状态滞后和不确定非线性系统自适应鲁棒控制
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摘要
众所周知,非线性广泛存在于客观世界,任何一个实际的动态系统都是非线性的,非线性系统已成为当前控制理论领域研究的热点和难点问题之一。同时不确定性和时滞性广泛存在于非线性系统中,并且会影响系统的稳定性。本文针对不确定因素和时滞特性对非线性系统的普遍性影响,开展鲁棒控制研究,做出了以下研究工作。
首先,论文利用偏微分变换技术、指数趋近滑模控制技术和Lyapunov稳定方法,研究了一类更广泛的不确定非线性系统的滑模控制器设计问题。提出的控制器克服了不确定性对系统的影响,确保系统在有限的时间内可以到达滑模面,并且能够有效地削弱系统抖动问题。最后通过仿真实验验证了所提出的控制方法的有效性。
其次,基于自适应控制和模糊控制理论,结合动态面控制方法,提出了一种简化的自适应模糊动态面控制器设计方法。在控制器设计过程中,仅采用一个模糊逻辑系统作为逼近器,使得所有的未知项得到补偿,同时采用自适应技术在线辨识未知参数和逼近误差上界。通过构造合适的Lyapunov函数,证明了闭环系统的所有信号为半全局最终一致有界。文中的控制方法克服了一类未知非线性时滞系统控制器设计过程中引入逼近器过多和传统Backstepping控制器设计中“复杂性膨胀”的问题。
最后,针对一类不确定非线性系统,提出了一种新的自适应模糊动态面控制器设计方案,解决了不确定非线性系统控制器设计过程中引入逼近器过多的问题。通过构造合适的Lyapunov函数,证明了闭环系统的所有信号为半全局最终一致有界。与滑模控制方法进行了比较,说明此方法的优越性。
The control problem of nonlinear systems has been the hot and difficult topic in the present control theory investigation. As we known that nonlinear systems exit in the world extensively, so it is important to investigate adaptive robust control of nonlinear systems. Based on the existing literature, some work has been done in this paper on adaptive robust control of nonlinear systems.
We first consider the design problem of robust sliding-model controller for a class of more extensive nonlinear time-delay systems. And a robust exponential approach law sliding mode control method is proposed for the system based on partial differential transformation, that can weakens the control input chattering effectively. Based on sliding control technique and Lyapunov stability method, the system can overcomes the influence of uncertainty, and the system state can be droved into a sliding-mode plane in finite time, and the system stability is also guaranteed.
Then, we focus on investigating the problem that too many approximators are used in the controller design of unknown nonlinear systems. Only one fuzzy logic system is employed as approximator to compensate all the unknown items, and at the same time, adaptive technology is adopted on line to identify the unknown parameter. The problem of explosion of complexity in backstepping design procedure is overcome by using the dynamic surface control method. It is proved by constructing appropriate Lyapunov function that all the signals of the closed-loop system are semi-globally ultimate uniformly bounded.
Finally, the problem of robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems has been investigated. Considering‘‘explosion of complexity’’in backstepping design procedure, a novel adaptive fuzzy dynamic surface model is proposed to approximate uncertain nonlinear functions by using only one fuzzy logic system. We prove the approximation capability of this model and apply it to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. It is proved by constructing appropriate Lyapunov functions that all signals of closed-loop systems are semi-globally ultimate uniform bounded. And this novel method is further investigated by comparing with the adaptive SMC (sliding mode control) method.
首先,论文利用偏微分变换技术、指数趋近滑模控制技术和Lyapunov稳定方法,研究了一类更广泛的不确定非线性系统的滑模控制器设计问题。提出的控制器克服了不确定性对系统的影响,确保系统在有限的时间内可以到达滑模面,并且能够有效地削弱系统抖动问题。最后通过仿真实验验证了所提出的控制方法的有效性。
其次,基于自适应控制和模糊控制理论,结合动态面控制方法,提出了一种简化的自适应模糊动态面控制器设计方法。在控制器设计过程中,仅采用一个模糊逻辑系统作为逼近器,使得所有的未知项得到补偿,同时采用自适应技术在线辨识未知参数和逼近误差上界。通过构造合适的Lyapunov函数,证明了闭环系统的所有信号为半全局最终一致有界。文中的控制方法克服了一类未知非线性时滞系统控制器设计过程中引入逼近器过多和传统Backstepping控制器设计中“复杂性膨胀”的问题。
最后,针对一类不确定非线性系统,提出了一种新的自适应模糊动态面控制器设计方案,解决了不确定非线性系统控制器设计过程中引入逼近器过多的问题。通过构造合适的Lyapunov函数,证明了闭环系统的所有信号为半全局最终一致有界。与滑模控制方法进行了比较,说明此方法的优越性。
The control problem of nonlinear systems has been the hot and difficult topic in the present control theory investigation. As we known that nonlinear systems exit in the world extensively, so it is important to investigate adaptive robust control of nonlinear systems. Based on the existing literature, some work has been done in this paper on adaptive robust control of nonlinear systems.
We first consider the design problem of robust sliding-model controller for a class of more extensive nonlinear time-delay systems. And a robust exponential approach law sliding mode control method is proposed for the system based on partial differential transformation, that can weakens the control input chattering effectively. Based on sliding control technique and Lyapunov stability method, the system can overcomes the influence of uncertainty, and the system state can be droved into a sliding-mode plane in finite time, and the system stability is also guaranteed.
Then, we focus on investigating the problem that too many approximators are used in the controller design of unknown nonlinear systems. Only one fuzzy logic system is employed as approximator to compensate all the unknown items, and at the same time, adaptive technology is adopted on line to identify the unknown parameter. The problem of explosion of complexity in backstepping design procedure is overcome by using the dynamic surface control method. It is proved by constructing appropriate Lyapunov function that all the signals of the closed-loop system are semi-globally ultimate uniformly bounded.
Finally, the problem of robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems has been investigated. Considering‘‘explosion of complexity’’in backstepping design procedure, a novel adaptive fuzzy dynamic surface model is proposed to approximate uncertain nonlinear functions by using only one fuzzy logic system. We prove the approximation capability of this model and apply it to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. It is proved by constructing appropriate Lyapunov functions that all signals of closed-loop systems are semi-globally ultimate uniform bounded. And this novel method is further investigated by comparing with the adaptive SMC (sliding mode control) method.
引文
1冯纯伯,费树岷.非线性控制系统分析与设计.北京:电子工业出版社, 1998
2 K. M. Zhou, J. C. Doyle. Essentials of Robust Control. New Jersey: Prentice-Hall Inc., 1998
3高为炳.非线性控制系统导论.北京:科学出版社, 1988
4 M. Vidyasagar. Nonlinear systems analysis. New York: Prentice-Hall, Inc., 1978
5 W. B. Gao. On the Absolute Stability and Stability Degree of Nonlinear Control Systems. China science, 1966, 15(1):107-122
6郑伟,徐洪,李士勇,张福恩.基于波波夫稳定判据的模糊控制器系统化设计方法.控制理论与应用, 2002, 19(4):644-646
7 J. M. Holtzman. Nonlinear Systems Theory. Prentice-hall, 1970
8 S. H. Wang, B. G. Xu, Y. H. Liu, etal. A review of the remote-control theories and methods for internet-based robots. Control theory & applications, 2008, 25(5):873-878
9 C. C. Hua, X. P. Guan, G. R. Duan. Variable structure adaptive fuzzy control for a class of nonlinear time-delay systems. Fuzzy Sets and Systems, 2004, (148):453-468
10 X. P. Guan, C. C. Hua. Synchronization of uncertain time delay chaotic systems using the adaptive fuzzy methods. Chinese Physical Letters, 2002, 19(8):1031-1034
11 Y. Hashimoto, H. S. Wu, K. Mizukami. Robust output tracking of nonlinear systems with mismatched uncertainties. International Journal of Control, 1999, 72(5):411-417
12 R. Marino, P. Tomei. Nonlinear output feedback tracking with almost disturbance decoupling. IEEE Transactions on Automatic Control, 1999, 44(1):18-28
13 Z. H. Peng, M. Wu, Z. X. Cai. I/O linearization based onμsynthesis for nonlinear robust control systems. Proceeding of 14th IFAC Conference,1999, 2:117-122
14 S. W. Su, B. D. O. Anderson, T. Brinsmead. Robust disturse suprssion for nonlinearsystems based on H∞control. Proceedings of the 33th Conference on Decision and Control, Sydney, 2000, 3013-3018
15 C. C. Hua, X. P. Guan, P. Shi, Robust stabilization of a class of nonlinear time-delay systems. Applied Mathematics and Compution, 2004, 155(3):737-752
16 J. Q. Huang, F. L. Lewis. Neural-network predictive control for nonlinear dynamic systems with time-delay. IEEE Transactions on Neural Networks, 2003, 14(2):377-389
17刘杨,郭晨,沈智鹏等.欠驱动船舶路径跟踪的神经网络稳定自适应控制.控制理论与应用, 2010,27(2):169-174
18张杰,赵峰.基于神经网络的非线性动态系统的多内模控制研究.系统仿真学报, 2008,20(18):4998-5005
19 K. S. Narendra, K. Parthasarathy. Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1990,1(1):4-27
20 X. M. Ren, A. B. Rad, P. T. Chan, W. L. Lo. Identification and control of continuous-time nonlinear systems via dynamic neural networks. IEEE Transactions on Industrial Electronics, 2003, 50(3):478-486
21王红旗,王庆林.移动机械手鲁棒自适应模糊控制.控制与决策, 2010,25(3):461-465
22尹作友,张化光.基于模糊T-S模型的非线性系统的H∞鲁棒容错控制.控制与决策, 2009,6(4):813-818
23 L. X. Wang. Stable Adaptive Fuzzy Control of Nonlinear Systems. IEEE Trans. Fuzzy Systems, 1993,1(2):146-155
24 M. Wang, B. Chen, X.P. Liu. Adaptive fuzzytracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets and Systems, 2008, 159 (8):949-967
25唐功友,逄海萍,孙慧影.不确定时滞系统的全局鲁棒最优滑模控制.控制理论与应用, 2009, 26(8):850-854
26 A. C. Huang, Y. S. Kuo. Sliding control of non-linear systems containing time-varying uncertainties with unknown bounds. International Journal of Control,2001, 74 (3):252-264
27 H. F. Chen, L. Guo. Identification and Stochastic Adaptive Control. Boston: Birkhauser, 1991
28 I. D. Landau, R. Lozano. Adaptive Control. London: Springer, 1998
29 H. C. Shu, T. Gang. On Matching Conditions for Adaptive State Tracking Control of Systems with Actuator Failures. IEEE Transactions on Automatic Control, 2002, 47(3):473-477
30 G. Tao, S. M. Joshi, X. L. Ma. Adaptive state feedback and tracking control of systems with actuator failures. IEEE Transactions on Automatic Control, 2001, 46(1):78-95
31 H. Han, C. Y. Su. Robust fuzzy control of nonlinear systems using shape adaptive radial basis functions. Fuzzy Sets and Systems, 2002, 125(1):23-38
32 S. S. Ge, C. Wang. Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica, 2002, 38(4):671-682
33 K. Zhou, J. C. Doyle, K. Glover. Robust and Optimal Control. Englewood, Clifls: Prentice-Hall, 1996
34 C. I. Byrnes, F. D. Priscoli, Isidori A. Output Regulation of Uncertain Nonlinear Systems. Boston: Birkhauser, 1997
35 P. Bolzern, P. Colaneri. Guaranteed Hin-finity robustness bounds for Wiener filtering and prediction. International Journal of Robust and Nonlinear Control, 2002, 12(1):41-56
36 D. S. Raffaella, I. Alberto. On the output regulation for linear systems in the presence of input saturation. IEEE Transactions on Automatic Control, 2001, 46(1):156-160
37 Y. C. Yong, Z. L. L, Tingshu H. Stability analysis of linear time-delay systems subject to input saturation. IEEE Transactions on Circuits and Systems I, 2002, 49(2):233-240
38 D. Liu, A. Molchanov. Criteria for robust absolute stability of time–varying nonlinear continuous-time systems. Automatica, 2002, 38(4):627-637
39 S. I. Niculescu, E. I. Verriest, L. Dugard, J. D. Dion. Stability and robust stability of time-delay systems: A guided tour. In: Stability and Control of Time-Delay Systems. Eds. London: Springer-Verlag, 1997
40 X. C. Jia, N. N. Zheng. Reliable grading robust stabilization for uncertain time-varying system Via dynamic compensater. Progress on Natural Science (Chinese), 2002, 12(9):60-67
41 V. Sampath, S. Palanki, J. C. Cockbum, J. P. Corriou. Robust controller design for temperature tracking problems in jacketed batch reactors. Journal of Process Control, 2002, 12(1):27-28
42 H. J. Uang, B. S. Chen. Robust adaptive optimal tracking design for uncertain missile systems: A fuzzy approach. Fuzzy Sets and Systems, 2002, 126(1):63-87
43 D. H. Popvic, D. J. Hill, Q. Wu. Optimal voltage security control of power systems. International Journal of Electrical power and Energy System, 2002, 24(4):305-320
44达飞鹏,宋文忠.基于模糊神经网络的滑模控制. 2000,17(1):128-132
45 Y. J. Huang, T. C. Kuo. Robust output tracking control for nonlinear time-varying robotic manipulators. Electrical Engineering, 2005, 87(1):47-55
46 J. J. E. Slotine, W. Li. Applied nonlinear control. Englewood Cliffs: Prentice-Hall, 1991
47 Y. J. Huang, T. C. Kuo. Robust position control of DC servomechanism with output measurement noise. Electrical Engineering, 2006, 88(3):223-338
48 K. Furuta. VSS type self-tuning control. IEEE Transactions on Industrial Electronics, 1993, 40(1):37-44
49 P. M. Lee, J. H. Oh. Improvements on VSS type self-tuning control for a tracking controller. IEEE Transactions on Industrial Electronics, 1998, 45(2):319-25
50 W. D. Chang, R. C. Hwang. Hsieh JG. Application of an auto-tuning neuron to sliding mode control. IEEE Trans. Syst. Man Cybern. C, 2002, 32(4):517-519
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52 H. Lee, E. Kim, H. J. Kang, M. Park. A new sliding-mode control with fuzzy boundary layer. Fuzzy Sets and Systems, 2001, 120(1):135-143
53 T. C. Kuo, Y. J. Huang, S. H. Chang. Sliding mode control with self-tuning law for uncertain nonlinear systems. ISA Transactions, 2008, 47(2):171-178
54周珊珊,董瑞,唐功友.离散时滞系统的最优滑模控制.控制与决策, 2010,25(2):299-306
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60 W. S. Chen, J. M. Li. Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans. Syst. Man Cybern. B, 2008, 38(1):258-266
61 Y. S. Fu, Z. H. Tian, S. J. Shi. Output feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatica Control, 2005, 50(6):847-851
62 D. Swaroop, J. K. Hedrick, P. P. Yip, Gerdes J C. Dynamic surface control for a class of nonlinear systems. IEEE Transactions on Automatic Control, 2000, 45(10):1893-1899
63 W. C. H. Daniel, J. M. Li, Y. G. Niu. Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Transactions on Neural Networks, 2005, 16(3):625-635
64 D. Wang, J. Huang. Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Transactions on Neural Networks, 2005, 16(1):195-202
65 C. C. Hua, X. P. Guan, P. Shi. Robust backstepping control for a class of time delay systems. IEEE Transactions on Automatic Control, 2005, 50(6):894-899
66 W. S. Chen, J. M. Li. Adaptive output-feedback regulation for nonlinear delayed systems using neural network. International Journal of Automation and Computing, 2008, 5(1):103-108
67 J. Y. Sung, B. P. Jin, H. C. Yoon. Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays. IEEE Transactions on Automatic Control, 2007, 52(12):2360-2365
68 I. Kanellakopoulos, P. V. Kokotovic, R. Marino. An extended direct scheme for robust adaptive nonlinear control. Automatic, 1991, 27(2):247-255
69 M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design. New York: Wiley, 1995
70 Z. P. Jiang, D. J. Hill. A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics. IEEE Trans. Automat. Contr., 1999, 44(9):1705-1711
71 M. Wang, B. Chen, P. Shi. Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems. IEEE Trans. Syst. Man Cybern. B Cybern, 2008, 38(3):721-30
72 H.F. Ho, Y.K. Wong, A.B. Rad. Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form. ISA Trans., 2008, 47(3):286-299
2 K. M. Zhou, J. C. Doyle. Essentials of Robust Control. New Jersey: Prentice-Hall Inc., 1998
3高为炳.非线性控制系统导论.北京:科学出版社, 1988
4 M. Vidyasagar. Nonlinear systems analysis. New York: Prentice-Hall, Inc., 1978
5 W. B. Gao. On the Absolute Stability and Stability Degree of Nonlinear Control Systems. China science, 1966, 15(1):107-122
6郑伟,徐洪,李士勇,张福恩.基于波波夫稳定判据的模糊控制器系统化设计方法.控制理论与应用, 2002, 19(4):644-646
7 J. M. Holtzman. Nonlinear Systems Theory. Prentice-hall, 1970
8 S. H. Wang, B. G. Xu, Y. H. Liu, etal. A review of the remote-control theories and methods for internet-based robots. Control theory & applications, 2008, 25(5):873-878
9 C. C. Hua, X. P. Guan, G. R. Duan. Variable structure adaptive fuzzy control for a class of nonlinear time-delay systems. Fuzzy Sets and Systems, 2004, (148):453-468
10 X. P. Guan, C. C. Hua. Synchronization of uncertain time delay chaotic systems using the adaptive fuzzy methods. Chinese Physical Letters, 2002, 19(8):1031-1034
11 Y. Hashimoto, H. S. Wu, K. Mizukami. Robust output tracking of nonlinear systems with mismatched uncertainties. International Journal of Control, 1999, 72(5):411-417
12 R. Marino, P. Tomei. Nonlinear output feedback tracking with almost disturbance decoupling. IEEE Transactions on Automatic Control, 1999, 44(1):18-28
13 Z. H. Peng, M. Wu, Z. X. Cai. I/O linearization based onμsynthesis for nonlinear robust control systems. Proceeding of 14th IFAC Conference,1999, 2:117-122
14 S. W. Su, B. D. O. Anderson, T. Brinsmead. Robust disturse suprssion for nonlinearsystems based on H∞control. Proceedings of the 33th Conference on Decision and Control, Sydney, 2000, 3013-3018
15 C. C. Hua, X. P. Guan, P. Shi, Robust stabilization of a class of nonlinear time-delay systems. Applied Mathematics and Compution, 2004, 155(3):737-752
16 J. Q. Huang, F. L. Lewis. Neural-network predictive control for nonlinear dynamic systems with time-delay. IEEE Transactions on Neural Networks, 2003, 14(2):377-389
17刘杨,郭晨,沈智鹏等.欠驱动船舶路径跟踪的神经网络稳定自适应控制.控制理论与应用, 2010,27(2):169-174
18张杰,赵峰.基于神经网络的非线性动态系统的多内模控制研究.系统仿真学报, 2008,20(18):4998-5005
19 K. S. Narendra, K. Parthasarathy. Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1990,1(1):4-27
20 X. M. Ren, A. B. Rad, P. T. Chan, W. L. Lo. Identification and control of continuous-time nonlinear systems via dynamic neural networks. IEEE Transactions on Industrial Electronics, 2003, 50(3):478-486
21王红旗,王庆林.移动机械手鲁棒自适应模糊控制.控制与决策, 2010,25(3):461-465
22尹作友,张化光.基于模糊T-S模型的非线性系统的H∞鲁棒容错控制.控制与决策, 2009,6(4):813-818
23 L. X. Wang. Stable Adaptive Fuzzy Control of Nonlinear Systems. IEEE Trans. Fuzzy Systems, 1993,1(2):146-155
24 M. Wang, B. Chen, X.P. Liu. Adaptive fuzzytracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets and Systems, 2008, 159 (8):949-967
25唐功友,逄海萍,孙慧影.不确定时滞系统的全局鲁棒最优滑模控制.控制理论与应用, 2009, 26(8):850-854
26 A. C. Huang, Y. S. Kuo. Sliding control of non-linear systems containing time-varying uncertainties with unknown bounds. International Journal of Control,2001, 74 (3):252-264
27 H. F. Chen, L. Guo. Identification and Stochastic Adaptive Control. Boston: Birkhauser, 1991
28 I. D. Landau, R. Lozano. Adaptive Control. London: Springer, 1998
29 H. C. Shu, T. Gang. On Matching Conditions for Adaptive State Tracking Control of Systems with Actuator Failures. IEEE Transactions on Automatic Control, 2002, 47(3):473-477
30 G. Tao, S. M. Joshi, X. L. Ma. Adaptive state feedback and tracking control of systems with actuator failures. IEEE Transactions on Automatic Control, 2001, 46(1):78-95
31 H. Han, C. Y. Su. Robust fuzzy control of nonlinear systems using shape adaptive radial basis functions. Fuzzy Sets and Systems, 2002, 125(1):23-38
32 S. S. Ge, C. Wang. Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica, 2002, 38(4):671-682
33 K. Zhou, J. C. Doyle, K. Glover. Robust and Optimal Control. Englewood, Clifls: Prentice-Hall, 1996
34 C. I. Byrnes, F. D. Priscoli, Isidori A. Output Regulation of Uncertain Nonlinear Systems. Boston: Birkhauser, 1997
35 P. Bolzern, P. Colaneri. Guaranteed Hin-finity robustness bounds for Wiener filtering and prediction. International Journal of Robust and Nonlinear Control, 2002, 12(1):41-56
36 D. S. Raffaella, I. Alberto. On the output regulation for linear systems in the presence of input saturation. IEEE Transactions on Automatic Control, 2001, 46(1):156-160
37 Y. C. Yong, Z. L. L, Tingshu H. Stability analysis of linear time-delay systems subject to input saturation. IEEE Transactions on Circuits and Systems I, 2002, 49(2):233-240
38 D. Liu, A. Molchanov. Criteria for robust absolute stability of time–varying nonlinear continuous-time systems. Automatica, 2002, 38(4):627-637
39 S. I. Niculescu, E. I. Verriest, L. Dugard, J. D. Dion. Stability and robust stability of time-delay systems: A guided tour. In: Stability and Control of Time-Delay Systems. Eds. London: Springer-Verlag, 1997
40 X. C. Jia, N. N. Zheng. Reliable grading robust stabilization for uncertain time-varying system Via dynamic compensater. Progress on Natural Science (Chinese), 2002, 12(9):60-67
41 V. Sampath, S. Palanki, J. C. Cockbum, J. P. Corriou. Robust controller design for temperature tracking problems in jacketed batch reactors. Journal of Process Control, 2002, 12(1):27-28
42 H. J. Uang, B. S. Chen. Robust adaptive optimal tracking design for uncertain missile systems: A fuzzy approach. Fuzzy Sets and Systems, 2002, 126(1):63-87
43 D. H. Popvic, D. J. Hill, Q. Wu. Optimal voltage security control of power systems. International Journal of Electrical power and Energy System, 2002, 24(4):305-320
44达飞鹏,宋文忠.基于模糊神经网络的滑模控制. 2000,17(1):128-132
45 Y. J. Huang, T. C. Kuo. Robust output tracking control for nonlinear time-varying robotic manipulators. Electrical Engineering, 2005, 87(1):47-55
46 J. J. E. Slotine, W. Li. Applied nonlinear control. Englewood Cliffs: Prentice-Hall, 1991
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