S S. Stability Theory of Switched Dynamical Systems. London: Springer, 2011
[5]	Wang X Y, Ge P, Sun Y K, et al. Control of FGC system based on multi-model adaptive control method. J Univ Sci Technol Beijing, 2004, 26(1): 99 doi: 10.3321/j.issn:1001-053X.2004.01.026 王修巖, 葛平, 孫一康, 等. 基于多模型自適應控制方法的FGC控制. 北京科技大學學報, 2004, 26(1):99 doi: 10.3321/j.issn:1001-053X.2004.01.026
[6]	Fei S M, Zhou Q. Advances on stability of switched systems. Mach Build Autom, 2014, 43(1): 1 doi: 10.3969/j.issn.1671-5276.2014.01.001 費樹岷, 周強. 切換系統穩定性研究綜述. 機械制造與自動化, 2014, 43(1):1 doi: 10.3969/j.issn.1671-5276.2014.01.001
[7]	Magill D. Optimal adaptive estimation of sampled stochastic processes. IEEE Trans Autom Control, 1965, 10(4): 434 doi: 10.1109/TAC.1965.1098191
[8]	Lainiotis D G. Partitioning: A unifying framework for adaptive systems-I: Estimation. Proc IEEE, 1976, 64(8): 1126 doi: 10.1109/PROC.1976.10284
[9]	Lainiotis D G. Partitioning: A unifying framework for adaptive systems-II: Control. Proc IEEE, 1976, 64(8): 1182 doi: 10.1109/PROC.1976.10289
[10]	Athans M, Castanon D, Dunn K, et al. The stochastic control of the F-8C aircraft using a multiple model adaptive control (MMAC) method-Part I: Equilibrium flight. IEEE Trans Autom Control, 1977, 22(5): 768 doi: 10.1109/TAC.1977.1101599
[11]	Lane D W, Maybeck P S. Multiple model adaptive estimation applied to the LAMBDA URV for failure detection and identification // Proceedings of 1994 33rd IEEE Conference on Decision and Control. Lake Buena Vista, 1994: 678
[12]	Yu C, Roy R J, Kaufman H, et al. Multiple-model adaptive predictive control of mean arterial pressure and cardiac output. IEEE Trans Biomed Eng, 1992, 39(8): 765 doi: 10.1109/10.148385
[13]	Moose R L, Vanlandingham H F, McCabe D H. Modeling and estimation for tracking maneuvering targets. IEEE Trans Aerosp Electron Syst, 1979, 15(3): 448
[14]	Li X R, Bar-Shalom Y. Design of an interacting multiple model algorithm for air traffic control tracking. IEEE Trans Control Syst Technol, 1993, 1(3): 186 doi: 10.1109/87.251886
[15]	Badr A, Binder Z, Rey D. Application of tracking multimodel control to a non-linear thermal process. Int J Syst Sci, 1990, 21(9): 1795 doi: 10.1080/00207729008910499
[16]	Badr A, Binder Z, Rey D. Weighted multi-model control. Int J Syst Sci, 1992, 23(1): 145 doi: 10.1080/00207729208949196
[17]	Nagib G, Gharieb W, Binder Z. Qualitative multi-model control using a learning approach. Int J Syst Sci, 1992, 23(6): 855 doi: 10.1080/00207729208949254
[18]	Aly A, Badr A, Binder Z. Multi-model control of MIMO systems: location and control algorithms. Int J Syst Sci, 1988, 19(9): 1687 doi: 10.1080/00207728808964069
[19]	Fekri S, Athans M, Pascoal A. Robust multiple model adaptive control (RMMAC): a case study. Int J Adapt Control Signal Process, 2007, 21(1): 1 doi: 10.1002/acs.944
[20]	Aguiar A P, Hassani V, Pascoal A M, et al. Identification and convergence analysis of a class of continuous-time multiple-model adaptive estimators. IFAC Proc Vol, 2008, 41(2): 8605 doi: 10.3182/20080706-5-KR-1001.01455
[21]	Hassani V, Aguiar A P, Pascoal A M, et al. A performance based model-set design strategy for multiple model adaptive estimation // 2009 European Control Conference (ECC). Budapest, 2009: 4516
[22]	Hassani V, Aguiar A P, Athans M, et al. Multiple model adaptive estimation and model identification usign a minimum energy criterion // 2009 American Control Conference. Missouri, 2009: 518
[23]	Hassani V, Athans M, Pascoal A M. An application of the RMMAC methodology to an unstable plant // 2009 17th Mediterranean Conference on Control and Automation. Thessaloniki, Greece, 2009: 37
[24]	Kuipers M, Ioannou P. Multiple model adaptive control with mixing. IEEE Trans Autom Control, 2010, 55(8): 1822 doi: 10.1109/TAC.2010.2042345
[25]	Baldi S, Ioannou P, Mosca E. Multiple model adaptive mixing control: the discrete-time case. IEEE Trans Autom Control, 2012, 57(4): 1040 doi: 10.1109/TAC.2011.2169620
[26]	He W G. Multiple model adaptive control for a category of systems with uncertain parameters. Acta Autom Sin, 1988, 14(3): 191 何文光. 一類不確定參數系統的多模型自適應控制. 自動化學報, 1988, 14(3):191
[27]	Wang W, Li X L. Multiple Model Adaptive Control. Beijing: Science Press, 2001 王偉, 李曉理. 多模型自適應控制. 北京: 科學出版社, 2001
[28]	Zheng Y H, Wang X, Li S Y, et al. Multiple models direct adaptive decoupling controller for a stochastic system. Acta Autom Sin, 2010, 36(9): 1295 鄭益慧, 王昕, 李少遠, 等. 隨機系統的多模型直接自適應解耦控制器. 自動化學報, 2010, 36(9):1295
[29]	Dong Z K, Wang X, Wang X B, et al. Application of weighted multiple models adaptive controller in the plate cooling process. Acta Autom Sin, 2010, 36(8): 1144 doi: 10.3724/SP.J.1004.2010.01144
[30]	Wang S H, Shen J, Li Y G. Multi-model control and its study progress. Ind Instrum Autom, 2008(1): 13 doi: 10.3969/j.issn.1000-0682.2008.01.004 王世虎, 沈炯, 李益國. 多模型控制方法及其研究進展. 工業儀表與自動化裝置, 2008(1):13 doi: 10.3969/j.issn.1000-0682.2008.01.004
[31]	Hu G L, Sun Y X. Advances and application of multiple model control method. Inform Control, 2004, 33(1): 72 doi: 10.3969/j.issn.1002-0411.2004.01.016 胡國龍, 孫優賢. 多模型控制方法的研究進展及其應用現狀. 信息與控制, 2004, 33(1):72 doi: 10.3969/j.issn.1002-0411.2004.01.016
[32]	Yuan X Y, Shi S J. Survey of multiple model based adaptive control. J Shanghai Jiaotong Univ, 1999, 33(5): 626 doi: 10.3321/j.issn:1006-2467.1999.05.033 袁向陽, 施頌椒. 基于多模型的自適應控制研究進展. 上海交通大學學報, 1999, 33(5):626 doi: 10.3321/j.issn:1006-2467.1999.05.033
[33]	Narendra K S, Han Z. The changing face of adaptive control: the use of multiple models. Annu Rev Control, 2011, 35(1): 1 doi: 10.1016/j.arcontrol.2011.03.010
[34]	Baram Y. Information, Consistent Estimation and Dynamic System Identification [Dissertation]. Massachusetts: Massachusetts Institute of Technology, 1976
[35]	Baram Y, Sandell N. An information theoretic approach to dynamical systems modeling and identification. IEEE Trans Autom Control, 1978, 23(1): 61 doi: 10.1109/TAC.1978.1101690
[36]	Baram Y, Sandell N. Consistent estimation on finite parameter sets with application to linear systems identification. IEEE Trans Autom Control, 1978, 23(3): 451 doi: 10.1109/TAC.1978.1101745
[37]	Kehagias A. Convergence properties of the Lainiotis partition algorithm. Control Comput, 1991, 19(1): 1
[38]	Zhou H, Narendra K S. New concepts in adaptive control using multiple models. IEEE Trans Autom Control, 2012, 57(1): 78 doi: 10.1109/TAC.2011.2152470
[39]	Chen W, Sun J, Chen C, et al. Adaptive control of a class of nonlinear systems using multiple models with smooth controller. Int J Robust Nonlinear Control, 2015, 25(6): 865 doi: 10.1002/rnc.3113
[40]	Zhang W C. Stable weighted multiple model adaptive control: discrete-time stochastic plant. Int J Adapt Control Signal Process, 2013, 27(7): 562 doi: 10.1002/acs.2328
[41]	Zhang W C. Further results on stable weighted multiple model adaptive control: discrete-time stochastic plant. Int J Adapt Control Signal Process, 2015, 29(12): 1497 doi: 10.1002/acs.2555
[42]	Zhang W C. Weighted multiple model adaptive control of discrete-time stochastic system with uncertain parameters. Acta Autom Sin, 2015, 41(3): 541 張維存. 參數不確定離散隨機系統的加權多模型自適應控制. 自動化學報, 2015, 41(3):541
[43]	Zhang W C. Stability of weighted multiple model adaptive control. Control Theory Appl, 2012, 29(12): 1657 張維存. 加權多模型自適應控制的穩定性. 控制理論與應用, 2012, 29(12):1657
[44]	Zhang W C, Liu J W, Hu G D. Stability analysis of robust multiple model adaptive control systems. Acta Autom Sin, 2015, 41(1): 113 張維存, 劉冀偉, 胡廣大. 魯棒多模型自適應控制系統的穩定性. 自動化學報, 2015, 41(1):113
[45]	Zhang J J, Fan S T, Zhang Z F, et al. Design and verification of intelligent multi-model adaptive control system of Tiangong-1 based on control moment gyros. Sci Sin Tech, 2014, 44(2): 131 張錦江, 范松濤, 張志方, 等. 天宮一號基于控制力矩陀螺的智能多模自適應姿態控制系統設計與驗證. 中國科學: 技術科學, 2014, 44(2):131
[46]	Chen L J, Narendra K S. Nonlinear adaptive control using neural networks and multiple models. Automatica, 2001, 37(8): 1245 doi: 10.1016/S0005-1098(01)00072-3
[47]	Fu Y, Chai T Y. Nonlinear multivariable adaptive control using multiple models and neural networks. Automatica, 2007, 43(6): 1101 doi: 10.1016/j.automatica.2006.12.010
[48]	Fu Y, Chai T Y. Indirect self-tuning control using multiple models for non-affine nonlinear systems. Int J Control, 2011, 84(6): 1031 doi: 10.1080/00207179.2011.588960
[49]	Huang M, Wang X, Wang Z L. Nonlinear adaptive controller using multiple models and neural networks based on zero order proximity boundedness. Control Decision, 2013, 28(9): 1315 黃淼, 王昕, 王振雷. 非線性零階接近有界多模型神經網絡自適應控制器. 控制與決策, 2013, 28(9):1315
[50]	Huang M, Wang X, Wang Z L. Multiple model adaptive control for a class of linear-bounded nonlinear systems. IEEE Trans Autom Control, 2015, 60(1): 271 doi: 10.1109/TAC.2014.2323161
[51]	Li X L, Jia C, Liu D X, et al. Nonlinear adaptive control using multiple models and dynamic neural networks. Neurocomputing, 2014, 36: 190
[52]	Li X L, Zhang X F, Jia C, et al. Multi-model adaptive control based on fuzzy neural networks. J Intell Fuzzy Syst, 2014, 27(2): 965
[53]	Li X L, Jia C, Wang K, et al. Trajectory tracking of nonlinear system using multiple series-parallel dynamic neural networks. Neurocomputing, 2015, 168: 1 doi: 10.1016/j.neucom.2015.06.024
[54]	Li J L, Yang G H. Development and prospect of adaptive fault-tolerant control. Control Decision, 2014, 29(11): 1921 李俊領, 楊光紅. 自適應容錯控制的發展與展望. 控制與決策, 2014, 29(11):1921
[55]	Lei H M, Shao L, Yang Z. Theory and Method for Multiple-Model Modeling and Control. Beijing: National Defense Industry Press, 2017 雷虎民, 邵雷, 楊遵. 多模型建模與控制的理論和方法. 北京: 國防工業出版社, 2017
[56]	Guo Y Y, Jiang B. Multiple model-based adaptive reconfiguration control for actuator fault. Acta Autom Sin, 2009, 35(11): 1452 doi: 10.3724/SP.J.1004.2009.01452
[57]	譚暢, 陶鋼, 齊瑞云. 多模型直接自適應執行器故障補償控制系統. 南京航空航天大學學報, 2011, 43(增刊):104) Tan C, Tao G, Qi R Y. Multiple-model based adaptive actuator failure compensation control scheme. J Nanjing Univ Aeron Astron, 2011, 43(增刊): 104
[58]	Boskovic J D, Mehra R K. Multiple-model adaptive flight control scheme for accommodation of actuator failures. J Guid Control Dyn, 2002, 25(4): 712 doi: 10.2514/2.4938
[59]	Qian M S, Jiang B, Yang H. Study on fault-tolerant control algorithm of switched system for attack UAV. Control Eng China, 2012, 19(2): 346 doi: 10.3969/j.issn.1671-7848.2012.02.041 錢默抒, 姜斌, 楊浩. 攻擊型無人機切換控制系統容錯算法研究. 控制工程, 2012, 19(2):346 doi: 10.3969/j.issn.1671-7848.2012.02.041
[60]	Tan C, Tao G, Yang H. Adaptive actuator failure compensation using multiple-model switching // 2014 European Control Conference (ECC). Strasbourg, 2014: 630
[61]	Chen F Y, Cai L, Jiang B, et al. Direct self-repairing control for a helicopter via quantum multi-model and disturbance observer. Int J Syst Sci, 2016, 47(3): 533 doi: 10.1080/00207721.2014.891669
[62]	Mahdianfar H, Ozgoli S, Momeni H R. Robust multiple model adaptive control: Modified using v-gap metric. Int J Robust Nonlinear Control, 2011, 21(18): 2027 doi: 10.1002/rnc.1673
[63]	Zhai J Y, Fei S M. Multiple-model switching control based on dynamic model bank. Control Theory Appl, 2009, 26(12): 1410 翟軍勇, 費樹岷. 基于動態模型庫的多模型切換控制. 控制理論與應用, 2009, 26(12):1410
[64]	Pan T H, Xue Z K, Li S Y. An online multi-model identification algorithm based on subtractive clustering. Acta Autom Sin, 2009, 35(2): 220 潘天紅, 薛振框, 李少遠. 基于減法聚類的多模型在線辨識算法. 自動化學報, 2009, 35(2):220
[65]	Shao L, Lei H M, Zhao Z B. Moving bank based online multiple-model modeling method. Control Decision, 2010, 25(1): 121 邵雷, 雷虎民, 趙宗寶. 一種基于滑動庫的多模型在線建模方法. 控制與決策, 2010, 25(1):121
[66]	Huang M, Wang X, Wang Z L. Multiple models adaptive control based on time series for a class of nonlinear systems. Acta Autom Sin, 2013, 39(5): 581 黃淼, 王昕, 王振雷. 一類非線性系統的基于時間序列的多模型自適應控制. 自動化學報, 2013, 39(5):581
[67]	Cong Q M, Yuan M Z, Chai T Y, et al. Online modeling for multi-model by adjusting the centers of operating ranges. Control Theory Appl, 2013, 30(6): 773 doi: 10.7641/CTA.2013.20695 叢秋梅, 苑明哲, 柴天佑, 等. 帶有工況中心修正的多模型在線建模. 控制理論與應用, 2013, 30(6):773 doi: 10.7641/CTA.2013.20695
[68]	Li Q L, Lei H M, Shao L, et al. Multiple-model modeling method based on differential evolution algorithm. Control Decision, 2010, 25(12): 1866 李慶良, 雷虎民, 邵雷, 等. 一種基于差分進化算法的多模型建模方法. 控制與決策, 2010, 25(12):1866
[69]	Shi S M, Wang X, Wang Z L. Dynamically optimized multiple model adaptive mixing control of dual estimators. Control Theory Appl, 2019, 36(4): 596 doi: 10.7641/CTA.2018.70906 史善孟, 王昕, 王振雷. 動態優化雙估計器的多模型自適應混合控制. 控制理論與應用, 2019, 36(4):596 doi: 10.7641/CTA.2018.70906
[70]	Chen S, Pan T H. Global optimized algorithm for weighted function of multi-model system // Proceedings of the 31st Chinese Control Conference. Hefei, 2012: 7052 陳山, 潘天紅. 多模型系統加權函數的全局優化算法/ /第31屆中國控制會議. 合肥, 2012: 7052
[71]	Chen D Q, Wang X, Wang Z L. Multi-models mixing H-infinity theory robust control. Control Theory Appl, 2018, 35(8): 1074 doi: 10.7641/CTA.2018.60718 陳登乾, 王昕, 王振雷. 多模型混合H∞型魯棒控制. 控制理論與應用, 2018, 35(8):1074 doi: 10.7641/CTA.2018.60718
[72]	Hassani V, Hespanha J P, Athans M, et al. Stability analysis of robust multiple model adaptive control. IFAC Proc Vol, 2011, 44(1): 350 doi: 10.3182/20110828-6-IT-1002.01194
[73]	Zhang W C. On the stability and convergence of self-tuning control—virtual equivalent system approach. Int J Control, 2010, 83(5): 879 doi: 10.1080/00207170903487421
[74]	Zhang W C, Chu T G, Wang L. A new theoretical framework for self-tuning control. Int J Inform Technol, 2005, 11(11): 123
[75]	Zhang W C. The convergence of parameter estimates is not necessary for a general self-tuning control system—stochastic plant // Proceedings of 48th IEEE Conference on Decision and Control. Shanghai, 2009: 3489
[76]	Zhang W, Li X L, Choi J Y. A unified analysis of switching multiple model adaptive control-Virtual equivalent system approach. IFAC Proc Vol, 2008, 41(2): 14403 doi: 10.3182/20080706-5-KR-1001.02440
[77]	Zhang Y Z, Li Q, Zhang W C. Weighted multiple model adaptive control with self-tuning model. Chin J Eng, 2018, 40(11): 1389 張玉振, 李擎, 張維存. 含有自校正模型的加權多模型自適應控制. 工程科學學報, 2018, 40(11):1389
[78]	Vinnicombe G. Frequency domain uncertainty and the graph topology. IEEE Trans Autom Control, 1993, 38(9): 1371 doi: 10.1109/9.237648