变论域自适应模糊控制的几种新方法
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摘要
变论域自适应模糊控制是一种论域动态调整的自适应模糊控制。相比自适应模糊控制,它有着许多优越的性能,如响应速度快、稳态精度高等等。本文以变论域自适应模糊控制为研究背景,针对控制器设计中存在的不足进行了研究,如伸缩因子参数设计、初始控制规则的依赖性、对不确定的界存在约束、状态要求完全可测等,提出了几种新的变论域自适应模糊控制器。本文的主要工作归纳如下：
1.通过分析伸缩因子参数对控制系统的暂态和稳态性能的影响,给出了这些参数的设计原则。首先,分析了控制量和伸缩函数斜率与系统控制性能的关系。在暂态阶段,控制量关于参数的导数越大,系统响应就越快；在稳态阶段,伸缩函数斜率越大,说明系统对输入变量的变化越灵敏。然后,通过研究控制量对参数的导数和伸缩函数在平衡点附近的斜率分析了伸缩因子中各参数对暂态和稳态控制性能的影响,得出了各参数的设计原则。
2.借助于Lyapunov综合分析方法,提出了三种变论域自适应模糊控制方案。首先,使用符号函数替代输入变量的伸缩运算,提出一种符号型自适应模糊控制。该方案不仅可以保证控制器设计的实时性和闭环系统的稳定性,而且还避免了伸缩因子的设计。其次,将后件参向量和积分调节因子融合组成新的参向量,提出一种基于参向量在线调整的变论域自适应模糊控制。该方案降低了对初始控制规则的依赖性。最后一种是鲁棒变论域自适应模糊控制。借助于自适应边界技术和σ-修正技术,该方案不但减弱了对非线性函数的界和模糊逼近误差的约束,而且还能保证闭环系统的稳定性。
3.针对一类含有模型不确定和外部干扰的多输入多输出仿射非线性系统,提出两种直接自适应模糊滑模控制方案。方案一同时使用两个模糊系统去估计等效控制律和切换控制律；方案二使用一个模糊系统估计等效控制律,一个变论域模糊系统逼近切换控制律。使用模糊切换项或变论域模糊切换项的目的是为了消除控制信号的抖振现象、加快系统响应；补偿控制项是用来补偿模糊逼近误差及外来干扰对系统的影响。基于Lyapnuov稳定性理论,两种控制方案都能保证闭环系统的稳定性,并能实现良好的跟踪性能。在存在系统不确定和外来干扰情形下,提出的两种控制方案都能有效地计算等效控制量和避免控制信号的抖振现象。仿真实验也证实了提出方案的可行性。
4.针对一类状态不完全可测的单输入单输出非线性系统,提出了一种基于观测器的变论域自适应模糊控制方案。首先建立了修正的理想控制律。然后利用变论域模糊系统去估计这个修正的理想控制律。最后,加入鲁棒控制项和跟踪误差估计反馈控制项分别去抑制集中不确定的影响和减小观测误差。基于SPR-Lyapunov设计方法,提出的控制方案不仅能保证在状态不完全可测条件下系统的稳定性,而且不会额外增加控制系统的动态阶数。
Variable universe adaptive fuzzy control is a type of adaptive fuzzy control with dynamic adjustment domain. Compared with the traditional adaptive fuzzy control, it has many ex-cellent properties, such as fast response, high steady precision, and so on. Taking variable universe adaptive fuzzy control as research background, this dissertation focuses on some prob-lems appeared in the existing literatures, such as parameter design of contraction-expansion factor, dependency on the initial control rule base, constraints on system uncertainty and fuzzy approximation error, immeasurable state, and so on. Several novel methods for solving these problems are proposed. The research work in this dissertation mainly includes following parts:
1. Through the analysis of the impact of contraction-expansion factor parameters on the transient and steady state performance of control systems, some design strategies for these parameters are derived. Firstly, a stretching function is defined and the relation between control law, the stretching function and control performance is analyzed. In the transient state, the higher the derivative of control law to parameter is, the faster the system response is. In the steady state, the bigger the slope of the stretching function is, the more sensitive the system to the change of input variable is. Then, through the study of the derivative of control quantity to the parameters and the slope of the stretching function near the equilibrium point, the effect of the parameters on the transient and steady state performance of the control system are analyzed and the design principle of each parameter is obtained.
2. In this dissertation, using Lyapunov method, three variable universe adaptive fuzzy con-trol schemes are put forward. Firstly, a symbolic function is employed to replace the stretching operation of input variable, and a symbol-type adaptive fuzzy control scheme is provided. The scheme not only ensures the real-time capability and stability of the closed-loop system, but also avoids the design of contraction-expansion factor. Secondly, the original parameter vector and the integral regulation factor are blended together to form a new parameter vector, and an adjusted parameter vector-based variable universe adaptive fuzzy control is proposed. The control scheme can be less dependent on the initial control rules. The third one is a robust variable universe adaptive fuzzy control scheme. By using adaptive boundary technique and σ-modification technique, the scheme can not only remove the constraints on nonlinear function and fuzzy approxima-tion error, but also guarantee the stability of the closed-loop system.
3. For a type of Multiple Input Multiple Output (MIMO) nonlinear system with uncertain-ties and external disturbances, two direct adaptive fuzzy sliding mode control schemes are developed. In the first one, two fuzzy systems are used to estimate the equivalent control law and the switching control law. In the second one, a fuzzy system is used to estimate the equivalent control law, and a variable universe fuzzy system is used to approximate the switching control law. In order to remove the chattering phenomena of control signal and speed the system response, fuzzy switching control terms (in scheme one) or variable universe fuzzy switching control terms (in scheme two) are utilized. And compensation control terms are applied to reduce the influence of fuzzy approximation error and exter-nal disturbances. Based on Lyapnuov stability theory, both of these schemes can ensure the stability of the closed-loop system and achieve the tracking task. In the presence of system uncertainties and external disturbances, using these two proposed schemes, the equivalent control law can be effectively calculated; also, the chattering phenomena of the control signal can be avoided.
4. For a type of Single Input Single Output (SISO) system with unmeasurable state variables, an observer-based direct adaptive fuzzy control scheme is developed. Firstly, a modified ideal control law is built. Then, a variable universe fuzzy system is employed to approx-imate the modified ideal control law. Finally, a robust control term and a tracking error estimation feedback control term are designed to suppress the influence of the lumped un-certainties and reduce the observation error, respectively. Based on SPR-Lyapunov design method, the proposed control scheme not only guarantees the stability of the closed-loop system under the condition of immeasurable states, but also requires no additional dy-namic orders for the control design.
1.通过分析伸缩因子参数对控制系统的暂态和稳态性能的影响,给出了这些参数的设计原则。首先,分析了控制量和伸缩函数斜率与系统控制性能的关系。在暂态阶段,控制量关于参数的导数越大,系统响应就越快；在稳态阶段,伸缩函数斜率越大,说明系统对输入变量的变化越灵敏。然后,通过研究控制量对参数的导数和伸缩函数在平衡点附近的斜率分析了伸缩因子中各参数对暂态和稳态控制性能的影响,得出了各参数的设计原则。
2.借助于Lyapunov综合分析方法,提出了三种变论域自适应模糊控制方案。首先,使用符号函数替代输入变量的伸缩运算,提出一种符号型自适应模糊控制。该方案不仅可以保证控制器设计的实时性和闭环系统的稳定性,而且还避免了伸缩因子的设计。其次,将后件参向量和积分调节因子融合组成新的参向量,提出一种基于参向量在线调整的变论域自适应模糊控制。该方案降低了对初始控制规则的依赖性。最后一种是鲁棒变论域自适应模糊控制。借助于自适应边界技术和σ-修正技术,该方案不但减弱了对非线性函数的界和模糊逼近误差的约束,而且还能保证闭环系统的稳定性。
3.针对一类含有模型不确定和外部干扰的多输入多输出仿射非线性系统,提出两种直接自适应模糊滑模控制方案。方案一同时使用两个模糊系统去估计等效控制律和切换控制律；方案二使用一个模糊系统估计等效控制律,一个变论域模糊系统逼近切换控制律。使用模糊切换项或变论域模糊切换项的目的是为了消除控制信号的抖振现象、加快系统响应；补偿控制项是用来补偿模糊逼近误差及外来干扰对系统的影响。基于Lyapnuov稳定性理论,两种控制方案都能保证闭环系统的稳定性,并能实现良好的跟踪性能。在存在系统不确定和外来干扰情形下,提出的两种控制方案都能有效地计算等效控制量和避免控制信号的抖振现象。仿真实验也证实了提出方案的可行性。
4.针对一类状态不完全可测的单输入单输出非线性系统,提出了一种基于观测器的变论域自适应模糊控制方案。首先建立了修正的理想控制律。然后利用变论域模糊系统去估计这个修正的理想控制律。最后,加入鲁棒控制项和跟踪误差估计反馈控制项分别去抑制集中不确定的影响和减小观测误差。基于SPR-Lyapunov设计方法,提出的控制方案不仅能保证在状态不完全可测条件下系统的稳定性,而且不会额外增加控制系统的动态阶数。
Variable universe adaptive fuzzy control is a type of adaptive fuzzy control with dynamic adjustment domain. Compared with the traditional adaptive fuzzy control, it has many ex-cellent properties, such as fast response, high steady precision, and so on. Taking variable universe adaptive fuzzy control as research background, this dissertation focuses on some prob-lems appeared in the existing literatures, such as parameter design of contraction-expansion factor, dependency on the initial control rule base, constraints on system uncertainty and fuzzy approximation error, immeasurable state, and so on. Several novel methods for solving these problems are proposed. The research work in this dissertation mainly includes following parts:
1. Through the analysis of the impact of contraction-expansion factor parameters on the transient and steady state performance of control systems, some design strategies for these parameters are derived. Firstly, a stretching function is defined and the relation between control law, the stretching function and control performance is analyzed. In the transient state, the higher the derivative of control law to parameter is, the faster the system response is. In the steady state, the bigger the slope of the stretching function is, the more sensitive the system to the change of input variable is. Then, through the study of the derivative of control quantity to the parameters and the slope of the stretching function near the equilibrium point, the effect of the parameters on the transient and steady state performance of the control system are analyzed and the design principle of each parameter is obtained.
2. In this dissertation, using Lyapunov method, three variable universe adaptive fuzzy con-trol schemes are put forward. Firstly, a symbolic function is employed to replace the stretching operation of input variable, and a symbol-type adaptive fuzzy control scheme is provided. The scheme not only ensures the real-time capability and stability of the closed-loop system, but also avoids the design of contraction-expansion factor. Secondly, the original parameter vector and the integral regulation factor are blended together to form a new parameter vector, and an adjusted parameter vector-based variable universe adaptive fuzzy control is proposed. The control scheme can be less dependent on the initial control rules. The third one is a robust variable universe adaptive fuzzy control scheme. By using adaptive boundary technique and σ-modification technique, the scheme can not only remove the constraints on nonlinear function and fuzzy approxima-tion error, but also guarantee the stability of the closed-loop system.
3. For a type of Multiple Input Multiple Output (MIMO) nonlinear system with uncertain-ties and external disturbances, two direct adaptive fuzzy sliding mode control schemes are developed. In the first one, two fuzzy systems are used to estimate the equivalent control law and the switching control law. In the second one, a fuzzy system is used to estimate the equivalent control law, and a variable universe fuzzy system is used to approximate the switching control law. In order to remove the chattering phenomena of control signal and speed the system response, fuzzy switching control terms (in scheme one) or variable universe fuzzy switching control terms (in scheme two) are utilized. And compensation control terms are applied to reduce the influence of fuzzy approximation error and exter-nal disturbances. Based on Lyapnuov stability theory, both of these schemes can ensure the stability of the closed-loop system and achieve the tracking task. In the presence of system uncertainties and external disturbances, using these two proposed schemes, the equivalent control law can be effectively calculated; also, the chattering phenomena of the control signal can be avoided.
4. For a type of Single Input Single Output (SISO) system with unmeasurable state variables, an observer-based direct adaptive fuzzy control scheme is developed. Firstly, a modified ideal control law is built. Then, a variable universe fuzzy system is employed to approx-imate the modified ideal control law. Finally, a robust control term and a tracking error estimation feedback control term are designed to suppress the influence of the lumped un-certainties and reduce the observation error, respectively. Based on SPR-Lyapunov design method, the proposed control scheme not only guarantees the stability of the closed-loop system under the condition of immeasurable states, but also requires no additional dy-namic orders for the control design.
引文
[1]胡寿松.自动控制原理(第五版)[M].北京：科学出版社,2007,386-401.
[2]Riccardo M, Patrizio T(著),姚郁,贺风华(译).非线性系统设计[M].北京：电子工业出版社,2006,1-74.
[3]Poincare H. Sur les courbes definies par les equations differentielles (III)[J]. Journal de mathematiques pures et appliquees,1885:167-244.
[4]高为炳.非线性控制系统导论[M].北京：科学出版社,1988.
[5]Krener A J, Isidori A, Respondek W. Partial and robust linearization by feedback[C]//Proc.22nd IEEE Conf. Decision Control.1983:126-130.
[6]Astrbm K J, Wittenmark B. Adaptive control[M]. 北京,科学出版社,2003:1-20.
[7]Astrom K J. Theory and applications of adaptive control-a survey[J]. Automatica,1983,19(5):471-486.
[8]Fu K. Learning control systems and intelligent control systems:An intersection of artifical intelligence and automatic control[J]. IEEE Transactions on Automatic Control,1971,16(1):70-72.
[9]刘金琨.智能控制(第2版)[M].北京,电子工业出版社,2009,1-10.
[10]Wang L X. Stable adaptive fuzzy controllers with application to inverted pendulum tracking[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,1996,26(5):677-691.
[11]Zadeh L A. Fuzzy sets [J]. Information and control,1965,8(3):338-353.
[12]Zadeh L A. Outline of a New Approach to the Analysis of Complex Systems and Decision Processes [J]. IEEE Transactions on Systems, Man, and Cybernetics,1973,3(1):28-44.
[13]Mamdani E H, Assilian S. A case study on the application of fuzzy set theory to automatic con-trol [C]//Proc. IFAC Stochastic Control Symp.1974.
[14]Mamdani E H, Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller[J]. Inter-national journal of man-machine studies,1975,7(1):1-13.
[15]Wang L X. Adaptive fuzzy systems and control:design and stability analysis[M]. Prentice-Hall, Engle-wood Cliffs, NJ,1994.
[16]Castro J L. Fuzzy logic controllers are universal approximators[J]. IEEE Transactions on Systems, Man, and Cybernetics,1995,25(4):629-635.
[17]Wang L X, Mendel J M. Fuzzy basis functions, universal approximation, and orthogonal least-squares learning[J]. IEEE Transactions on Neural Networks,1992,3(5):807-814.
[18]Wang L X. Stable adaptive fuzzy control of nonlinear systems [J]. IEEE Transactions on Fuzzy Systems, 1993,1(2):146-155.
[19]Golea N, Golea A, Benmahammed K. Fuzzy model reference adaptive control[J]. IEEE Transactions on Fuzzy Systems,2002,10(4):436-444.
[20]李洪兴.从模糊控制的数学本质看模糊逻辑的成功[J].模糊系统与数学,1995,9(2)：1-14.
[21]Oh S Y, Park D J. Self-tuning fuzzy controller with variable universe of discourse[C]. Systems, Man and Cybernetics,1995. Intelligent Systems for the 21st Century., IEEE International Conference on. IEEE,1995,3:2628-2632.
[22]Elkan C, Berenji H R, Chandrasekaran B, et al. The paradoxical success of fuzzy logic[J]. IEEE expert, 1994,9(4):3-49.
[23]李洪兴.模糊控制的数学本质与一类高精度模糊控制器的设计[J].控制理论与应用,1997,14(6)：868-876.
[24]Li H X. Adaptive fuzzy controllers based on variable universe [J]. Science in China Series E-Technological Sciences,1999,42(1):10-20.
[25]Li H X, Miao Z H, Lee E S. Variable universe stable adaptive fuzzy control of a nonlinear system [J]. Computers and Mathematics with Applications,2002,44(5):799-815.
[26]Li H X, Miao Z H, Wang J Y. Variable universe adaptive fuzzy control on the quadruple inverted pendulum [J]. Science in China Series E-Technological Sciences,2002,45(2):213-224.
[27]Li H X, Wang J Y, Feng Y B, et al. Hardware implementation of the quadruple inverted pendulum with single motor[J]. Progress in Natural Science,2004,14(9):822-827.
[28]邵诚,董希文,王晓芳.变论域模糊控制器伸缩因子的选择方法[J].信息与控制,2010,39(5)：536-541.
[29]Long Z Q, Xu Y B, Liu C. Fuzzy control algorithm based on variable universe of discourse and its expansion-contraction factors[J]. Journal of Convergence Information Technology,2012,7(19):570-577.
[30]赵云涛,工京,谢新亮,等.基于多层蚁群算法的变论域模糊控制[J].模式识别与人工智能,2009,22(5)：794-798.
[31]张巍巍,王京,王慧,赵云涛.混沌系统的变论域模糊控制算法研究[J].物理学报,2011,60(1)：(010511)1-9.
[32]陈富国,邓冠男,谭彦华.一种改进的三级倒立摆变论域模糊控制器设计[J].控制理论与应用,2010,27(2)：233-237.
[33]袁清坷,石亚平,张明天,等.基于变论域电阻点焊模糊神经网络控制方法[J].焊接学报,2010,31(1)：25-30.
[34]李力,邹砚湖.海底采矿车路径跟踪的变论域模糊控制[J].中南大学学报(自然科学版),2012,43(2)：489-496.
[35]黄之初,杨建林,蒋冬青.二级可变论域模糊控制器的设计与仿真试验[J].武汉理工大学学报,2005,27(8)：87-90.
[36]崔宝侠,杨继平,方博.新型变论域模糊控制器在交通信号控制中的应用[J].系统仿真学报,2007,19(2)：380-383.
[37]Li L F, Liu X Y, Chen W F. A variable universe fuzzy control algorithm based on fuzzy neural network [C]. Proceedings of the 7th World Congress on Intelligent Control and Automation,2008:4352-4356.
[38]Long Z, Liang X, Yang L. Some approximation properties of adaptive fuzzy systems with variable universe of discourse[J]. Information Sciences,2010,180(16):2991-3005.
[39]龙祖强,梁昔明,阎纲.变论域模糊控制器的万能逼近性及其逼近条件[J].中南大学学报(自然科学版),2012,43(8)：3046-3052.
[40]Wang J, Qiao G D, Deng B.H∞ variable universe adaptive fuzzy control for chaotic system[J]. Chaos Solitons and Fractals,2005,24:1075-1086.
[41]Wang J, Chen L, Deng B. Synchronization of Ghostburster neuron in external electrical stimulation via H∞ variable universe fuzzy adaptive control[J]. Chaos, Solitons and Fractals,2009,39(5):2076-2085.
[42]Wang J, Zhang Z, Li H Y. Synchronization of FitzHugh-Nagumosystems in EES via H-infinity variable universe adaptive fuzzy control[J]. Chaos Solitons and Fractals,2008,36:1332-1339.
[43]Guo C, Zhao J X, Chen Z Q, et al. H∞ variable universe fuzzy control for hysteretic systems[J].中国科学技术大学学报,2007,37(9)：1130-1136.
[44]Pan Y, Er M J, Huang D, et al. Adaptive fuzzy control with guaranteed convergence of optimal approx-imation error[J]. Fuzzy Systems, IEEE Transactions on,2011,19(5):807-818.
[45]潘永平,黄道平,孙宗海.不确定非线性系统高精度自适应模糊控制[J].电子科技大学学报,2012,41(1)：54-59.
[46]Che Y Q, Wang J, Chan W L, et al. Chaos synchronization of coupled neurons under electrical stimula-tion via robust adaptive fuzzy control[J]. Nonlinear Dynamics,2010,61(4):847-857.
[47]Wang J, Ye X, Si W. Robust ISS-satisficing fuzzy control of chaotic systems[C]. Intelligent Systems Design and Applications,2006. ISDA'06. Sixth International Conference on. IEEE,2006,1:293-298.
[48]王宇飞,姜长生.近空间飞行器直接自适应变论域模糊滑模控制[J].系统工程与电子技术,2011,33(3)：633-637.
[49]岳士弘,张绍杰,李平.变论域自适应模糊控制器失真率的计算[J].控制理论与应用,2005,22(5)：807-809,819.
[50]余涛,于文俊,李章文.基于Q学习算法的变论域模糊控制新算法[J].控制理论与应用,2011,28(11)：1645-1650.
[51]路永坤,夏超英.改进变论域模糊控制及其在混沌系统中的应用[J].天津大学学报,2010,43(8)：749-754.
[52]Phan P A, Gale T J. Direct adaptive fuzzy control with a self-structuring algorithm[J]. Fuzzy Sets and Systems,2008,159(8):871-899.
[53]Wang J, Qiao G D, Deng B. Observer-based robust adaptive variable universe fuzzy control for chaotic system[J]. Chaos, Solitons and Fractals,2005,23(3):1013-1032.
[54]Shan W W, Ma Y, Newcomb R W, et al. Analog circuit implementation of a variable universe adaptive fuzzy logic controller[J]. IEEE Transactions on Circuits and Systems-II:Express Briefs,2008,55(10): 976-980.
[55]Shan W, Jin D, Jin W, et al. VLSI implementation of a self-tuning fuzzy controller based on variable universe of discourse[M]. Fuzzy Systems and Knowledge Discovery. Springer Berlin Heidelberg,2005: 1044-1052.
[56]单伟伟,靳东明,梁艳.变论域自适应模糊控制器的CMOS模拟电路芯片实现[J].电子学报,2009,37(5)：913-917.
[57]王其东,王祺明,陈无畏.磁流变半主动悬架变论域模糊控制研究[J].振动工程学报,2009,22(5)：512-518.
[58]方子帆,邓兆祥.汽车磁流变半主动悬架控制方法研究[J].中国机械工程,2007,18(9)：1121-1124.
[59]杨建伟,董军哲,李捷.基于变论域模糊控制的磁流变半主动悬架多口标优化[J].汽车工程,2012,34(3)：260-266.
[60]陈杰平,冯武堂,郭万山,等.整车磁流变减振器半主动悬架变论域模糊控制策略[J].农业机械学报,2011,42(5)：7-13.
[61]王东亮,顾亮,马国新.油气悬架变论域模糊控制仿真分析与试验研究[J].北京理工大学学报,2009,29(4)：314-317.
[62]宁响亮,谭平,周福霖.公路桥梁振动控制的变论域自适应模糊控制算法[J].振动工程学报,2009,22(3)：262-267.
[63]白寒,管成,吴彦来.推土机半物理试验系统与作业效率复合控制研究[J].农业机械学报,2010,41(1)：34-40.
[64]邓义斌,黄荣华,程伟,等.发动机电控冷却系统设计及试验[J].内燃机工程,2012,33(3)：54-58.
[65]白寒,管成,冯培恩.电液比例系统变论域自适应模糊滑模控制[J].电机与控制学报,2009,13(5)：728-733.
[66]Zhang Y, Wang J, Li H. Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H∞ regulator[J]. Journal of Systems Science and Complexity, 2012,25(5):856-872.
[67]张永立,程会锋,李洪兴.三级倒立摆的自动摆起与稳定控制[J].控制理论与应用,2011,28(1)：37-45.
[68]赵国亮,张永立,李洪兴.区间Ⅱ型变论域自适应模糊逻辑控制器[J].大连理工大学学报,2012,52(6)：914-920.
[69]Liu Y, Miao D, Peng Y, et al. Variable universe adaptive fuzzy sliding mode controller for a class of nonlinear system[M]. Computational Intelligence. Springer Berlin Heidelberg,2006:73-84.
[70]李树江,胡韶华,吴海.基于LQR和变论域模糊控制的吊车防摆控制[J].控制与决策,2006,21(3)：289-292.
[71]裘智峰,黄灯,桂卫华,等.基于变论域插值模糊PID控制系统的研究与应用[J].仪器仪表学报,2008,29(11)：2435-2440.
[72]余涛,于文俊,李章文.基于CPS标准的AGC变论域模糊松弛控制方法[J].电力系统自动化,2009,33(23)：37-41.
[73]侯国莲,李泉,张建华.变论域自适应模糊滑模多变量控制算法及其在单元机组协调控制中的应用[J].中国电机工程学报,2005,25：114-121.
[74]张丽,徐玉琴,王增平,等.包含同步发电机及电压源逆变器接口的微网控制策略[J].电网技术,2011,35(3)：170-176.
[75]揭海宝,康积涛,李平.基于变论域模糊PID控制的同步发电机励磁研究[J].电力自动化设备,2011,31(6)：101-104.
[76]黄悦华,徐阳,周星辰,等.基于变论域模糊PI的双馈风力发电机空载并网控制[J].微特电机,2011,39(4)：69-72.
[77]黄悦华,徐阳,周星辰.基于变论域模糊控制的无刷双馈风力发电系统空载并网控制[J].电力自动化设备,2012,32(2)：99-103.
[78]汪义旺,曹丰文,高金生.光伏发电MPPT的变论域自适应模糊控制[J].太阳能学报,2012,33(3)：473-477.
[79]Tong S W, Liu G P. Real-time simplified variable domain fuzzy control of PEM fuel cell flow systems[J]. European journal of control,2008,14(3):223-233.
[80]叶建雄,张华,杨武强.焊缝跟踪的变论域自适应模糊控制[J].焊接学报,2005,26(12)：32-34.
[81]刘辉,庞佑霞,唐勇,等.基于灰色蚁群组合预测的生物质气化炉双闭环控制[J].农业机械学报,2012,43(1)：94-100.
[82]吕燕,吴敏,雷琪,等.钛坯天然气加热炉多工况炉温模糊优化控制[J].化工学报,2011,62(8)：2140-2145.
[83]李劫,张文根,丁凤其,等.基于在线智能辨识的模糊专家控制方法及其应用[J].中南大学学报：自然科学版,2004,35(6)：911-914.
[84]邝先验,许伦辉,黄艳国.交通信号公交优先控制策略及智能控制方法[J].控制理论与应用,2012,29(10)：1284-1290.
[85]刘胜,王宇超,傅荟璇.船舶航向保持变论域模糊-最小二乘支持向量机复合控制[J].控制理论与应用,2011,28(4)：485-490.
[86]刘胜,常绪成,李高云.船舶双舵同步补偿控制[J].控制理论与应用,2010,27(12)：1631-1636.
[87]方炜,姜长生.空间飞行器的自适应变论域模糊预测控制[J].控制与决策,2008,23(12)：1373-1377,1388.
[88]Wang Y, Lu Y. Design of longitudinal predictive re-entry guidance law based on variable universe fuzzy-PI composite control[J]. Journal of Control Theory and Applications,2012,10(2):264-267.
[89]宋乐鹏,董志明,向李娟,等.变量喷雾流量阀的变论域自适应模糊PID控制[J].农业工程学报,2010,26(11)：114-118.
[90]Xie K M, Wang F, Xie G, et al. Application of fuzzy control base on changeable universe to superheated steam temperature control system[J]. Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Springer Berlin Heidelberg,2003,2039:358-362.
[91]吕红丽,段培永,崔玉珍,等.新型模糊PID控制及在HVAC系统的应用[J].控制理论与应用,200926(11)：1277-1281.
[92]王江,乔国栋,邓斌.混沌系统变论域自适应模糊控制[J].天津大学学报,2005,38(10)：847-852.
[93]Li H X. Interpolation mechanism of fuzzy control [J]. Science in China Series E-Technological Sci-ences,1998,41(3):312-320.
[94]杨明,刘先忠.矩阵论[M].华中科技大学出版社,2003.
[95]李成章,黄玉民.数学分析(上册)[M].北京,科学出版社,1999,81-95.
[96]Ioannou P A, Sun J. Robust adaptive control[M]. Courier Dover Publications,2012:66-134.
[97]Slotine J J E, Li W. Applied Nonlinear Control[M]. New Jersey:Prentice-Hall,1991.
[98]Hwang C L. A novel Takagi-Sugeno-based robust adaptive fuzzy sliding-mode controller[J]. IEEE Transactions on Fuzzy Systems,2004,12(5):676-687.
[99]Ting C H, Mahfouf M, Nassef A, et al. Real-time adaptive automation system based on identification of operator functional state in simulated process control operations[J]. Systems, Man and Cybernetics, Part A:Systems and Humans, IEEE Transactions on,2010,40(2):251-262.
[100]Chan PT, Rad A B, Wang J. Indirect adaptive fuzzy sliding mode control:Part II:parameter projection and supervisory control[J]. Fuzzy Sets and Systems,2001,122(1):31-43.
[101]Park J H, Seo S J, Park G T. Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors [J]. Fuzzy Sets and Systems,2003,133(1):19-36.
[102]Buckley J J. Sugeno type controllers are universal controllers[J]. Fuzzy sets and systems,1993,53(3): 299-303.
[103]Hu H, Woo P Y. Fuzzy supervisory sliding-mode and neural-network control for robotic manipula-tors[J]. IEEE Transactions on Industrial Electronics,2006,53(3):929-940.
[104]Song Z, Yi J, Zhao D, et al. A computed torque controller for uncertain robotic manipulator systems: Fuzzy approach[J]. Fuzzy Sets and Systems,2005,154(2):208-226.
[105]Wu L, Su X, Shi P. Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems[J]. Automatica,2012,48(8):1929-1933.
[106]Fei J, Xin M. Robust adaptive sliding mode controller for semi-active vehicle suspension system[J]. International Journal of Innovative Computing, Information and Control,2012,8(1):691-700.
[107]Khan Q, Bhatti A I, Iqbal M, et al. Dynamic integral sliding mode control for SISO uncertain nonlinear systems [J]. International Journal of Innovative Computing, Information and Control,2012,8(7):4621-4633.
[108]Ertugrul M, Kaynak O. Neuro sliding mode control of robotic manipulators [J]. Mechatronics,2000, 10(1):239-263.
[109]Su X, Shi P, Wu L, et al. A novel control design on discrete-time Takagi-Sugeno fuzzy sys-tems with time-varying delays[J]. IEEE Transactions on fuzzy systems,2012, DOI:10.1109 /TFUZZ.2012.2226941.
[110]Su X, Shi P, Wu L, et al. A novel approach to filter design for TS fuzzy discrete-time systems with time-varying delay[J]. IEEE Transactions on fuzzy systems,2012,20(6):1114-1129.
[111]Wu L, Su X, Shi P, et al. Model approximation for discrete-time state-delay systems in the T-S fuzzy framework[J]. IEEE Transactions on Fuzzy Systems,2011,19(2):366-378.
[112]Zhou Q, Shi P, Xu S, et al. Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach[J]. IEEE Transactions on Fuzzy Systems,2013,21(2):301-313.
[113]Zhou Q, Shi P, Lu J J, et al. Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems,2011; 19(5):972-982.
[114]Labiod S, Boucherit M S, Guerra T M. Adaptive fuzzy control of a class of MIMO nonlinear sys-tems[J]. Fuzzy sets and systems,2005,151(1):59-77.
[115]Boulkroune A, Tadjine M, M'saad M, et al. Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction[J]. Fuzzy sets and systems,2010,161(6):797-820.
[116]Ho H F, Wong Y K, Rad A B. Robust fuzzy tracking control for robotic manipulators[J]. Simulation Modelling Practice and Theory,2007,15(7):801-816.
[117]Abdelhameed M M. Enhancement of sliding mode controller by fuzzy logic with application to robotic manipulators[J]. Mechatronics,2005,15(4):439-458.
[118]Guan P, Liu X J, Liu J Z. Adaptive fuzzy sliding mode control for flexible satellite[J]. Engineering Applications of Artificial Intelligence,2005,18(4):451-459.
[119]Lin T C, Chang S W, Hsu C H. Robust adaptive fuzzy sliding mode control for a class of uncertain discrete-time nonlinear systems[J]. International Journal of Innovative Computing, Information and Control,2012,8(1):347-359.
[120]Roopaei M, Zolghadri Jahromi M. Chattering-free fuzzy sliding mode control in MIMO uncertain systems[J]. Nonlinear Analysis:Theory, Methods and Applications,2009,71(10):4430-4437.
[121]Yau H T, Chen C L. Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic sys-tems[J]. Chaos, Solitons and Fractals,2006,30(3):709-718.
[122]Sadati N, Ghadami R. Adaptive multi-model sliding mode control of robotic manipulators using soft computing[J]. Neurocomputing,2008,71(13):2702-2710.
[123]Lee H, Kim E, Kang H J, et al. A new sliding-mode control with fuzzy boundary layer[J]. Fuzzy Sets and Systems,2001,120(1):135-143.
[124]Hwang Y R, Tomizuka M. Fuzzy smoothing algorithms for variable structure systems[J]. IEEE Trans-actions on Fuzzy Systems,1994,2(4):277-284.
[125]Korayem M H, Haghighi R, Korayem A H, et al. Determining maximum load carrying capacity of planar flexible-link robot:closed-loop approach[J]. Robotica,2010,28(7):959-973.
[126]Chen J Y. Rule regulation of fuzzy sliding mode controller design:Direct adaptive approach[J]. Fuzzy sets and Systems,2001,120(1):159-168.
[127]Yoo B, Ham W. Adaptive fuzzy sliding mode control of nonlinear system[J]. IEEE Transactions on Fuzzy Systems,1998,6(2):315-321.
[128]Frikha S, Djemel M, Derbel N. Observer based adaptive neuro-sliding mode control for MIMO non-linear systems[J]. International Journal of Control, Automation and Systems,2010,8(2):257-265.
[129]Wang J, Rad A B, Chan P T. Indirect adaptive fuzzy sliding mode control:Part I:fuzzy switching[J]. Fuzzy sets and systems,2001,122(1):21-30.
[130]Roopaei M, Zolghadri M, Meshksar S. Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems[J]. Communications in Nonlinear Science and Numerical Simulation,2009,14(9): 3670-3681.
[131]Aloui S, Pages O, El Hajjaji A, et al. Improved fuzzy sliding mode control for a class of MIMO nonlinear uncertain and perturbed systems[J]. Applied Soft Computing,2011,11(1):820-826.
[132]Phan P A, Gale T. Two-Mode Adaptive Fuzzy Control With Approximation Error Estimator [J]. IEEE Transactions on Fuzzy Systems,2007,15(5):943-955.
[133]Nekoukar V, Erfanian A. Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems[J]. Fuzzy Sets and Systems,2011,179(1):34-49.
[134]Faieghi M R, Delavari H, Baleanu D. A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations[J]. Communications in Nonlinear Science and Numerical Simulation, 2012,17(2):1021-1030.
[135]Chang Y C. Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and H∞ approaches[J]. IEEE Transactions on Fuzzy Systems,2001,9(2):278-292.
[136]Labiod S, Guerra T M. Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems[J]. Fuzzy sets and systems,2007,158(10):1126-1137.
[137]Driankov D, Hellendoorn H, Palm R. Some research directions in fuzzy control[C]. Theoretical aspects of fuzzy control. John Wiley and Sons, Inc.,1995:281-312.
[138]Park J H, Park G T. Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems[J]. IEE Proceedings-Control Theory and Applications,2003,150(2):189-197.
[139]Pan Y P, Zhou Y, Sun T R, et al. Composite adaptive fuzzy H∞ tracking control of uncertain nonlinear systems [J]. Neurocomputing,2013,99:15-24.
[140]Hyun C H, Park C W, Kim S. Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design[J]. Information Sciences,2010,180(11):2314-2327.
[141]Chemachema M. Output feedback direct adaptive neural network control for uncertain SISO nonlinear systems using a fuzzy estimator of the control error[J]. Neural Networks,2012,36:25-34.
[142]Boulkroune A, M'saad M. On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign[J]. Fuzzy Sets and Systems,2012,201:71-85.
[143]Liu Y J, Tong S C, Wang W, et al. Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications[J]. International Journal of Control, Automation and Systems,2009,7(4): 681-690.
[144]Wang C H, Liu H L, Lin T C. Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems[J]. IEEE Transactions on Fuzzy Systems,2002, 10(1):39-49.
[145]Tong S, Li H X, Wang W. Observer-based adaptive fuzzy control for SISO nonlinear systems[J]. Fuzzy Sets and Systems,2004,148(3):355-376.
[146]Leu Y G, Lee T T, Wang W Y. Observer-based adaptive fuzzy-neural control for unknown nonlin-ear dynamical systems[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics, 1999,29(5):583-591.
[147]Leu Y G, Wang W Y, Lee T T. Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems[J]. IEEE Transactions on Neural Networks,2005,16(4):853-861.
[148]Wang W Y, Cheng C Y, Leu Y G. An on-line GA-based output feedback direct adaptive fuzzy-neural controller for uncertain nonlinear systems [J]. IEEE Transactions on Systems Man Cybernet. Part B: Cybernet,2004,34(1):334-345.
[149]Park J H, Park G T, Kim S H, et al. Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer[J]. Fuzzy Sets and Systems,2005,151(1):21-42.
[150]Kung C C, Chen T H. Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems[J]. Fuzzy Sets and Systems,2005,155(2):292-308.
[151]Boulkroune A, Tadjine M, M'saad M, et al. How to design a fuzzy adaptive controller based on ob-servers for uncertain affine nonlinear systems[J]. Fuzzy Sets and Systems,2008,159(8):926-948.
[152]Macnab C J B. Preventing bursting in approximate-adaptive control when using local basis func-tions[J]. Fuzzy Sets and Systems,2009,160(4):439-462.
[153]Belarbi K, Chemachema M. Stable direct adaptive neural network controller with a fuzzy estimator of the control error for a class of perturbed nonlinear systems[J]. Control Theory and Applications, TET, 2007,1(5):1398-1404.
[154]Macnab C J B. Preventing bursting in approximate-adaptive control when using local basis func-tions[J]. Fuzzy Sets and Systems,2009; 160(4):439-462.
[155]Lee C. Fuzzy logic in control systems:Fuzzy logic controller, part I[J]. IEEE Transactions on Systems, Man, and Cybernetics,1990,20:404-418.
[156]Wang J, Si W, Li H. Robust ISS-satisficing variable universe indirect fuzzy control for chaotic sys-tems[J]. Chaos, Solitons and Fractals,2009,39(1):28-38.
[157]Liu Y J, Tong S C, Li T S. Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems[J]. Fuzzy Sets and Systems,2011,164(1):25-44.
[158]Purwar S, Kar I N, Jha A N. Adaptive control of robot manipulators using fuzzy logic systems under actuator constraints[J]. Fuzzy Sets and Systems,2005,152(3):651-664.
[159]Li H X, Tong S. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems[J]. IEEE Transactions on Fuzzy Systems,2003,11(1):24-34.
[160]Rojas I, Pomares H, Gonzalez J, et al. Adaptive fuzzy controller:Application to the control of the temperature of a dynamic room in real time[J]. Fuzzy Sets and Systems,2006,157(16):2241-2258.
[161]Sala A, Guerra T M, Babuska R. Perspectives of fuzzy systems and control[J]. Fuzzy Sets and Systems, 2005,156(3):432-444.
[162]Yau H T, Yan J J. Adaptive sliding mode control of a high-precision ball-screw-driven stage[J]. Non-linear Analysis:Real World Applications,2009,10(3):1480-1489.
[163]Green A, Sasiadek J Z. Heuristic design of a fuzzy controller for a flexible robot[J]. IEEE Transactions on Control Systems Technology,2006,14(2):293-300.
[164]李家炜.一种新的模糊控制器的优化方法[J].控制理论与应用,2002,9(2)：279-283.
[165]Zhang Z, Chang J. A fuzzy control algorithm with high controlling precision[J]. Fuzzy sets and sys-tems,2003,140(2):375-385.
[166]Li Y, Tong S. Adaptive fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters[J]. Neurocomputing,2011,74(10):1557-1563.
[167]李丽娜,柳洪义,罗忠,等.模糊PID复合控制算法改进及应用[J].东北大学学报：自然科学版,2009,30(2)：274-278.
[2]Riccardo M, Patrizio T(著),姚郁,贺风华(译).非线性系统设计[M].北京：电子工业出版社,2006,1-74.
[3]Poincare H. Sur les courbes definies par les equations differentielles (III)[J]. Journal de mathematiques pures et appliquees,1885:167-244.
[4]高为炳.非线性控制系统导论[M].北京：科学出版社,1988.
[5]Krener A J, Isidori A, Respondek W. Partial and robust linearization by feedback[C]//Proc.22nd IEEE Conf. Decision Control.1983:126-130.
[6]Astrbm K J, Wittenmark B. Adaptive control[M]. 北京,科学出版社,2003:1-20.
[7]Astrom K J. Theory and applications of adaptive control-a survey[J]. Automatica,1983,19(5):471-486.
[8]Fu K. Learning control systems and intelligent control systems:An intersection of artifical intelligence and automatic control[J]. IEEE Transactions on Automatic Control,1971,16(1):70-72.
[9]刘金琨.智能控制(第2版)[M].北京,电子工业出版社,2009,1-10.
[10]Wang L X. Stable adaptive fuzzy controllers with application to inverted pendulum tracking[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,1996,26(5):677-691.
[11]Zadeh L A. Fuzzy sets [J]. Information and control,1965,8(3):338-353.
[12]Zadeh L A. Outline of a New Approach to the Analysis of Complex Systems and Decision Processes [J]. IEEE Transactions on Systems, Man, and Cybernetics,1973,3(1):28-44.
[13]Mamdani E H, Assilian S. A case study on the application of fuzzy set theory to automatic con-trol [C]//Proc. IFAC Stochastic Control Symp.1974.
[14]Mamdani E H, Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller[J]. Inter-national journal of man-machine studies,1975,7(1):1-13.
[15]Wang L X. Adaptive fuzzy systems and control:design and stability analysis[M]. Prentice-Hall, Engle-wood Cliffs, NJ,1994.
[16]Castro J L. Fuzzy logic controllers are universal approximators[J]. IEEE Transactions on Systems, Man, and Cybernetics,1995,25(4):629-635.
[17]Wang L X, Mendel J M. Fuzzy basis functions, universal approximation, and orthogonal least-squares learning[J]. IEEE Transactions on Neural Networks,1992,3(5):807-814.
[18]Wang L X. Stable adaptive fuzzy control of nonlinear systems [J]. IEEE Transactions on Fuzzy Systems, 1993,1(2):146-155.
[19]Golea N, Golea A, Benmahammed K. Fuzzy model reference adaptive control[J]. IEEE Transactions on Fuzzy Systems,2002,10(4):436-444.
[20]李洪兴.从模糊控制的数学本质看模糊逻辑的成功[J].模糊系统与数学,1995,9(2)：1-14.
[21]Oh S Y, Park D J. Self-tuning fuzzy controller with variable universe of discourse[C]. Systems, Man and Cybernetics,1995. Intelligent Systems for the 21st Century., IEEE International Conference on. IEEE,1995,3:2628-2632.
[22]Elkan C, Berenji H R, Chandrasekaran B, et al. The paradoxical success of fuzzy logic[J]. IEEE expert, 1994,9(4):3-49.
[23]李洪兴.模糊控制的数学本质与一类高精度模糊控制器的设计[J].控制理论与应用,1997,14(6)：868-876.
[24]Li H X. Adaptive fuzzy controllers based on variable universe [J]. Science in China Series E-Technological Sciences,1999,42(1):10-20.
[25]Li H X, Miao Z H, Lee E S. Variable universe stable adaptive fuzzy control of a nonlinear system [J]. Computers and Mathematics with Applications,2002,44(5):799-815.
[26]Li H X, Miao Z H, Wang J Y. Variable universe adaptive fuzzy control on the quadruple inverted pendulum [J]. Science in China Series E-Technological Sciences,2002,45(2):213-224.
[27]Li H X, Wang J Y, Feng Y B, et al. Hardware implementation of the quadruple inverted pendulum with single motor[J]. Progress in Natural Science,2004,14(9):822-827.
[28]邵诚,董希文,王晓芳.变论域模糊控制器伸缩因子的选择方法[J].信息与控制,2010,39(5)：536-541.
[29]Long Z Q, Xu Y B, Liu C. Fuzzy control algorithm based on variable universe of discourse and its expansion-contraction factors[J]. Journal of Convergence Information Technology,2012,7(19):570-577.
[30]赵云涛,工京,谢新亮,等.基于多层蚁群算法的变论域模糊控制[J].模式识别与人工智能,2009,22(5)：794-798.
[31]张巍巍,王京,王慧,赵云涛.混沌系统的变论域模糊控制算法研究[J].物理学报,2011,60(1)：(010511)1-9.
[32]陈富国,邓冠男,谭彦华.一种改进的三级倒立摆变论域模糊控制器设计[J].控制理论与应用,2010,27(2)：233-237.
[33]袁清坷,石亚平,张明天,等.基于变论域电阻点焊模糊神经网络控制方法[J].焊接学报,2010,31(1)：25-30.
[34]李力,邹砚湖.海底采矿车路径跟踪的变论域模糊控制[J].中南大学学报(自然科学版),2012,43(2)：489-496.
[35]黄之初,杨建林,蒋冬青.二级可变论域模糊控制器的设计与仿真试验[J].武汉理工大学学报,2005,27(8)：87-90.
[36]崔宝侠,杨继平,方博.新型变论域模糊控制器在交通信号控制中的应用[J].系统仿真学报,2007,19(2)：380-383.
[37]Li L F, Liu X Y, Chen W F. A variable universe fuzzy control algorithm based on fuzzy neural network [C]. Proceedings of the 7th World Congress on Intelligent Control and Automation,2008:4352-4356.
[38]Long Z, Liang X, Yang L. Some approximation properties of adaptive fuzzy systems with variable universe of discourse[J]. Information Sciences,2010,180(16):2991-3005.
[39]龙祖强,梁昔明,阎纲.变论域模糊控制器的万能逼近性及其逼近条件[J].中南大学学报(自然科学版),2012,43(8)：3046-3052.
[40]Wang J, Qiao G D, Deng B.H∞ variable universe adaptive fuzzy control for chaotic system[J]. Chaos Solitons and Fractals,2005,24:1075-1086.
[41]Wang J, Chen L, Deng B. Synchronization of Ghostburster neuron in external electrical stimulation via H∞ variable universe fuzzy adaptive control[J]. Chaos, Solitons and Fractals,2009,39(5):2076-2085.
[42]Wang J, Zhang Z, Li H Y. Synchronization of FitzHugh-Nagumosystems in EES via H-infinity variable universe adaptive fuzzy control[J]. Chaos Solitons and Fractals,2008,36:1332-1339.
[43]Guo C, Zhao J X, Chen Z Q, et al. H∞ variable universe fuzzy control for hysteretic systems[J].中国科学技术大学学报,2007,37(9)：1130-1136.
[44]Pan Y, Er M J, Huang D, et al. Adaptive fuzzy control with guaranteed convergence of optimal approx-imation error[J]. Fuzzy Systems, IEEE Transactions on,2011,19(5):807-818.
[45]潘永平,黄道平,孙宗海.不确定非线性系统高精度自适应模糊控制[J].电子科技大学学报,2012,41(1)：54-59.
[46]Che Y Q, Wang J, Chan W L, et al. Chaos synchronization of coupled neurons under electrical stimula-tion via robust adaptive fuzzy control[J]. Nonlinear Dynamics,2010,61(4):847-857.
[47]Wang J, Ye X, Si W. Robust ISS-satisficing fuzzy control of chaotic systems[C]. Intelligent Systems Design and Applications,2006. ISDA'06. Sixth International Conference on. IEEE,2006,1:293-298.
[48]王宇飞,姜长生.近空间飞行器直接自适应变论域模糊滑模控制[J].系统工程与电子技术,2011,33(3)：633-637.
[49]岳士弘,张绍杰,李平.变论域自适应模糊控制器失真率的计算[J].控制理论与应用,2005,22(5)：807-809,819.
[50]余涛,于文俊,李章文.基于Q学习算法的变论域模糊控制新算法[J].控制理论与应用,2011,28(11)：1645-1650.
[51]路永坤,夏超英.改进变论域模糊控制及其在混沌系统中的应用[J].天津大学学报,2010,43(8)：749-754.
[52]Phan P A, Gale T J. Direct adaptive fuzzy control with a self-structuring algorithm[J]. Fuzzy Sets and Systems,2008,159(8):871-899.
[53]Wang J, Qiao G D, Deng B. Observer-based robust adaptive variable universe fuzzy control for chaotic system[J]. Chaos, Solitons and Fractals,2005,23(3):1013-1032.
[54]Shan W W, Ma Y, Newcomb R W, et al. Analog circuit implementation of a variable universe adaptive fuzzy logic controller[J]. IEEE Transactions on Circuits and Systems-II:Express Briefs,2008,55(10): 976-980.
[55]Shan W, Jin D, Jin W, et al. VLSI implementation of a self-tuning fuzzy controller based on variable universe of discourse[M]. Fuzzy Systems and Knowledge Discovery. Springer Berlin Heidelberg,2005: 1044-1052.
[56]单伟伟,靳东明,梁艳.变论域自适应模糊控制器的CMOS模拟电路芯片实现[J].电子学报,2009,37(5)：913-917.
[57]王其东,王祺明,陈无畏.磁流变半主动悬架变论域模糊控制研究[J].振动工程学报,2009,22(5)：512-518.
[58]方子帆,邓兆祥.汽车磁流变半主动悬架控制方法研究[J].中国机械工程,2007,18(9)：1121-1124.
[59]杨建伟,董军哲,李捷.基于变论域模糊控制的磁流变半主动悬架多口标优化[J].汽车工程,2012,34(3)：260-266.
[60]陈杰平,冯武堂,郭万山,等.整车磁流变减振器半主动悬架变论域模糊控制策略[J].农业机械学报,2011,42(5)：7-13.
[61]王东亮,顾亮,马国新.油气悬架变论域模糊控制仿真分析与试验研究[J].北京理工大学学报,2009,29(4)：314-317.
[62]宁响亮,谭平,周福霖.公路桥梁振动控制的变论域自适应模糊控制算法[J].振动工程学报,2009,22(3)：262-267.
[63]白寒,管成,吴彦来.推土机半物理试验系统与作业效率复合控制研究[J].农业机械学报,2010,41(1)：34-40.
[64]邓义斌,黄荣华,程伟,等.发动机电控冷却系统设计及试验[J].内燃机工程,2012,33(3)：54-58.
[65]白寒,管成,冯培恩.电液比例系统变论域自适应模糊滑模控制[J].电机与控制学报,2009,13(5)：728-733.
[66]Zhang Y, Wang J, Li H. Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H∞ regulator[J]. Journal of Systems Science and Complexity, 2012,25(5):856-872.
[67]张永立,程会锋,李洪兴.三级倒立摆的自动摆起与稳定控制[J].控制理论与应用,2011,28(1)：37-45.
[68]赵国亮,张永立,李洪兴.区间Ⅱ型变论域自适应模糊逻辑控制器[J].大连理工大学学报,2012,52(6)：914-920.
[69]Liu Y, Miao D, Peng Y, et al. Variable universe adaptive fuzzy sliding mode controller for a class of nonlinear system[M]. Computational Intelligence. Springer Berlin Heidelberg,2006:73-84.
[70]李树江,胡韶华,吴海.基于LQR和变论域模糊控制的吊车防摆控制[J].控制与决策,2006,21(3)：289-292.
[71]裘智峰,黄灯,桂卫华,等.基于变论域插值模糊PID控制系统的研究与应用[J].仪器仪表学报,2008,29(11)：2435-2440.
[72]余涛,于文俊,李章文.基于CPS标准的AGC变论域模糊松弛控制方法[J].电力系统自动化,2009,33(23)：37-41.
[73]侯国莲,李泉,张建华.变论域自适应模糊滑模多变量控制算法及其在单元机组协调控制中的应用[J].中国电机工程学报,2005,25：114-121.
[74]张丽,徐玉琴,王增平,等.包含同步发电机及电压源逆变器接口的微网控制策略[J].电网技术,2011,35(3)：170-176.
[75]揭海宝,康积涛,李平.基于变论域模糊PID控制的同步发电机励磁研究[J].电力自动化设备,2011,31(6)：101-104.
[76]黄悦华,徐阳,周星辰,等.基于变论域模糊PI的双馈风力发电机空载并网控制[J].微特电机,2011,39(4)：69-72.
[77]黄悦华,徐阳,周星辰.基于变论域模糊控制的无刷双馈风力发电系统空载并网控制[J].电力自动化设备,2012,32(2)：99-103.
[78]汪义旺,曹丰文,高金生.光伏发电MPPT的变论域自适应模糊控制[J].太阳能学报,2012,33(3)：473-477.
[79]Tong S W, Liu G P. Real-time simplified variable domain fuzzy control of PEM fuel cell flow systems[J]. European journal of control,2008,14(3):223-233.
[80]叶建雄,张华,杨武强.焊缝跟踪的变论域自适应模糊控制[J].焊接学报,2005,26(12)：32-34.
[81]刘辉,庞佑霞,唐勇,等.基于灰色蚁群组合预测的生物质气化炉双闭环控制[J].农业机械学报,2012,43(1)：94-100.
[82]吕燕,吴敏,雷琪,等.钛坯天然气加热炉多工况炉温模糊优化控制[J].化工学报,2011,62(8)：2140-2145.
[83]李劫,张文根,丁凤其,等.基于在线智能辨识的模糊专家控制方法及其应用[J].中南大学学报：自然科学版,2004,35(6)：911-914.
[84]邝先验,许伦辉,黄艳国.交通信号公交优先控制策略及智能控制方法[J].控制理论与应用,2012,29(10)：1284-1290.
[85]刘胜,王宇超,傅荟璇.船舶航向保持变论域模糊-最小二乘支持向量机复合控制[J].控制理论与应用,2011,28(4)：485-490.
[86]刘胜,常绪成,李高云.船舶双舵同步补偿控制[J].控制理论与应用,2010,27(12)：1631-1636.
[87]方炜,姜长生.空间飞行器的自适应变论域模糊预测控制[J].控制与决策,2008,23(12)：1373-1377,1388.
[88]Wang Y, Lu Y. Design of longitudinal predictive re-entry guidance law based on variable universe fuzzy-PI composite control[J]. Journal of Control Theory and Applications,2012,10(2):264-267.
[89]宋乐鹏,董志明,向李娟,等.变量喷雾流量阀的变论域自适应模糊PID控制[J].农业工程学报,2010,26(11)：114-118.
[90]Xie K M, Wang F, Xie G, et al. Application of fuzzy control base on changeable universe to superheated steam temperature control system[J]. Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Springer Berlin Heidelberg,2003,2039:358-362.
[91]吕红丽,段培永,崔玉珍,等.新型模糊PID控制及在HVAC系统的应用[J].控制理论与应用,200926(11)：1277-1281.
[92]王江,乔国栋,邓斌.混沌系统变论域自适应模糊控制[J].天津大学学报,2005,38(10)：847-852.
[93]Li H X. Interpolation mechanism of fuzzy control [J]. Science in China Series E-Technological Sci-ences,1998,41(3):312-320.
[94]杨明,刘先忠.矩阵论[M].华中科技大学出版社,2003.
[95]李成章,黄玉民.数学分析(上册)[M].北京,科学出版社,1999,81-95.
[96]Ioannou P A, Sun J. Robust adaptive control[M]. Courier Dover Publications,2012:66-134.
[97]Slotine J J E, Li W. Applied Nonlinear Control[M]. New Jersey:Prentice-Hall,1991.
[98]Hwang C L. A novel Takagi-Sugeno-based robust adaptive fuzzy sliding-mode controller[J]. IEEE Transactions on Fuzzy Systems,2004,12(5):676-687.
[99]Ting C H, Mahfouf M, Nassef A, et al. Real-time adaptive automation system based on identification of operator functional state in simulated process control operations[J]. Systems, Man and Cybernetics, Part A:Systems and Humans, IEEE Transactions on,2010,40(2):251-262.
[100]Chan PT, Rad A B, Wang J. Indirect adaptive fuzzy sliding mode control:Part II:parameter projection and supervisory control[J]. Fuzzy Sets and Systems,2001,122(1):31-43.
[101]Park J H, Seo S J, Park G T. Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors [J]. Fuzzy Sets and Systems,2003,133(1):19-36.
[102]Buckley J J. Sugeno type controllers are universal controllers[J]. Fuzzy sets and systems,1993,53(3): 299-303.
[103]Hu H, Woo P Y. Fuzzy supervisory sliding-mode and neural-network control for robotic manipula-tors[J]. IEEE Transactions on Industrial Electronics,2006,53(3):929-940.
[104]Song Z, Yi J, Zhao D, et al. A computed torque controller for uncertain robotic manipulator systems: Fuzzy approach[J]. Fuzzy Sets and Systems,2005,154(2):208-226.
[105]Wu L, Su X, Shi P. Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems[J]. Automatica,2012,48(8):1929-1933.
[106]Fei J, Xin M. Robust adaptive sliding mode controller for semi-active vehicle suspension system[J]. International Journal of Innovative Computing, Information and Control,2012,8(1):691-700.
[107]Khan Q, Bhatti A I, Iqbal M, et al. Dynamic integral sliding mode control for SISO uncertain nonlinear systems [J]. International Journal of Innovative Computing, Information and Control,2012,8(7):4621-4633.
[108]Ertugrul M, Kaynak O. Neuro sliding mode control of robotic manipulators [J]. Mechatronics,2000, 10(1):239-263.
[109]Su X, Shi P, Wu L, et al. A novel control design on discrete-time Takagi-Sugeno fuzzy sys-tems with time-varying delays[J]. IEEE Transactions on fuzzy systems,2012, DOI:10.1109 /TFUZZ.2012.2226941.
[110]Su X, Shi P, Wu L, et al. A novel approach to filter design for TS fuzzy discrete-time systems with time-varying delay[J]. IEEE Transactions on fuzzy systems,2012,20(6):1114-1129.
[111]Wu L, Su X, Shi P, et al. Model approximation for discrete-time state-delay systems in the T-S fuzzy framework[J]. IEEE Transactions on Fuzzy Systems,2011,19(2):366-378.
[112]Zhou Q, Shi P, Xu S, et al. Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach[J]. IEEE Transactions on Fuzzy Systems,2013,21(2):301-313.
[113]Zhou Q, Shi P, Lu J J, et al. Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems,2011; 19(5):972-982.
[114]Labiod S, Boucherit M S, Guerra T M. Adaptive fuzzy control of a class of MIMO nonlinear sys-tems[J]. Fuzzy sets and systems,2005,151(1):59-77.
[115]Boulkroune A, Tadjine M, M'saad M, et al. Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction[J]. Fuzzy sets and systems,2010,161(6):797-820.
[116]Ho H F, Wong Y K, Rad A B. Robust fuzzy tracking control for robotic manipulators[J]. Simulation Modelling Practice and Theory,2007,15(7):801-816.
[117]Abdelhameed M M. Enhancement of sliding mode controller by fuzzy logic with application to robotic manipulators[J]. Mechatronics,2005,15(4):439-458.
[118]Guan P, Liu X J, Liu J Z. Adaptive fuzzy sliding mode control for flexible satellite[J]. Engineering Applications of Artificial Intelligence,2005,18(4):451-459.
[119]Lin T C, Chang S W, Hsu C H. Robust adaptive fuzzy sliding mode control for a class of uncertain discrete-time nonlinear systems[J]. International Journal of Innovative Computing, Information and Control,2012,8(1):347-359.
[120]Roopaei M, Zolghadri Jahromi M. Chattering-free fuzzy sliding mode control in MIMO uncertain systems[J]. Nonlinear Analysis:Theory, Methods and Applications,2009,71(10):4430-4437.
[121]Yau H T, Chen C L. Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic sys-tems[J]. Chaos, Solitons and Fractals,2006,30(3):709-718.
[122]Sadati N, Ghadami R. Adaptive multi-model sliding mode control of robotic manipulators using soft computing[J]. Neurocomputing,2008,71(13):2702-2710.
[123]Lee H, Kim E, Kang H J, et al. A new sliding-mode control with fuzzy boundary layer[J]. Fuzzy Sets and Systems,2001,120(1):135-143.
[124]Hwang Y R, Tomizuka M. Fuzzy smoothing algorithms for variable structure systems[J]. IEEE Trans-actions on Fuzzy Systems,1994,2(4):277-284.
[125]Korayem M H, Haghighi R, Korayem A H, et al. Determining maximum load carrying capacity of planar flexible-link robot:closed-loop approach[J]. Robotica,2010,28(7):959-973.
[126]Chen J Y. Rule regulation of fuzzy sliding mode controller design:Direct adaptive approach[J]. Fuzzy sets and Systems,2001,120(1):159-168.
[127]Yoo B, Ham W. Adaptive fuzzy sliding mode control of nonlinear system[J]. IEEE Transactions on Fuzzy Systems,1998,6(2):315-321.
[128]Frikha S, Djemel M, Derbel N. Observer based adaptive neuro-sliding mode control for MIMO non-linear systems[J]. International Journal of Control, Automation and Systems,2010,8(2):257-265.
[129]Wang J, Rad A B, Chan P T. Indirect adaptive fuzzy sliding mode control:Part I:fuzzy switching[J]. Fuzzy sets and systems,2001,122(1):21-30.
[130]Roopaei M, Zolghadri M, Meshksar S. Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems[J]. Communications in Nonlinear Science and Numerical Simulation,2009,14(9): 3670-3681.
[131]Aloui S, Pages O, El Hajjaji A, et al. Improved fuzzy sliding mode control for a class of MIMO nonlinear uncertain and perturbed systems[J]. Applied Soft Computing,2011,11(1):820-826.
[132]Phan P A, Gale T. Two-Mode Adaptive Fuzzy Control With Approximation Error Estimator [J]. IEEE Transactions on Fuzzy Systems,2007,15(5):943-955.
[133]Nekoukar V, Erfanian A. Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems[J]. Fuzzy Sets and Systems,2011,179(1):34-49.
[134]Faieghi M R, Delavari H, Baleanu D. A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations[J]. Communications in Nonlinear Science and Numerical Simulation, 2012,17(2):1021-1030.
[135]Chang Y C. Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and H∞ approaches[J]. IEEE Transactions on Fuzzy Systems,2001,9(2):278-292.
[136]Labiod S, Guerra T M. Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems[J]. Fuzzy sets and systems,2007,158(10):1126-1137.
[137]Driankov D, Hellendoorn H, Palm R. Some research directions in fuzzy control[C]. Theoretical aspects of fuzzy control. John Wiley and Sons, Inc.,1995:281-312.
[138]Park J H, Park G T. Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems[J]. IEE Proceedings-Control Theory and Applications,2003,150(2):189-197.
[139]Pan Y P, Zhou Y, Sun T R, et al. Composite adaptive fuzzy H∞ tracking control of uncertain nonlinear systems [J]. Neurocomputing,2013,99:15-24.
[140]Hyun C H, Park C W, Kim S. Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design[J]. Information Sciences,2010,180(11):2314-2327.
[141]Chemachema M. Output feedback direct adaptive neural network control for uncertain SISO nonlinear systems using a fuzzy estimator of the control error[J]. Neural Networks,2012,36:25-34.
[142]Boulkroune A, M'saad M. On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign[J]. Fuzzy Sets and Systems,2012,201:71-85.
[143]Liu Y J, Tong S C, Wang W, et al. Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications[J]. International Journal of Control, Automation and Systems,2009,7(4): 681-690.
[144]Wang C H, Liu H L, Lin T C. Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems[J]. IEEE Transactions on Fuzzy Systems,2002, 10(1):39-49.
[145]Tong S, Li H X, Wang W. Observer-based adaptive fuzzy control for SISO nonlinear systems[J]. Fuzzy Sets and Systems,2004,148(3):355-376.
[146]Leu Y G, Lee T T, Wang W Y. Observer-based adaptive fuzzy-neural control for unknown nonlin-ear dynamical systems[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics, 1999,29(5):583-591.
[147]Leu Y G, Wang W Y, Lee T T. Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems[J]. IEEE Transactions on Neural Networks,2005,16(4):853-861.
[148]Wang W Y, Cheng C Y, Leu Y G. An on-line GA-based output feedback direct adaptive fuzzy-neural controller for uncertain nonlinear systems [J]. IEEE Transactions on Systems Man Cybernet. Part B: Cybernet,2004,34(1):334-345.
[149]Park J H, Park G T, Kim S H, et al. Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer[J]. Fuzzy Sets and Systems,2005,151(1):21-42.
[150]Kung C C, Chen T H. Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems[J]. Fuzzy Sets and Systems,2005,155(2):292-308.
[151]Boulkroune A, Tadjine M, M'saad M, et al. How to design a fuzzy adaptive controller based on ob-servers for uncertain affine nonlinear systems[J]. Fuzzy Sets and Systems,2008,159(8):926-948.
[152]Macnab C J B. Preventing bursting in approximate-adaptive control when using local basis func-tions[J]. Fuzzy Sets and Systems,2009,160(4):439-462.
[153]Belarbi K, Chemachema M. Stable direct adaptive neural network controller with a fuzzy estimator of the control error for a class of perturbed nonlinear systems[J]. Control Theory and Applications, TET, 2007,1(5):1398-1404.
[154]Macnab C J B. Preventing bursting in approximate-adaptive control when using local basis func-tions[J]. Fuzzy Sets and Systems,2009; 160(4):439-462.
[155]Lee C. Fuzzy logic in control systems:Fuzzy logic controller, part I[J]. IEEE Transactions on Systems, Man, and Cybernetics,1990,20:404-418.
[156]Wang J, Si W, Li H. Robust ISS-satisficing variable universe indirect fuzzy control for chaotic sys-tems[J]. Chaos, Solitons and Fractals,2009,39(1):28-38.
[157]Liu Y J, Tong S C, Li T S. Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems[J]. Fuzzy Sets and Systems,2011,164(1):25-44.
[158]Purwar S, Kar I N, Jha A N. Adaptive control of robot manipulators using fuzzy logic systems under actuator constraints[J]. Fuzzy Sets and Systems,2005,152(3):651-664.
[159]Li H X, Tong S. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems[J]. IEEE Transactions on Fuzzy Systems,2003,11(1):24-34.
[160]Rojas I, Pomares H, Gonzalez J, et al. Adaptive fuzzy controller:Application to the control of the temperature of a dynamic room in real time[J]. Fuzzy Sets and Systems,2006,157(16):2241-2258.
[161]Sala A, Guerra T M, Babuska R. Perspectives of fuzzy systems and control[J]. Fuzzy Sets and Systems, 2005,156(3):432-444.
[162]Yau H T, Yan J J. Adaptive sliding mode control of a high-precision ball-screw-driven stage[J]. Non-linear Analysis:Real World Applications,2009,10(3):1480-1489.
[163]Green A, Sasiadek J Z. Heuristic design of a fuzzy controller for a flexible robot[J]. IEEE Transactions on Control Systems Technology,2006,14(2):293-300.
[164]李家炜.一种新的模糊控制器的优化方法[J].控制理论与应用,2002,9(2)：279-283.
[165]Zhang Z, Chang J. A fuzzy control algorithm with high controlling precision[J]. Fuzzy sets and sys-tems,2003,140(2):375-385.
[166]Li Y, Tong S. Adaptive fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters[J]. Neurocomputing,2011,74(10):1557-1563.
[167]李丽娜,柳洪义,罗忠,等.模糊PID复合控制算法改进及应用[J].东北大学学报：自然科学版,2009,30(2)：274-278.