一类非线性时滞系统的自适应控制器设计
|
摘要
严格来说,实际控制系统都是非线性的,并具有不确定性,如参数摄动、未建模动态或外部干扰等。因此,系统的期望性能可能会被破坏。此外,时滞的存在使非线性系统的控制分析和设计问题变得更加复杂和困难。所以,研究带有不确定性的非线性时滞系统具有重要的理论和实践意义。
对于非线性时滞系统的稳定性分析和控制器设计,一种有效的方法是基于Lyapunov-Krasovskii泛函法。本论文为补偿未知时滞项的影响,用Lyapunov-Krasovskii泛函构造候选Lyapunov函数。针对一类带有不确定性的状态滞后的非线性系统,设计了能够保证闭环系统稳定的鲁棒自适应控制器。在控制器设计过程中应用Lyapunov稳定性理论来证明闭环系统的稳定性。
针对一类带有未知时滞项、未知参数和未知非线性函数的严格反馈非线性系统,通过结合反步设计方法和鲁棒控制策略,设计了一种鲁棒自适应控制器。通过引入一种合适的偶函数,解决了控制器的奇异性问题。证明了所提出的设计方法能保证闭环系统的所有信号是全局一致最终有界的,并且跟踪误差信号将收敛于原点的一个小邻域内。仿真实例说明了控制器的有效性。
针对一类带有未知非线性函数的严格反馈非线性时滞系统,设计了一种自适应神经网络控制器。本论文选择径向基函数神经网络逼近未知的非线性函数。所提出的控制方案能保证闭环系统的所有信号是全局一致最终有界的。证明了跟踪误差信号将收敛于一个小紧集内。仿真实例验证了所提出方法的有效性。
针对同一个二阶系统,在相同条件下对鲁棒自适应控制器和基于径向基函数神经网络的自适应控制器进行比较。仿真实例表明基于径向基函数神经网络设计的自适应控制器具有较好的控制特性。
Strictly speaking, practical control systems are nonlinear, and always have uncertainties such as parameters perturbation, unmodeled dynamics or external disturbances, etc. So the system specified performance may be damaged. In addition, the existence of time delays may make the control analysis and design of nonlinear systems more complex and difficult. Therefore, the study of nonlinear time-delay systems with uncertainties has an important theoretical and practical significance.
For the stability analysis and controller design of nonlinear time-delay systems, an effective method is based on the Lyapunov-Krasovskii functionals. In this thesis, Lyapunov-Krasovskii functionals were used to construct the Lyapunov function candidates such that the uncertainties from unknown time delays were compensated for. Robust adaptive controllers were designed for a class of uncertain nonlinear systems with delays in the state, which can guarantee the stability of the closed-loop systems. To prove the stability of the closed-loop systems, Lyapunov’s stability theory was applied in the controller design.
By combining backstepping design procedure with robust control strategy, a robust adaptive controller was proposed for a class of strict-feedback nonlinear systems with both unknown time delays and uncertainties from unknown parameters and nonlinear functions. Controller singularity problems were avoided by introducing an appropriate even function. It was proven that the proposed design procedure was able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems. The tracking error was shown to converge to a small neighborhood of the origin. A simulation example was provided to illustrate the validity of the proposed controller.
An adaptive neural network controller was presented for a class of strict-feedback nonlinear time-delay systems with unknown nonlinear functions. A radial basis function neural network was chosen to approximate the unknown nonlinear functions in this thesis. The developed control scheme was able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems. The tracking error was proven to converge to a small compact set. A simulation example was provided to illustrate the effectiveness of the proposed approach.
For the same second-order system, a robust adaptive controller was compared with an adaptive controller based on radial basis function neural network under the same conditions. Simulation results were provided to show the proposed neural network adaptive controller has well control behavior.
对于非线性时滞系统的稳定性分析和控制器设计,一种有效的方法是基于Lyapunov-Krasovskii泛函法。本论文为补偿未知时滞项的影响,用Lyapunov-Krasovskii泛函构造候选Lyapunov函数。针对一类带有不确定性的状态滞后的非线性系统,设计了能够保证闭环系统稳定的鲁棒自适应控制器。在控制器设计过程中应用Lyapunov稳定性理论来证明闭环系统的稳定性。
针对一类带有未知时滞项、未知参数和未知非线性函数的严格反馈非线性系统,通过结合反步设计方法和鲁棒控制策略,设计了一种鲁棒自适应控制器。通过引入一种合适的偶函数,解决了控制器的奇异性问题。证明了所提出的设计方法能保证闭环系统的所有信号是全局一致最终有界的,并且跟踪误差信号将收敛于原点的一个小邻域内。仿真实例说明了控制器的有效性。
针对一类带有未知非线性函数的严格反馈非线性时滞系统,设计了一种自适应神经网络控制器。本论文选择径向基函数神经网络逼近未知的非线性函数。所提出的控制方案能保证闭环系统的所有信号是全局一致最终有界的。证明了跟踪误差信号将收敛于一个小紧集内。仿真实例验证了所提出方法的有效性。
针对同一个二阶系统,在相同条件下对鲁棒自适应控制器和基于径向基函数神经网络的自适应控制器进行比较。仿真实例表明基于径向基函数神经网络设计的自适应控制器具有较好的控制特性。
Strictly speaking, practical control systems are nonlinear, and always have uncertainties such as parameters perturbation, unmodeled dynamics or external disturbances, etc. So the system specified performance may be damaged. In addition, the existence of time delays may make the control analysis and design of nonlinear systems more complex and difficult. Therefore, the study of nonlinear time-delay systems with uncertainties has an important theoretical and practical significance.
For the stability analysis and controller design of nonlinear time-delay systems, an effective method is based on the Lyapunov-Krasovskii functionals. In this thesis, Lyapunov-Krasovskii functionals were used to construct the Lyapunov function candidates such that the uncertainties from unknown time delays were compensated for. Robust adaptive controllers were designed for a class of uncertain nonlinear systems with delays in the state, which can guarantee the stability of the closed-loop systems. To prove the stability of the closed-loop systems, Lyapunov’s stability theory was applied in the controller design.
By combining backstepping design procedure with robust control strategy, a robust adaptive controller was proposed for a class of strict-feedback nonlinear systems with both unknown time delays and uncertainties from unknown parameters and nonlinear functions. Controller singularity problems were avoided by introducing an appropriate even function. It was proven that the proposed design procedure was able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems. The tracking error was shown to converge to a small neighborhood of the origin. A simulation example was provided to illustrate the validity of the proposed controller.
An adaptive neural network controller was presented for a class of strict-feedback nonlinear time-delay systems with unknown nonlinear functions. A radial basis function neural network was chosen to approximate the unknown nonlinear functions in this thesis. The developed control scheme was able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems. The tracking error was proven to converge to a small compact set. A simulation example was provided to illustrate the effectiveness of the proposed approach.
For the same second-order system, a robust adaptive controller was compared with an adaptive controller based on radial basis function neural network under the same conditions. Simulation results were provided to show the proposed neural network adaptive controller has well control behavior.
引文
[1]刘兴堂.应用自适应控制[M].西安:西北工业大学出版社, 2003
[2]陈新海,李言俊,周军.自适应控制及应用[M].西安:西北工业大学出版社, 1998
[3] Whitaker H. P., Yamron J., Kezer A. Design of Model Reference Adaptive Control Systems for Aircraft Report-164[R]. Cambridge: Instrumentation Lab, MIT, 1958
[4] Parks P. C. Lyapunov Redesign of Model Reference Adaptive Control Systems[J]. IEEE Trans. Automatic Control, 1966, 11: 362-367
[5] Landau I. D. A Hyperstability for Model Reference Adaptive Control Systems[J]. IEEE Trans. Automatic Control, 1969, 14: 552-555
[6] Narendra K. S., Annaswamy A. M. Stable Adaptive Systems[M]. New York: Prentice Hall, 1989
[7] Ioannou P A., Sun Jing. Robust Adaptive Control[M]. New York: Prentice Hall, 1995
[8]董文瀚,孙秀霞,林岩.反推自适应控制的发展及应用[J].控制与决策, 2006, 21(10): 1081-1102
[9]胡跃明.非线性控制系统理论与应用[M].北京:国防工业出版社, 2002
[10] Kanellakopoulos I., Kokotovic P. V., et al. Systematic Design of Adaptive Controllers for Feedback Linearizable Systems[J]. IEEE trans. Automat. Control, 1991, 36(11): 1241-1253
[11] Taylor D. G., Kokotovic P. V., Marino R., Kanellakopoulos I. Adaptive Regulation of Nonlinear Systems with Unmodeled Dynamics[J]. IEEE Trans. Automatic Control, 1989, 34: 405-412
[12] Kanellakopoulos I., Kokotovic P. V., Marino R. An Extended Direct Scheme for Robust Adaptive Nonlinear Control[J]. Automatica, 1991, 27(2): 247-255
[13] Sastry S. S., Isidari A. Adaptive Control of Linearizable Systems[J]. IEEE Trans. Automatic Control, 1989, 34(11): 1123-1131
[14] Krstic M., Kanellakopoulos I., Kokotovic P. V. Adaptive Nonlinear Control without Overparametrization[J]. System and Control Letters, 1992, 19(3): 177-185
[15] Krstic M., Kanellakopoulos I., Kokotovic P .V. Nonlinear and Adaptive Control Design[M]. New York: Wiley, 1995
[16]陈为胜.非线性时滞系统自适应神经网络迭代学习控制[D].西安:西安电子科技大学, 2004
[17] P. Pepe. Some Results on Adaptive Tracking for a Class of Nonlinear Time Delay Systems [C]. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, 2001: 997–1002
[18] Nguang S. K. Robust Stabilization of Time-Delay Nonlinear Systems[J]. IEEE Trans. Automat. Contr., 2000, 45(4): 756-761
[19] Fu Y., Tian Z., Shi S. State Feedback Stabilization for a Class of Stochastic Time-Delay Nonlinear Systems[J]. IEEE Trans. Automat. Contr., 2003, 48(2): 282-286
[20] Zhou Shaosheng, Feng Gang, Nguang S. K. Comments on“Robust Stabilization of Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2002, 47(9): 1586
[21] Li Guangwei, Zang Chuanzhi, Liu Xiaoping. Comments on“Robust Stabilization of Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2003, 48(5): 908
[22] Guan Xinping, Hua Changchun, Duan Guangren. Comments on“Robust Stabilization of Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2003, 48(5): 907-908
[23] Hua C., Guan X. Comments on“State Feedback Stabilization for a Class of Stochastic Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2004, 49(7): 1216
[24]杨青.非线性预测控制器设计及其应用[D].东营:中国石油大学(华东), 2006
[25] Yesidirek A., Lewis F. L. Feedback Linearization Using Neural Networks[J]. Automatica, 1995, 31: 1659-1664
[26] Fabri S., Kadirkananathan V. Dynamic Structure Neural Networks for Stable Adaptive Control of Nonlinear Systems[J]. IEEE Trans. Neural Networks, 1996, 7: 1151-1167
[27] Ge S. S., Hang C. C., Zhang T. Nonlinear Adaptive Control Using Neural Networks and Its Application to CSTR Systems[J]. Journal of Process Control, 1998, 9: 313-323
[28] Ge S. S., Hang C. C., Zhang T. Adaptive Neural Network Control of Nonlinear Systems by State and Output Feedback[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B Cybernetics, 1999, 29(6): 818-828
[29] Ge S. S., Hang C. C., Zhang T. A Direct Method for Robust Adaptive Nonlinear Control with Guaranteed Transient Performance[J]. Systems and Control Letters, 1999,37: 275-284
[30] Zhang T., Ge S. S., Hang C. C. Design and Performance Analysis of a Direct Adaptive Controller for Nonlinear Systems[J]. Automatica, 1999, 35: 1809-1817
[31] Zhang T., Ge S. S., Hang C. C. Stable Adaptive Control for a Class of Nonlinear Systems Using a Modified Lyapunov Functions[J]. IEEE Transactions on Automatic Control, 2000, 45(3): 125-132
[32] Polycarpou M. M. Stable Adaptive Neural Control Scheme for Nonlinear Systems[J]. IEEE Trans. Automat. Control, 1996, 41(3): 447-451
[33] Polycarpou M. M., Mears M. J. Stable Adaptive Tracking of Uncertainty Systems Using Nonlinearly Parameterized On-line Approximators[J]. International Journal of Control, 1998, 70(3): 363-384
[34] Wang W. Y., Chan M. L. Adaptive Fuzzy Control for Strict-feedback Canonical Nonlinear Systems with H∞Tracking Performance[J]. IEEE Sys. M. C-Part B, 2000, 30(6): 878-885
[35] Zhang T., Ge S. S., Hang C. C. Adaptive Neural Network Control for Strict-feedback Nonlinear Systems Using Backstepping Design[J]. Automatica, 2000, 36: 1835-1846
[36] Ge S. S., Wang Cong. Direct Adaptive NN Control of a Class of Nonlinear Systems[J]. IEEE Trans. Neural Networks, 2002, 13(1): 214-221
[37] Ge S. S., Wang Jing. Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems[J]. IEEE Transactions Neural Networks, 2002, 13(6): 1409-1419
[38] Ge S. S., Li G. Y., Lee T. H. Adaptive NN Control for a Class of Strict-feedback Discrete-time Nonlinear Systems[J]. Automatica, 2003, 39: 807-819
[39] Choi Jin Young, Farrell Jay A. Adaptive Observer Backstepping Control Using Neural Networks[J]. IEEE Trans. Neural Networks, 2001, 12(5): 1103-1112
[40] Stoev Julian, Choi Jin Young, Farrell Jay A. Adaptive Control for Output Feedback Nonlinear Systems in the Presence of Modeling Errors[J]. Automatica, 2002, 38: 1761-1767
[41] Ge S. S., Hong F., Lee T. H. Adaptive Neural Network Control of Nonlinear Systems with Unknown Time Delays[J]. IEEE Transactions on Automatic. Control, 2003,48(11): 2004–2010
[42] Ge S. S., Hong F., Lee T. H. Adaptive Neural Control of Nonlinear Time-Delay Systems with Unknown Virtual Control Coefficients[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(1): 499-516
[43] Daniel W. C. Ho, Li Junmin, Niu Yugang. Adaptive Neural Control for a Class of Nonlinearly Parametric Time-Delay Systems[J]. IEEE Trans. Neural Networks, 2005, 16(3): 625-635
[44]薛秀莉,杨青,李树荣.基于RBFNN的时滞非线性系统自适应控制器设计[C].第二十五届中国控制会议,哈尔滨, 2006: 1118-1122
[45] Li Shurong, Xue Xiuli, Yang Qing. Adaptive NN-based Controller Design for a Class of Time-delay Nonlinear Systems[C]. 2nd IEEE Conference on Industrial Electronic and Application, Harbin, 2007: 994-999
[46] Jankovic M. Control Lyapunov-Razumikhin Functions and Robust Stabilization of Time Delay Systems[J]. IEEE Trans. Automat. Control, 2001, 46(7): 1048-1060
[47]李树荣,薛秀莉,杨青.一类自适应神经网络控制器的设计[J].石油大学学报(自然科学版), 2008; 32(1): 138-142
[48] Zhang T., Ge S. S., Hang C. C., Chai T. Y. Adaptive Control of First-Order Systems with Nonlinear Parameterization[J]. IEEE Trans. Automat. Control, 2000, 45(8): 1512-1516
[49] Ge S. S., Hong F., Lee T. H. Robust Adaptive Control of Nonlinear Systems with Unknown Time Delays[J]. Automatica, 2005, 41: 1181-1190
[50] Ye Xudong, Jiang Jingping. Adaptive Nonlinear Design without a Priori Knowledge of Control Directions[J]. IEEE Trans. Automat. Control, 1998, 43(11): 1617-1621
[51]陈刚.不确定非线性系统的鲁棒自适应控制研究[D].杭州:浙江大学, 2006
[52] Ye X., Ding Z. Robust Tracking Control of Uncertain Nonlinear Systems with Unknown Control Directions[J]. System and Control Letters, 2001, 42(1): 1-10
[53] Ding Z. Adaptive Control of Nonlinear Systems with Unknown Virtual Control Coefficients[J]. International Journal of Adaptive Control Signal Processing, 2000, 14(5): 505-510
[54] Du Hongbin, Shao Huihe, Yao Pingjing. Adaptive Neural Network Control for a Classof Low-Triangular-Structured Nonlinear Systems[J]. IEEE Trans. Neural Networks, 2006, 17(2): 509-514
[55] Polycarpou M. M., Ioannou P. A. A Robust Adaptive Nonlinear Control Design[J]. Automatica, 1996, 32(3): 423-427
[56]龚怀云,寿纪麟,王绵森.应用泛函分析[M].西安:西安交通大学出版社, 1985
[57]李广民,刘三阳.应用泛函分析原理[M].西安:西安电子科技大学出版社, 2003
[58]丁晓庆.工科数学分析[M].北京:科学出版社, 2002
[59]罗家洪.矩阵分析引论[M].广州:华南理工大学出版社, 2000
[60]郭淑会.基于神经网络的一类非仿射非线性系统自适应控制[D].东营:中国石油大学(华东), 2005
[61]张愿章. Young不等式的证明及应用[J].河南科学, 2004, 22(1): 23-29
[62]邢家省,苏克勤,陶鹏飞. Young不等式与Young逆不等式的应用[J].周口师范学院学报, 2007, 24(2): 37-39
[63]郑大钟.线性系统理论[M].北京:清华大学出版社, 2002
[64]高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社, 2003
[2]陈新海,李言俊,周军.自适应控制及应用[M].西安:西北工业大学出版社, 1998
[3] Whitaker H. P., Yamron J., Kezer A. Design of Model Reference Adaptive Control Systems for Aircraft Report-164[R]. Cambridge: Instrumentation Lab, MIT, 1958
[4] Parks P. C. Lyapunov Redesign of Model Reference Adaptive Control Systems[J]. IEEE Trans. Automatic Control, 1966, 11: 362-367
[5] Landau I. D. A Hyperstability for Model Reference Adaptive Control Systems[J]. IEEE Trans. Automatic Control, 1969, 14: 552-555
[6] Narendra K. S., Annaswamy A. M. Stable Adaptive Systems[M]. New York: Prentice Hall, 1989
[7] Ioannou P A., Sun Jing. Robust Adaptive Control[M]. New York: Prentice Hall, 1995
[8]董文瀚,孙秀霞,林岩.反推自适应控制的发展及应用[J].控制与决策, 2006, 21(10): 1081-1102
[9]胡跃明.非线性控制系统理论与应用[M].北京:国防工业出版社, 2002
[10] Kanellakopoulos I., Kokotovic P. V., et al. Systematic Design of Adaptive Controllers for Feedback Linearizable Systems[J]. IEEE trans. Automat. Control, 1991, 36(11): 1241-1253
[11] Taylor D. G., Kokotovic P. V., Marino R., Kanellakopoulos I. Adaptive Regulation of Nonlinear Systems with Unmodeled Dynamics[J]. IEEE Trans. Automatic Control, 1989, 34: 405-412
[12] Kanellakopoulos I., Kokotovic P. V., Marino R. An Extended Direct Scheme for Robust Adaptive Nonlinear Control[J]. Automatica, 1991, 27(2): 247-255
[13] Sastry S. S., Isidari A. Adaptive Control of Linearizable Systems[J]. IEEE Trans. Automatic Control, 1989, 34(11): 1123-1131
[14] Krstic M., Kanellakopoulos I., Kokotovic P. V. Adaptive Nonlinear Control without Overparametrization[J]. System and Control Letters, 1992, 19(3): 177-185
[15] Krstic M., Kanellakopoulos I., Kokotovic P .V. Nonlinear and Adaptive Control Design[M]. New York: Wiley, 1995
[16]陈为胜.非线性时滞系统自适应神经网络迭代学习控制[D].西安:西安电子科技大学, 2004
[17] P. Pepe. Some Results on Adaptive Tracking for a Class of Nonlinear Time Delay Systems [C]. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, 2001: 997–1002
[18] Nguang S. K. Robust Stabilization of Time-Delay Nonlinear Systems[J]. IEEE Trans. Automat. Contr., 2000, 45(4): 756-761
[19] Fu Y., Tian Z., Shi S. State Feedback Stabilization for a Class of Stochastic Time-Delay Nonlinear Systems[J]. IEEE Trans. Automat. Contr., 2003, 48(2): 282-286
[20] Zhou Shaosheng, Feng Gang, Nguang S. K. Comments on“Robust Stabilization of Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2002, 47(9): 1586
[21] Li Guangwei, Zang Chuanzhi, Liu Xiaoping. Comments on“Robust Stabilization of Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2003, 48(5): 908
[22] Guan Xinping, Hua Changchun, Duan Guangren. Comments on“Robust Stabilization of Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2003, 48(5): 907-908
[23] Hua C., Guan X. Comments on“State Feedback Stabilization for a Class of Stochastic Time-Delay Nonlinear Systems”[J]. IEEE Trans. Automat. Contr., 2004, 49(7): 1216
[24]杨青.非线性预测控制器设计及其应用[D].东营:中国石油大学(华东), 2006
[25] Yesidirek A., Lewis F. L. Feedback Linearization Using Neural Networks[J]. Automatica, 1995, 31: 1659-1664
[26] Fabri S., Kadirkananathan V. Dynamic Structure Neural Networks for Stable Adaptive Control of Nonlinear Systems[J]. IEEE Trans. Neural Networks, 1996, 7: 1151-1167
[27] Ge S. S., Hang C. C., Zhang T. Nonlinear Adaptive Control Using Neural Networks and Its Application to CSTR Systems[J]. Journal of Process Control, 1998, 9: 313-323
[28] Ge S. S., Hang C. C., Zhang T. Adaptive Neural Network Control of Nonlinear Systems by State and Output Feedback[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B Cybernetics, 1999, 29(6): 818-828
[29] Ge S. S., Hang C. C., Zhang T. A Direct Method for Robust Adaptive Nonlinear Control with Guaranteed Transient Performance[J]. Systems and Control Letters, 1999,37: 275-284
[30] Zhang T., Ge S. S., Hang C. C. Design and Performance Analysis of a Direct Adaptive Controller for Nonlinear Systems[J]. Automatica, 1999, 35: 1809-1817
[31] Zhang T., Ge S. S., Hang C. C. Stable Adaptive Control for a Class of Nonlinear Systems Using a Modified Lyapunov Functions[J]. IEEE Transactions on Automatic Control, 2000, 45(3): 125-132
[32] Polycarpou M. M. Stable Adaptive Neural Control Scheme for Nonlinear Systems[J]. IEEE Trans. Automat. Control, 1996, 41(3): 447-451
[33] Polycarpou M. M., Mears M. J. Stable Adaptive Tracking of Uncertainty Systems Using Nonlinearly Parameterized On-line Approximators[J]. International Journal of Control, 1998, 70(3): 363-384
[34] Wang W. Y., Chan M. L. Adaptive Fuzzy Control for Strict-feedback Canonical Nonlinear Systems with H∞Tracking Performance[J]. IEEE Sys. M. C-Part B, 2000, 30(6): 878-885
[35] Zhang T., Ge S. S., Hang C. C. Adaptive Neural Network Control for Strict-feedback Nonlinear Systems Using Backstepping Design[J]. Automatica, 2000, 36: 1835-1846
[36] Ge S. S., Wang Cong. Direct Adaptive NN Control of a Class of Nonlinear Systems[J]. IEEE Trans. Neural Networks, 2002, 13(1): 214-221
[37] Ge S. S., Wang Jing. Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems[J]. IEEE Transactions Neural Networks, 2002, 13(6): 1409-1419
[38] Ge S. S., Li G. Y., Lee T. H. Adaptive NN Control for a Class of Strict-feedback Discrete-time Nonlinear Systems[J]. Automatica, 2003, 39: 807-819
[39] Choi Jin Young, Farrell Jay A. Adaptive Observer Backstepping Control Using Neural Networks[J]. IEEE Trans. Neural Networks, 2001, 12(5): 1103-1112
[40] Stoev Julian, Choi Jin Young, Farrell Jay A. Adaptive Control for Output Feedback Nonlinear Systems in the Presence of Modeling Errors[J]. Automatica, 2002, 38: 1761-1767
[41] Ge S. S., Hong F., Lee T. H. Adaptive Neural Network Control of Nonlinear Systems with Unknown Time Delays[J]. IEEE Transactions on Automatic. Control, 2003,48(11): 2004–2010
[42] Ge S. S., Hong F., Lee T. H. Adaptive Neural Control of Nonlinear Time-Delay Systems with Unknown Virtual Control Coefficients[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(1): 499-516
[43] Daniel W. C. Ho, Li Junmin, Niu Yugang. Adaptive Neural Control for a Class of Nonlinearly Parametric Time-Delay Systems[J]. IEEE Trans. Neural Networks, 2005, 16(3): 625-635
[44]薛秀莉,杨青,李树荣.基于RBFNN的时滞非线性系统自适应控制器设计[C].第二十五届中国控制会议,哈尔滨, 2006: 1118-1122
[45] Li Shurong, Xue Xiuli, Yang Qing. Adaptive NN-based Controller Design for a Class of Time-delay Nonlinear Systems[C]. 2nd IEEE Conference on Industrial Electronic and Application, Harbin, 2007: 994-999
[46] Jankovic M. Control Lyapunov-Razumikhin Functions and Robust Stabilization of Time Delay Systems[J]. IEEE Trans. Automat. Control, 2001, 46(7): 1048-1060
[47]李树荣,薛秀莉,杨青.一类自适应神经网络控制器的设计[J].石油大学学报(自然科学版), 2008; 32(1): 138-142
[48] Zhang T., Ge S. S., Hang C. C., Chai T. Y. Adaptive Control of First-Order Systems with Nonlinear Parameterization[J]. IEEE Trans. Automat. Control, 2000, 45(8): 1512-1516
[49] Ge S. S., Hong F., Lee T. H. Robust Adaptive Control of Nonlinear Systems with Unknown Time Delays[J]. Automatica, 2005, 41: 1181-1190
[50] Ye Xudong, Jiang Jingping. Adaptive Nonlinear Design without a Priori Knowledge of Control Directions[J]. IEEE Trans. Automat. Control, 1998, 43(11): 1617-1621
[51]陈刚.不确定非线性系统的鲁棒自适应控制研究[D].杭州:浙江大学, 2006
[52] Ye X., Ding Z. Robust Tracking Control of Uncertain Nonlinear Systems with Unknown Control Directions[J]. System and Control Letters, 2001, 42(1): 1-10
[53] Ding Z. Adaptive Control of Nonlinear Systems with Unknown Virtual Control Coefficients[J]. International Journal of Adaptive Control Signal Processing, 2000, 14(5): 505-510
[54] Du Hongbin, Shao Huihe, Yao Pingjing. Adaptive Neural Network Control for a Classof Low-Triangular-Structured Nonlinear Systems[J]. IEEE Trans. Neural Networks, 2006, 17(2): 509-514
[55] Polycarpou M. M., Ioannou P. A. A Robust Adaptive Nonlinear Control Design[J]. Automatica, 1996, 32(3): 423-427
[56]龚怀云,寿纪麟,王绵森.应用泛函分析[M].西安:西安交通大学出版社, 1985
[57]李广民,刘三阳.应用泛函分析原理[M].西安:西安电子科技大学出版社, 2003
[58]丁晓庆.工科数学分析[M].北京:科学出版社, 2002
[59]罗家洪.矩阵分析引论[M].广州:华南理工大学出版社, 2000
[60]郭淑会.基于神经网络的一类非仿射非线性系统自适应控制[D].东营:中国石油大学(华东), 2005
[61]张愿章. Young不等式的证明及应用[J].河南科学, 2004, 22(1): 23-29
[62]邢家省,苏克勤,陶鹏飞. Young不等式与Young逆不等式的应用[J].周口师范学院学报, 2007, 24(2): 37-39
[63]郑大钟.线性系统理论[M].北京:清华大学出版社, 2002
[64]高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社, 2003