模糊双曲正切模型研究综述

会国涛; 张化光; 汪刚; 解相朋; 吴振宁

doi:10.3724/SP.J.1004.2013.01849

模糊双曲正切模型研究综述

doi: 10.3724/SP.J.1004.2013.01849

1.
东北大学信息科学与工程学院沈阳 110819;
2.
东北大学流程工业综合自动化国家重点实验室沈阳 110819;
3.
华中科技大学控制系武汉 430074

基金项目:

国家重点基础研究发展计划(973计划)(2009CB320601),国家自然科学基金(61034005,61374124),中国博士后科学基金(2013M542018)资助

详细信息

作者简介:
张化光东北大学信息科学与工程学院教授. 主要研究方向为自适应动态规划,模糊控制, 网络控制混沌控制. E-mail: zhanghuaguang@mail.neu.edu.cn

计量
- 文章访问数: 1890
- HTML全文浏览量: 80
- PDF下载量: 1992
- 被引次数: 0
出版历程
- 收稿日期: 2013-07-02
- 修回日期: 2013-08-28
- 刊出日期: 2013-11-20

Research on Fuzzy Hyperbolic Tangent Model： A Review

1.
School of Information Science and Engineering, Northeastern University, Shenyang 110819;
2.
State Key Laboratory of Synthetical Automation for Process Industries, Shenyang 110819;
3.
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074

Funds:

Supported by National Basic Research Program of China (973 Program) (2009CB320601), National Natural Science Foundation of China (61034005, 61374124), and China Postdoctoral Science Foundation Funded Project (2013M542018)

摘要

摘要: 模糊双曲正切模型(Fuzzy hyperbolic tangent model, FHM)是一种全局模糊模型也是一种神经网络模型. 根据此模型设计的控制器能够实现系统的性能指标达到最优. FHM与其他模糊模型相比,更加适用于对多变量及系统内部信息所知有限的非线性系统进行建模. 本文依据FHM的模型发展历程对现有的研究成果加以总结, 并对这一研究领域内待解决的问题和未来发展方向作了进一步的展望.
- 模糊双曲正切模型 /
- 广义模糊双曲正切模型 /
- 时滞模糊双曲正切模型 /
- 神经网络
Abstract: Fuzzy hyperbolic tangent model (FHM) is a global fuzzy model and also a neural network model. The controller based on the FHM can achieve the optimal performance index of the whole system. Compared to the existing fuzzy models, the FHM is more suitable to model a multi-variable nonlinear system, in which the information of plant is insufficient. This paper presents a survey of achievements in order of the development on the modeling of FHM. Finally, the problems and the future research direction are analyzed and discussed.
- Fuzzy hyperbolic tangent model (FHM) /
- general fuzzy hyperbolic tangent model /
- delay fuzzy hyperbolictangent model /
- neural network

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参考文献(85)

[1]	Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338-358
[2]	Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics, 1973, 3(1): 28-44
[3]	Mamdani E H. Application of fuzzy algorithms for control of simple dynamic plant. In: Proceedings of the 1974 Institution of Electrical Engineers. IEEE, 1974, 121(12): 1585-1588
[4]	Chen B, Liu X P, Lin C, Liu K F. Robust H∞ control of Takagi-Sugeno fuzzy systems with state and input time delays. Fuzzy Sets and Systems, 2009, 160(4): 403-422
[5]	Lam H K. Polynomial fuzzy-model-based control systems: stability analysis via piecewise-linear membership functions. IEEE Transactions on Fuzzy Systems, 2011, 19(3): 588-593
[6]	Lee D H, Park J B, Joo Y H. A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems. Information Sciences, 2012, 185(1): 230-248
[7]	Ding B C. Improving the asymptotically necessary and sufficient conditions for stability of fuzzy control. Fuzzy Sets and Systems, 2010, 161(21): 2793-2804
[8]	Feng J, Wang S Q. Reliable fuzzy control for a class of nonlinear networked control systems with time delay. Acta Automatica Sinica, 2012, 38(7): 1091-1099
[9]	Kolman E, Margaliot M. Are artificial neural networks white boxes? IEEE Transactions on Neural Networks, 2005, 16(4): 844-852
[10]	Pan J T, Guerra T M, Fei S M, Jaadari A. Nonquadratic stabilization of continuous T-S fuzzy models: LMI solution for a local approach. IEEE Transactions on Fuzzy Systems, 2012, 20(3): 594-602
[11]	Wang L X, Mendel J M. Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Transactions on Neural Networks, 1992, 3(5): 807-814
[12]	Zadeh L A. The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences, 1975, 9(1): 43-80
[13]	Pedrycz W. An approach to the analysis of fuzzy systems. International Journal of Control, 1981, 34(3): 403-421
[14]	Zhang Hua-Guang, Quan Yong-Bing. Modeling and control based on fuzzy hyperbolic model. Acta Automatica Sinica, 2000, 26(6): 729-735(张化光, 全永兵. 模糊双曲正切模型的建模方法与控制器设计. 自动化学报, 2000, 26(6): 729-735)
[15]	Zhang H G, Quan Y B. Modeling, identification, and control of a class of nonlinear systems. IEEE Transactions on Fuzzy Systems, 2001, 9(2): 349-354
[16]	Zeng X J, Singh M G. Approximation theory of fuzzy systems-SISO case. IEEE Transactions on Fuzzy Systems, 1994, 2(2): 162-176
[17]	Wang L X. Fuzzy systems as universal approximations. In: Proceeding of the 1992 IEEE International Conference on Fuzzy Systems. San Diego: IEEE, 1992. 1163-1170
[18]	Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 1985, 15(1): 116-132
[19]	Sugeno M, Yasukawa T. A fuzzy logic-based approach to qualitative modeling. IEEE Transactions on Fuzzy Systems, 1993, 1(1): 7-25
[20]	Cao S G, Rees N W, Feng G. Analysis and design for a class of complex control systems, Part I: fuzzy modelling and identification. Automatica, 1997, 33(6): 1017-1028
[21]	Cao S G, Rees N W, Feng G. Analysis and design for a class of complex control systems, Part II: fuzzy controller design. Automatica, 1997, 33(6): 1029-1039
[22]	Cao S G, Rees N W, Feng G. Quadratic stability analysis and design of continuous-time fuzzy control systems. International Journal of Systems Science, 1996, 27(2): 193-203
[23]	Li Shao-Yuan, Wang Qun-Xian, Li Huan-Zhi, Chen Zeng-Qiang, Yuan Zhu-Zhi. Identification and control based on Sugeno's fuzzy model. Acta Automatica Sinica, 1999, 25(4): 488-492(李少远, 王群仙, 李焕芝, 陈增强, 袁著祉. Sugeno模糊模型的辨识与控制. 自动化学报, 1999, 25(4): 488-492)
[24]	Huang Miao, Wang Xin, Wang Zhen-Lei. Multiple models adaptive control based on time series for a class of nonlinear systems. Acta Automatica Sinica, 2013, 39(5): 581-586 (黄淼, 王昕, 王振雷. 一类非线性系统的基于时间序列的多模型自适应控制. 自动化学报, 2013, 39(5): 581-586)
[25]	Kim E, Park M, Ji S, Park M. A new approach to fuzzy modeling. IEEE Transactions on Fuzzy Systems, 1997, 5(3): 328-337
[26]	Messner S, Golodnikov A, Gritsevskii A. A stochastic version of the dynamic linear programming model MESSAGE III. Energy, 1996, 21(9): 775-784
[27]	Zhang Hua-Guang, Zhang Xin, Luo Yan-Hong, Yang Jun. An overview of research on adaptive dynamic programming. Acta Automatica Sinica, 2013, 39(4): 303-311 (张化光, 张欣, 罗艳红, 杨珺. 自适应动态规划综述. 自动化学报, 2013, 39(4): 303-311)
[28]	Wei Qing-Lai, Zhang Hua-Guang, Liu De-Rong, Zhao Yan. An optimal control scheme for a class of discrete-time nonlinear systems with time delays using adaptive dynamic programming. Acta Automatica Sinica, 2010, 36(1): 121-129 (魏庆来, 张化光, 刘德荣, 赵琰. 基于自适应动态规划的一类带有时滞的离散时间非线性系统的最优控制策略. 自动化学报, 2010, 36(1): 121-129)
[29]	Liu D R, Javaherian H, Kovalenko O, Huang T. Adaptive critic learning techniques for engine torque and air-fuel ratio control. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2008, 38(4): 988-993
[30]	Vamvoudakis K G, Lewis F L. Multi-player non-zero-sum games: online adaptive learning solution of coupled Hamilton-Jacobi equations. Automatica, 2011, 47(8): 1556-1569
[31]	Mo Ju-Hua, Huang Min, Wang Xing-Wei. Application of a pull strategy based on fuzzy control for production control of assembly line. Acta Automatica Sinica, 2011, 37(1): 118-123 (莫巨华, 黄敏, 王兴伟. 基于模糊控制的拉式策略在装配生产控制中的应用. 自动化学报, 2011, 37(1): 118-123)
[32]	Ioannidis S, Tsourveloudis N, Valavanis K. Fuzzy supervisory control of manufacturing systems. IEEE Transactions on Robotics and Automation, 2004, 20(3): 379-389
[33]	Li R H, Zhang Y. Fuzzy logic controller based on genetic algorithms. Fuzzy Sets and Systems, 1996, 83(1): 1-10
[34]	Joo Y H, Hwang H S, Kim K B, Woo K B. Fuzzy system modeling by fuzzy partition and GA hybrid schemes. Fuzzy Sets and Systems, 1997, 86(3): 279-288
[35]	You S S, Wook C, et al. A fuzzy modeling method with a GA hybrid scheme. In: Proceedings of the 2nd Asian Control Conference, 1997. 529-53
[36]	Barber M J, Clark J W. Detecting network communities by propagating labels under constraints. Physical Review E, 2009, 80(2): 026129
[37]	Yang Dong-Yong, Chen Jin-Yin. Research on detector generation algorithm based on multiple populations GA. Acta Automatica Sinica, 2009, 35(4): 425-432(杨东勇, 陈晋音. 基于多种群遗传算法的检测器生成算法研究. 自动化学报, 2009, 35(4): 425-432)
[38]	Marino R, Tomei P. An iterative learning control for a class of partially feedback linearizable systems. IEEE Transactions on Automatic Control, 2009, 54(8): 1991-1996
[39]	Li X D, Xiao T F, Zheng H X. Adaptive discrete-time iterative learning control for non-linear multiple input multiple output systems with iteration-varying initial error and reference trajectory. IET Control Theory and Applications, 2011, 5(9): 1131-1139
[40]	Zhang Hua-Guang. Fuzzy Hyperbolic Tangent Model-Modeling, Control, Application. Beijing: Science Press, 2008(张化光. 模糊双曲正切模型——建模, 控制, 应用. 北京: 科学出版社, 2008
[41]	Li Hong-Ru, Gu Shu-Sheng. A fast parallel algorithm for a recurrent neural network. Acta Automatica Sinica, 2004, 30(4): 516-522 (李鸿儒, 顾树生. 一种递归神经网络的快速并行算法. 自动化学报, 2004, 30(4): 516-522)
[42]	Han Min, Wang Xin-Ying. An effective online sparse learning algorithm for echo state networks. Acta Automatica Sinica, 2011, 37(12): 1536-1540 (韩敏, 王新迎. 一种有效的储备池在线稀疏学习算法. 自动化学报, 2011, 37(12): 1536-1540)
[43]	Steil J J. Online stability of backpropagation-decorrela-tion recurrent learning. Neurocomputing, 2006, 69(7-9): 642-650
[44]	Margaliot M, Langholz G. Hyperbolic optimal control and fuzzy control. IEEE Transactions on Systems, Man, and Cybernetics, Part A, 1999, 29(1): 1-10
[45]	Yang J, Liu D R, Feng J, Zhang H G. Controller design for a class of nonlinear systems based on fuzzy hyperbolic model. In: Proceedings of the 6th World Congress on Control and Automation. Dalian: WCICA, 2006. 873-877
[46]	Yang Jun, Zhang Hua-Guang. Design of integral sliding mode controller based on fuzzy hyperbolic model. CAAI Transactions on Intelligent Systems, 2008, 3(1): 62-65 (杨珺, 张化光. 基于模糊双曲模型的积分滑模控制. 智能系统学报, 2008, 3(1): 62-65)
[47]	Yang Jun, Zhang Hua-Guang, Zheng Cheng-De. Design of reliable controller based on fuzzy hyperbolic model. Control and Decision, 2008, 23(2): 167-170 (杨珺, 张化光, 郑成德. 基于模糊双曲模型的可靠控制器设计. 控制与决策, 2008, 23(2): 167-170)
[48]	Yang Jun, Zhang Hua-Guang. Design of mixed H_{2/H_{∞ controller based on fuzzy hyperbolic model. Journal of Northeastern University, 2008, 29(4): 460-463 (杨珺, 张化光. 基于模糊双曲模型的混合H_{2/H_{∞控制. 东北大学学报, 2008, 29(4): 460-463)
[49]	Yang Jun, Zhang Hua-Guang, Yang Dong-Sheng. Design of non-fragile controller based on fuzzy hyperbolic model and simulation. Journal of System Simulation, 2009, 21(12): 3790-3793(杨珺, 张化光, 杨东升. 基于模糊双曲模型的非脆弱控制及其仿真研究. 系统仿真学报, 2009, 21(12): 3790-3793)
[50]	Margaliot M, Langholz G. A new approach to fuzzy modeling and control of discrete-time systems. IEEE Transactions on Fuzzy Systems, 2003, 11(4): 486-494
[51]	Yang J, Zhang H G, Wang Y C, Lun S X. Networked control for a class of nonlinear systems based on fuzzy hyperbolic model. In: Proceedings of the 2008 Chinese Control and Decision Conference. Yantai: CCDC, 2008. 323-328.
[52]	Margaliot M, Langholz G. Fuzzy control of a benchmark problem: a computing with words approach. IEEE Transactions on Fuzzy Systems, 2004, 12(2): 230-235
[53]	Zhang Hua-Guang, Wang Zhi-Liang, Li Ming, Quan Yong-Bing, Zhang Ming-Jun. Generalized fuzzy hyperbolic model: a universal approximator. Acta Automatica Sinica, 2004, 30(3): 416-422(张化光, 王智良, 黎明, 全永兵, 张明君. 广义模糊双曲正切模型: 一个万能逼近器. 自动化学报, 2004, 30(3): 416-422)
[54]	Zhang H G, Liang H L, Liu D. Two new operators in rough set theory with application to fuzzy sets. Information Science, 2004, 166(1-4): 147-165
[55]	Zhang H G, Li M, Cai L L. Fuzzy adaptive control of nonlinear processes with feedforward compensator and its application. Cybernetics and Systems, 2002, 33(2): 171-187
[56]	Zhang Ming-Jun, Zhang Hua-Guang. Adaptive controller based generalized fuzzy hyperbolic model. Control and Decision, 2004, 19(11): 1301-1304 (张明君, 张化光. 基于广义模糊双曲正切模型的自适应控制器. 控制与决策, 2004, 19(11): 1301-1304)
[57]	Zhang Ming-Jun, Zhang Hua-Guang. A robust direct adaptive fuzzy control algorithm. Journal of Northeastern University, 2006, 27(1): 5-8 (张明君, 张化光. 一种鲁棒直接自适应模糊控制算法. 东北大学学报, 2006, 27(1): 5-8)
[58]	Zhang H G, Zhang M J. Robust direct adaptive fuzzy control for nonlinear MIMO systems. Progress in Natural Science, 2006, 16(10): 1098-1105
[59]	Zhang M J, Zhang H G. Robust adaptive fuzzy control based on generalized fuzzy hyperbolic. In: Proceedings of the 16th IFAC Worlds Congress, 2005
[60]	Zhang Ji-Lie, Zhang Hua-Guang, Luo Yan-Hong, Liang Hong-Jing. Nearly optimal control scheme using adaptive dynamic programming based on generalized fuzzy hyperbolic model. Acta Automatica Sinica, 2013, 39(2): 142-149 (张吉烈, 张化光, 罗艳红, 梁洪晶. 基于广义模糊双曲模型的自适应动态规划最优控制设计. 自动化学报, 2013, 39(2): 142-149)
[61]	Gao Dao-Xiang, Xue Ding-Yu. Fuzzy adaptive control of manipulators based on the generalized hyperbolic model. Control and Decision, 2006, 21(10): 1124-1128, 1133 (高道祥, 薛定宇. 基于广义双曲正切模型的机器人模糊自适应控制. 控制与决策, 2006, 21(10): 1124-1128, 1133)
[62]	Zhang H G, Yang J. Delay-dependent stability of a class of nonlinear systems with time delays based on fuzzy hyperbolic model. In: Proceedings of the 2006 International Conference on Intelligent Computing: Part II. Heidelberg: Springer-Verlag Berlin. 2006, 4114: 20-31
[63]	Yang J, Zhang H G, Liu D R. A novel control scheme for a class of nonlinear systems with time delays based on fuzzy hyperbolic model. In: Proceedings of the 10th International Conference on Fuzzy systems. Automation, Robotics, and Vision, Hanoi, Vietnam, 2008
[64]	Zhang H G, Gong Q X, Wang Y C. Delay-dependent robust H_∞ control for uncertain fuzzy hyperbolic systems with multiple delays. Progress in Natural Science, 2008, 18(1): 97-104
[65]	Wang Yi-Zhong, Zhang Hua-Guang. Control and simulation of stochastic hyperbolic tangent model. Journal of System Simulation, 2008, 20(10): 2689-2692 (王以忠, 张化光. 随机双曲正切模型的控制与仿真. 系统仿真学报, 2008, 20(10): 2689-2692)
[66]	Zhang H G, Lun S X, Liu D R. Fuzzy H_{∞ filter design for a class of nonlinear discrete-time systems with multiple time delay. IEEE Transactions on Fuzzy Systems, 2007, 15(3): 453-469
[67]	Liu X R, Zhang H G, Dai J. Delay-dependent robust and reliable H_∞ fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems. Fuzzy Sets and Systems, 2010, 161(6): 872-892
[68]	Zhang H G, Liu X R, Gong Q X, Chen B. New sufficient conditions for robust H_{∞ fuzzy hyperbolic tangent control of uncertain nonlinear systems with time-varying delay. Fuzzy Sets and Systems, 2010, 161(15): 1993-2011
[69]	Liu Xin-Rui, Zhang Hua-Guang. Sample-data decentralized H_{∞ reliable hyperbolic control for uncertain fuzzy large-scale systems with time-varying delay. Acta Automatica Sinica, 2009, 35(12): 1534-1540 (刘鑫蕊, 张化光. 不确定时变时滞模糊大系统的采样分散可靠H_{∞双曲控制. 2009, 35(12): 1534-1540)
[70]	Wang G, Zhang H G, Chen B, Tong S C. Fuzzy hyperbolic neural network with time-varying delays. Fuzzy Sets and Systems, 2010, 161(19): 2533-2551
[71]	Zhang H G, Liu D. Fuzzy Modeling and Fuzzy Control. Boston, Basel, Berlin: Birkhauser, 2006
[72]	Zhang H G, Wang Z L, Liu D. Chaotifying fuzzy hyperbolic model using adaptive inverse optimal control approach. International Journal of Bifurcation and Chaos, 2004, 14(10): 3505-3517
[73]	Zhang H G, Wang Z L, Wang Z L, Liu D R. Chaotifying fuzzy hyperbolic model using impulsive and nonlinear feedback control approaches. International Journal of Bifurcation and Chaos, 2005, 15(8): 2603-2610
[74]	Zhang H G, Wang Z L, Liu D R. Chaotification of FHM model: an adaptive inverse optimal control approach. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 2005, 11(S1): 45-52
[75]	Liu Y J, Tong S C, Chen C L P. Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Transactions on Fuzzy Systems, 2013, 21(2): 275-288
[76]	Zhou Q, Shi P, Xu S Y, Li H Y. Adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach. IEEE Transactions on Fuzzy Systems, 2013, 21(2): 301-313
[77]	Su X J, Shi P, Wu L G, Song Y D. A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays. IEEE Transactions on Fuzzy Systems, 2013, 21(4): 655-671
[78]	Kim S Y. Relaxation technique for a Takagi-Sugeno fuzzy control design based on a continuous-time fuzzy weighting-dependent Lyapunov function. IEEE Transactions on Fuzzy Systems, 2013, 21(4): 761-766
[79]	Zhang H G, Xie X P. Relaxed stability conditions for continuous-time T-S fuzzy control systems via augmented multi-indexed matrix approach. IEEE Transactions on Fuzzy Systems, 2011, 19(3): 478-492
[80]	Zhang H G, Xie X P, Tong S C. Homogenous polynomially parameter-dependent H_{∞ filter designs of discrete-time fuzzy systems. IEEE Transactions on Systems, Man, and Cybernetics Part-B: Cybernetics, 2011, 41(5): 1313-1322
[81]	Xie X P, Ma H J, Zhao Y, Ding D W, Wang Y C. Control synthesis of discrete-time T-S fuzzy systems based on a novel non-PDC control scheme. IEEE Transactions on Fuzzy Systems, 2013, 21(1): 147-157
[82]	Ding D W, Li X L, Xie X P. Further studies on relaxed stabilization conditions for discrete-time two-dimension Takagi-Sugeno fuzzy systems. Information Sciences, 2012, 189 (2): 143-154
[83]	Chen Jun, Gao Ze-Feng, Liu Fei. Stochastic stabilization for a class of fuzzy bilinear jump systems. Acta Automatica Sinica, 2013, 39(5): 587-593 (陈珺, 高泽峰, 刘飞. 一类模糊双线性跳变系统的随机镇定问题. 自动化学报, 2013, 39(5): 587-593)
[84]	Zhao Da-Yong, Chai Tian-You. Fuzzy switching control for sump level interval and hydrocyclone pressure in regrinding process. Acta Automatica Sinica, 2013, 39(5): 556-564 (赵大勇, 柴天佑. 再磨过程泵池液位区间与给矿压力模糊切换控制. 自动化学报, 2013, 39(5): 556-564)
[85]	Wang Yong-Fu, Wang Dian-Hui, Chai Tian-You. State estimate-based friction fuzzy modeling and robust adaptive control. Acta Automatica Sinica, 2011, 37(2): 245-252 (王永富, 王殿辉, 柴天佑. 基于状态估计的摩擦模糊建模与鲁棒自适应控制. 自动化学报, 2011, 37(2): 245-252)