Adaptive Control Based on Neural Networks for an Uncertain 2-DOF Helicopter System With Input Deadzone and Output Constraints
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摘要
In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter.
In this paper, a study of control for an uncertain 2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter.
In this paper, a study of control for an uncertain 2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter.
引文
[1] W. Gao and Z. P. Jiang,"Data-driven adaptive optimal output-feedback control of a 2-dof helicopter,"in Proc. American Control Conf., pp. 2512-2517, 2016.
[2] F. Wang and Y. Gao,"On frequency sensitivity and mode orthogonality of flexible robotic manipulators,"IEEE/CAA J. Autom. Sinica, vol. 3,no. 5, pp. 394-397, Oct. 2016.
[3] N. Malla, U. Tamrakar, D. Shrestha, Z. Ni, and R. Tonkoski,"Online learning control for harmonics reduction based on current controlled voltage source power inverters,"IEEE/CAA J. Autom. Sinica, vol. 4, no.3, pp. 447-457, 2017.
[4] Z. Wang, R. Lu, and H. Wang,"Finite-time trajectory tracking control of a class of nonlinear discrete-time systems,"IEEE Trans. Syst. Man&Cyber. Syst., vol. 47, no. 7, pp. 1679-1687, 2017.
[5] Y. Ouyang, W. He, and X. Li,"Reinforcement learning control of a single-link flexible robotic manipulator,"IET Control Theory&Applications, vol. 11, no. 9, pp. 1426-1433, 2017.
[6] F. Zhang, P. Huang, Z. Meng, Y. Zhang, and Z. Liu,"Dynamics analysis and controller design for maneuverable tethered space net robot,"J.Guidance Control&Dynamics, vol. 40, no, 11, pp. 2828-2843, 2017.
[7] L. Dong, X. Zhong, C. Sun, and H. He,"Event-triggered adaptive dynamic programming for continuous-time systems with control constraints,"IEEE Trans. Neural Networks and Learning Syst., vol. 28, no.8, pp. 1941-1952, Aug. 2017.
[8] W. He, Z. Li, and C. L. P. Chen,"A survey of human-centered intelligent robots:issues and challenges,"IEEE/CAA J. Autom. Sinica, vol. 4, no.4, pp. 602-609, 2017.
[9] B. Sun, C. Yang,H. Zhu,Y. Li,and W. Gui,"Modeling, optimization,and control of solution purification process in zinc hydrometallurgy,"IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 564-576, Mar. 2018.
[10] Y. Li and S. Tong,"Adaptive fuzzy output constrained control design for multi-input multioutput stochastic nonstrict-feedback nonlinear systems,"IEEE Trans. Cyber., vol. 47, no. 12, pp. 4086-4095, Dec. 2017.
[11] W. He, Z. Yan, C. Sun, and Y. Chen,"Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer,"IEEE Trans. Cyber., vol. 47, no. 10, pp. 3452-3465, Oct. 2017.
[12] Y. Guo, B. Jiang, and Y. Zhang,"A novel robust attitude control for quadrotor aircraft subject to actuator faults and wind gusts,"IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 292-300, Jan. 2018.
[13] J. Na and G. Herrmann,"Online adaptive approximate optimal tracking control with simplified dual approximation structure for continuous-time unknown nonlinear systems,"IEEE/CAA J. Autom. Sinica, vol. 1, no. 4,pp. 412-422, Oct. 2014.
[14] S.-L. Dai,C. Wang,and M. Wang,"Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems,"IEEE Trans. Neural Networks and Learning Syst., vol. 25, no. 1, pp.111-123,2014.
[15] M. Yue, L. Wang, and T. Ma,"Neural network based terminal sliding mode control for wmrs affected by an augmented ground friction with slippage effect,"IEEE/CAA J.Autom. Sinica, vol. 4, no. 3, pp. 498-506,2017.
[16] D. Carnevale and A. Astolfi,"Semi-global multi-frequency estimation in the presence of deadzone and saturation,"IEEE Trans. Autom. Control,vol. 59, no. 7, pp. 1913-1918, Jul. 2014.
[17] W. He, T. Meng, X. He, and C. Sun,"Iterative learning control for a flapping wing micro aerial vehicle under distributed disturbances,"IEEE Trans. Cyber., vol. 49, no. 4, pp. 1524-1535, Apr. 2019.
[18] X. Zhao, H. Yang, W. Xia, and X. Wang,"Adaptive fuzzy hierarchical sliding-mode control for a class of mimo nonlinear time-delay systems with input saturation,"IEEE Trans. Fuzzy Syst., vol. 25, no. 5, pp. 1062-1077, Oct. 2017.
[19] B. Xu, Z. Shi, F. Sun, and W. He,"Barrier lyapunov function based learning control of hypersonic flight vehicle with AOA constraint and actuator faults,"IEEE Trans. Cyber., vol. 49, no. 3, pp. 1047-1057,Mar. 2019.
[20] L. Xue, C. Sun, D. Wunsch, Y. Zhou, and F. Yu,"An adaptive strategy via reinforcement learning for the prisoner's dilemma game,"IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 301-310, Jan. 2018.
[21] S. Zhang, Y. Dong, Y. Ouyang, Z. Yin, and K. Peng,"Adaptive neural control for robotic manipulators with output constraints and uncertainties."IEEE Trans. Neural Networks and Learning Syst.,vol.29, no. 11, pp. 5554-5564, Nov. 2018.
[22] C. Lian,Z. Zeng,W. Yao, H. Tang,and C. L. P. Chen,"Landslide displacement prediction with uncertainty based on neural networks with random hidden weights,"IEEE Trans. Neural Networks and Learning Syst., vol. 27, no. 12, pp. 2683-2695, Dec. 2016.
[23] S. Zhang, Z. Wang, D. Ding, and H. Shu,"Fuzzy filtering with randomly occurring parameter uncertainties, interval delays, and channel fadings."IEEE Trans. Cyber., vol. 44, no. 3, pp. 406-417, Mar. 2014.
[24] Y. J. Liu, C. L. Chen, G. X. Wen, and S. Tong,"Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems,"IEEE Trans. Neural Networks, vol. 22, no. 7, pp. 1162-1167,2011.
[25] C. Sun, W. He, W. Ge, and C. Chang,"Adaptive neural network control of biped robots,"IEEE Trans. Syst., Man, and Cyber.:Syst., vol. 47, no.2, pp. 315-326, Feb. 2017.
[26] T. Zhang, M. Xia, Y. Yi, and Q. Shen,"Adaptive neural dynamic surface control of pure-feedback nonlinear systems with full state constraints and dynamic uncertainties,"IEEE Trans. Syst., Man, and Cyber.:Syst., vol.47, no. 8, pp. 2378-2387, Aug. 2017.
[27] C. Yang, Y. Jiang, Z. Li, W. He, and C.-Y. So,"Neural control of bimanual robots with guaranteed global stability and motion precision,"IEEE Trans. Industrial Informatics, vol. 13, no. 3, pp. 1162-1171, 2017.
[28] M. Chen, S. Y. Shao, and B. Jiang,"Adaptive neural control of uncertain nonlinear systems using disturbance observer,"IEEE Trans. Cyber., vol.47, no. 10, pp. 3110-3123, Oct. 2017.
[29] C. Yang, X. Wang, L. Cheng, and H. Ma,"Neural-learning-based telerobot control with guaranteed performance,"IEEE Trans. Cyber.,vol. 47, no. 10, pp. 3148-3159, Oct. 2017.
[30] R. Cui, C. Yang, Y. Li, and S. Sharma,"Adaptive neural network control of auvs with control input nonlinearities using reinforcement learning,"IEEE Trans. Syst., Man, and Cyber.:Syst., vol. 47, no. 6, pp. 1019-1029, Jun. 2017.
[31] W. He, Y. Ouyang, and J. Hong,"Vibration control of a flexible robotic manipulator in the presence of input deadzone,"IEEE Trans. Industrial Informatics, vol. 13, no. 1, pp. 48-59, 2017.
[32] M. Alfaro-Ponce, A. A. Cruz, and I. Chairez,"Adaptive identifier for uncertain complex nonlinear systems based on continuous neural networks,"IEEE Trans. Neural Networks and Learning Syst., vol. 25,no. 3, pp. 483-494, Mar. 2014.
[33] M. Chen, P. Shi, and C. C. Lim,"Adaptive neural fault-tolerant control of a 3-dof model helicopter system,"IEEE Trans.Syst.,Man, and Cyber.:Syst., vol. 46, no. 2, pp. 260-270, Feb. 2016.
[34] X. He, W. He, J. Shi, and C. Sun,"Boundary vibration control of variable length crane systems in two-dimensional space with output constraints,"IEEE/ASME Trans. Mechatronics, vol. 22, no. 10, pp. 1952-1962, Oct.2017.
[35] W. Meng, Q. Yang, J. Si, and Y. Sun,"Adaptive neural control of a class of output-constrained nonaffine systems,"IEEE Trans. Cyber., vol. 46,no. 1, pp. 85-95, Jan. 2016.
[36] Y. J. Liu, S. Lu, and S. Tong,"Neural network controller design for an uncertain robot with time-varying output constraint,"IEEE Trans. Syst.,Man, and Cyber.:Syst., vol. 47, no. 8, pp. 2060-2068, Aug. 2017.
[37] B. S. Kim and S. J. Yoo,"Approximation-based adaptive control of uncertain non-linear pure-feedback systems with full state constraints,"IET Control Theory&Applications, vol. 8, no. 17, pp. 2070-2081,2014.
[38] Z. L. Tang, S. S. Ge, K. P. Tee, and W. He,"Adaptive neural control for an uncertain robotic manipulator with joint space constraints,"Int.J. Control, vol. 89, no. 7, pp. 1-33, 2016.
[39] Y. J. Liu, D. J. Li, and S. Tong,"Adaptive output feedback control for a class of nonlinear systems with full-state constraints,"Int. J. Control,vol. 87, no. 2, pp. 281-290, 2014.
[40] Quanser 2-DOF Helicopter Reference Manual, Accessed on:December13, 2018.[Online], available:http://www2.ece.ohio-state.edu/~passino/Quanser2DOFheli.pdf.
[41] Z. L. Tang, S. S. Ge, K. P. Tee, and W. He,"Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints,"IEEE Trans. Syst. Man&Cyber. Syst., vol. 46,no. 12, pp. 1618-1629, 2016.
[2] F. Wang and Y. Gao,"On frequency sensitivity and mode orthogonality of flexible robotic manipulators,"IEEE/CAA J. Autom. Sinica, vol. 3,no. 5, pp. 394-397, Oct. 2016.
[3] N. Malla, U. Tamrakar, D. Shrestha, Z. Ni, and R. Tonkoski,"Online learning control for harmonics reduction based on current controlled voltage source power inverters,"IEEE/CAA J. Autom. Sinica, vol. 4, no.3, pp. 447-457, 2017.
[4] Z. Wang, R. Lu, and H. Wang,"Finite-time trajectory tracking control of a class of nonlinear discrete-time systems,"IEEE Trans. Syst. Man&Cyber. Syst., vol. 47, no. 7, pp. 1679-1687, 2017.
[5] Y. Ouyang, W. He, and X. Li,"Reinforcement learning control of a single-link flexible robotic manipulator,"IET Control Theory&Applications, vol. 11, no. 9, pp. 1426-1433, 2017.
[6] F. Zhang, P. Huang, Z. Meng, Y. Zhang, and Z. Liu,"Dynamics analysis and controller design for maneuverable tethered space net robot,"J.Guidance Control&Dynamics, vol. 40, no, 11, pp. 2828-2843, 2017.
[7] L. Dong, X. Zhong, C. Sun, and H. He,"Event-triggered adaptive dynamic programming for continuous-time systems with control constraints,"IEEE Trans. Neural Networks and Learning Syst., vol. 28, no.8, pp. 1941-1952, Aug. 2017.
[8] W. He, Z. Li, and C. L. P. Chen,"A survey of human-centered intelligent robots:issues and challenges,"IEEE/CAA J. Autom. Sinica, vol. 4, no.4, pp. 602-609, 2017.
[9] B. Sun, C. Yang,H. Zhu,Y. Li,and W. Gui,"Modeling, optimization,and control of solution purification process in zinc hydrometallurgy,"IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 564-576, Mar. 2018.
[10] Y. Li and S. Tong,"Adaptive fuzzy output constrained control design for multi-input multioutput stochastic nonstrict-feedback nonlinear systems,"IEEE Trans. Cyber., vol. 47, no. 12, pp. 4086-4095, Dec. 2017.
[11] W. He, Z. Yan, C. Sun, and Y. Chen,"Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer,"IEEE Trans. Cyber., vol. 47, no. 10, pp. 3452-3465, Oct. 2017.
[12] Y. Guo, B. Jiang, and Y. Zhang,"A novel robust attitude control for quadrotor aircraft subject to actuator faults and wind gusts,"IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 292-300, Jan. 2018.
[13] J. Na and G. Herrmann,"Online adaptive approximate optimal tracking control with simplified dual approximation structure for continuous-time unknown nonlinear systems,"IEEE/CAA J. Autom. Sinica, vol. 1, no. 4,pp. 412-422, Oct. 2014.
[14] S.-L. Dai,C. Wang,and M. Wang,"Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems,"IEEE Trans. Neural Networks and Learning Syst., vol. 25, no. 1, pp.111-123,2014.
[15] M. Yue, L. Wang, and T. Ma,"Neural network based terminal sliding mode control for wmrs affected by an augmented ground friction with slippage effect,"IEEE/CAA J.Autom. Sinica, vol. 4, no. 3, pp. 498-506,2017.
[16] D. Carnevale and A. Astolfi,"Semi-global multi-frequency estimation in the presence of deadzone and saturation,"IEEE Trans. Autom. Control,vol. 59, no. 7, pp. 1913-1918, Jul. 2014.
[17] W. He, T. Meng, X. He, and C. Sun,"Iterative learning control for a flapping wing micro aerial vehicle under distributed disturbances,"IEEE Trans. Cyber., vol. 49, no. 4, pp. 1524-1535, Apr. 2019.
[18] X. Zhao, H. Yang, W. Xia, and X. Wang,"Adaptive fuzzy hierarchical sliding-mode control for a class of mimo nonlinear time-delay systems with input saturation,"IEEE Trans. Fuzzy Syst., vol. 25, no. 5, pp. 1062-1077, Oct. 2017.
[19] B. Xu, Z. Shi, F. Sun, and W. He,"Barrier lyapunov function based learning control of hypersonic flight vehicle with AOA constraint and actuator faults,"IEEE Trans. Cyber., vol. 49, no. 3, pp. 1047-1057,Mar. 2019.
[20] L. Xue, C. Sun, D. Wunsch, Y. Zhou, and F. Yu,"An adaptive strategy via reinforcement learning for the prisoner's dilemma game,"IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 301-310, Jan. 2018.
[21] S. Zhang, Y. Dong, Y. Ouyang, Z. Yin, and K. Peng,"Adaptive neural control for robotic manipulators with output constraints and uncertainties."IEEE Trans. Neural Networks and Learning Syst.,vol.29, no. 11, pp. 5554-5564, Nov. 2018.
[22] C. Lian,Z. Zeng,W. Yao, H. Tang,and C. L. P. Chen,"Landslide displacement prediction with uncertainty based on neural networks with random hidden weights,"IEEE Trans. Neural Networks and Learning Syst., vol. 27, no. 12, pp. 2683-2695, Dec. 2016.
[23] S. Zhang, Z. Wang, D. Ding, and H. Shu,"Fuzzy filtering with randomly occurring parameter uncertainties, interval delays, and channel fadings."IEEE Trans. Cyber., vol. 44, no. 3, pp. 406-417, Mar. 2014.
[24] Y. J. Liu, C. L. Chen, G. X. Wen, and S. Tong,"Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems,"IEEE Trans. Neural Networks, vol. 22, no. 7, pp. 1162-1167,2011.
[25] C. Sun, W. He, W. Ge, and C. Chang,"Adaptive neural network control of biped robots,"IEEE Trans. Syst., Man, and Cyber.:Syst., vol. 47, no.2, pp. 315-326, Feb. 2017.
[26] T. Zhang, M. Xia, Y. Yi, and Q. Shen,"Adaptive neural dynamic surface control of pure-feedback nonlinear systems with full state constraints and dynamic uncertainties,"IEEE Trans. Syst., Man, and Cyber.:Syst., vol.47, no. 8, pp. 2378-2387, Aug. 2017.
[27] C. Yang, Y. Jiang, Z. Li, W. He, and C.-Y. So,"Neural control of bimanual robots with guaranteed global stability and motion precision,"IEEE Trans. Industrial Informatics, vol. 13, no. 3, pp. 1162-1171, 2017.
[28] M. Chen, S. Y. Shao, and B. Jiang,"Adaptive neural control of uncertain nonlinear systems using disturbance observer,"IEEE Trans. Cyber., vol.47, no. 10, pp. 3110-3123, Oct. 2017.
[29] C. Yang, X. Wang, L. Cheng, and H. Ma,"Neural-learning-based telerobot control with guaranteed performance,"IEEE Trans. Cyber.,vol. 47, no. 10, pp. 3148-3159, Oct. 2017.
[30] R. Cui, C. Yang, Y. Li, and S. Sharma,"Adaptive neural network control of auvs with control input nonlinearities using reinforcement learning,"IEEE Trans. Syst., Man, and Cyber.:Syst., vol. 47, no. 6, pp. 1019-1029, Jun. 2017.
[31] W. He, Y. Ouyang, and J. Hong,"Vibration control of a flexible robotic manipulator in the presence of input deadzone,"IEEE Trans. Industrial Informatics, vol. 13, no. 1, pp. 48-59, 2017.
[32] M. Alfaro-Ponce, A. A. Cruz, and I. Chairez,"Adaptive identifier for uncertain complex nonlinear systems based on continuous neural networks,"IEEE Trans. Neural Networks and Learning Syst., vol. 25,no. 3, pp. 483-494, Mar. 2014.
[33] M. Chen, P. Shi, and C. C. Lim,"Adaptive neural fault-tolerant control of a 3-dof model helicopter system,"IEEE Trans.Syst.,Man, and Cyber.:Syst., vol. 46, no. 2, pp. 260-270, Feb. 2016.
[34] X. He, W. He, J. Shi, and C. Sun,"Boundary vibration control of variable length crane systems in two-dimensional space with output constraints,"IEEE/ASME Trans. Mechatronics, vol. 22, no. 10, pp. 1952-1962, Oct.2017.
[35] W. Meng, Q. Yang, J. Si, and Y. Sun,"Adaptive neural control of a class of output-constrained nonaffine systems,"IEEE Trans. Cyber., vol. 46,no. 1, pp. 85-95, Jan. 2016.
[36] Y. J. Liu, S. Lu, and S. Tong,"Neural network controller design for an uncertain robot with time-varying output constraint,"IEEE Trans. Syst.,Man, and Cyber.:Syst., vol. 47, no. 8, pp. 2060-2068, Aug. 2017.
[37] B. S. Kim and S. J. Yoo,"Approximation-based adaptive control of uncertain non-linear pure-feedback systems with full state constraints,"IET Control Theory&Applications, vol. 8, no. 17, pp. 2070-2081,2014.
[38] Z. L. Tang, S. S. Ge, K. P. Tee, and W. He,"Adaptive neural control for an uncertain robotic manipulator with joint space constraints,"Int.J. Control, vol. 89, no. 7, pp. 1-33, 2016.
[39] Y. J. Liu, D. J. Li, and S. Tong,"Adaptive output feedback control for a class of nonlinear systems with full-state constraints,"Int. J. Control,vol. 87, no. 2, pp. 281-290, 2014.
[40] Quanser 2-DOF Helicopter Reference Manual, Accessed on:December13, 2018.[Online], available:http://www2.ece.ohio-state.edu/~passino/Quanser2DOFheli.pdf.
[41] Z. L. Tang, S. S. Ge, K. P. Tee, and W. He,"Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints,"IEEE Trans. Syst. Man&Cyber. Syst., vol. 46,no. 12, pp. 1618-1629, 2016.