Neural Network-based Finite-time Control of Nonlinear Systems with Unknown Dead-zones: Application to Quadrotors
Abstract
Over the years, researchers have addressed several control problems of various classes of nonlinear systems. This article considers a class of uncertain strict feedback nonlinear system with unknown external disturbances and asymmetric input dead-zone. Designing a tracking controller for such system is very complex and challenging. This article aims to design a finite-time adaptive neural network backstepping tracking control for the nonlinear system under consideration. In addition, all unknown disturbances and nonlinear functions are lumped together and approximated by radial basis function neural network (RBFNN). Moreover, no prior information about the boundedness of the dead-zone parameters is required in the controller design. With the aid of a Lyapunov candidate function, it has been shown that the tracking errors converge near the origin in finite-time. Simulation results testify that the proposed control approach can force the output to follow the reference trajectory in a short time despite the presence of asymmetric input dead-zone and external disturbances. At last, in order to highlight the effectiveness of the proposed control method, it is applied to a quadrotor unmanned aerial vehicle (UAV).
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M. Chen, S. S. Ge, and B. V. E. How, “Robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities,” IEEE Transactions on Neural Networks, vol. 21, no. 5, pp. 796–812, May 2010.
M. S. Mahmoud, M. Maaruf, and S. El-Ferik, “Neuro-adaptive output feedback control of the continuous polymerization reactor subjected to parametric uncertainties and external disturbances,” ISA transactions, vol. 112, pp. 1–11, 2021.
C. Lascu, S. Jafarzadeh, M. S. Fadali, and F. Blaabjerg, “Direct torque control with feedback linearization for induction motor drives,” IEEE Transactions on Power Electronics, vol. 32, no. 3, pp. 2072–2080, March 2017.
S. Yang, P. Wang, and Y. Tang, “Feedback linearization-based current control strategy for modular multilevel converters,” IEEE Transactions on Power Electronics, vol. 33, no. 1, pp. 161–174, Jan 2018.
A. Polyakov, “Sliding mode control design using canonical homogeneous norm,” International Journal of Robust and Nonlinear Control, vol. 29, no. 3, pp. 682–701, 2019.
Z.-Y. Sun, Y. Shao, and C.-C. Chen, “Fast finite-time stability and its application in adaptive control of high-order nonlinear system,” Automatica, vol. 106, pp. 339 – 348, 2019.
Z. Anjum and Y. Guo, “Finite time fractional-order adaptive backstepping fault tolerant control of robotic manipulator,” International Journal of Control, Automation and Systems, vol. 19, no. 1, pp. 301–310, 2021.
X. Wang, J. Zhou, B. Qin, Y. Luo, C. Hu, and J. Pang, “Individual pitch control of wind turbines based on svm load estimation and lidar measurement,” IEEE Access, vol. 9, pp. 143 913–143 921, 2021.
M. Maaruf and S. El Ferik, “Distributed control method for heterogeneous multiagent systems subjected to faults,” in 2021 18th International MultiConference on Systems, Signals & Devices (SSD). IEEE, 2021, pp. 1328–1333.
X. Shi, Y. Cheng, C. Yin, S. Dadras, and X. Huang, “Design of fractionalorder backstepping sliding mode control for quadrotor uav,” Asian Journal of Control, vol. 21, no. 1, pp. 156–171, 2019.
N. Nikdel, M. Badamchizadeh, V. Azimirad, and M. Nazari, “Adaptive backstepping control for an n-degree of freedom robotic manipulator based on combined state augmentation,” Robotics and ComputerIntegrated Manufacturing, vol. 44, pp. 129 – 143, 2017.
X. Yin and et al., “Adaptive backstepping control for maximizing marine current power generation based on uncertainty and disturbance estimation,” International Journal of Electrical Power & Energy Systems, vol. 117, p. 105329, 2020.
S. Butt and H. Aschemann, “Adaptive backstepping control for an engine cooling system with guaranteed parameter convergence under mismatched parameter uncertainties,” Control Engineering Practice, vol. 64, pp. 195–204, 2017.
H. Pang, X. Zhang, J. Chen, and K. Liu, “Design of a coordinated adaptive backstepping tracking control for nonlinear uncertain active suspension system,” Applied Mathematical Modelling, vol. 76, pp. 479 – 494, 2019.
J. Li, Y. Wang, X. Zhao, and P. Qi, “Model free adaptive control of large and flexible wind turbine rotors with controllable flaps,” Renewable Energy, vol. 180, pp. 68–82, 2021.
Kang Wu, Zhongcai Zhang, and Changyin Sun, “Disturbance-observerbased output feedback control of non-linear cascaded systems with external disturbance,” IET Control Theory & Applications, vol. 12, pp. 738–744, April 2018.
S. Qi, H.-D. Wang, H.-N. Wu, and L. Guo, “Composite antidisturbance control for nonlinear systems via nonlinear disturbance observer and dissipative control,” International Journal of Robust and Nonlinear Control, vol. 29, no. 12, pp. 4056–4068, 2019.
W. Liu and P. Li, “Disturbance observer-based fault-tolerant adaptive control for nonlinearly parameterized systems,” IEEE Transactions on Industrial Electronics, vol. 66, no. 11, pp. 8681–8691, 2019.
B. Xu, F. Sun, Y. Pan, and B. Chen, “Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 1854–1862, 2017.
S. C. Barreto and P. T. Szemes, “Training and analysis of hyperparameters in neural networks for computer vision applications: A didactic approach,” in 2022 IEEE 20th Jubilee World Symposium on Applied Machine Intelligence and Informatics (SAMI), 2022, pp. 383–388.
C. M. Horvath, J. Botzheim, T. Thomessen, and P. Korondi, “Bacterial memetic algorithm trained fuzzy system-based model of single weld bead geometry,” IEEE Access, vol. 8, pp. 164 864–164 881, 2020.
S. El Ferik, M. S. Mahmoud, and M. Maaruf, “Robust adaptive sliding mode control of nonlinear systems using neural network,” in 2020 17th International Multi-Conference on Systems, Signals & Devices (SSD), 2020, pp. 591–596.
M. Chu, Q. Jia, and H. Sun, “Backstepping control for flexible joint with friction using wavelet neural networks and l2-gain approach,” Asian Journal of Control, vol. 20, no. 2, pp. 856–866, 2018.
Y. Pan, C. Yang, M. Pratama, and H. Yu, “Composite learning adaptive
backstepping control using neural networks with compact supports,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 12, pp. 1726–1738, 2019.
Y. Ji, H. Zhou, and Q. Zong, “Adaptive neural network command filtered backstepping control of pure-feedback systems in presence of full state constraints,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 5, pp. 829–842, 2019.
J. Peng and R. Dubay, “Adaptive fuzzy backstepping control for a class of uncertain nonlinear strict-feedback systems based on dynamic surface control approach,” Expert Systems with Applications, vol. 120, pp. 239–252, 2019.
W. Min and Q. Liu, “An improved adaptive fuzzy backstepping control for nonlinear mechanical systems with mismatched uncertainties,” Automatika, vol. 60, no. 1, pp. 1–10, 2019.
D. Xu, J. Huang, X. Su, and P. Shi, “Adaptive command-filtered fuzzy backstepping control for linear induction motor with unknown end effect,” Information Sciences, vol. 477, pp. 118–131, 2019.
H. Wang, K. Xu, and J. Qiu, “Event-triggered adaptive fuzzy fixed-time tracking control for a class of nonstrict-feedback nonlinear systems,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 68, no. 7, pp. 3058–3068, 2021.
L.-P. Xin, B. Yu, L. Zhao, and J. Yu, “Adaptive fuzzy backstepping control for a two continuous stirred tank reactors process based on dynamic surface control approach,” Applied Mathematics and Computation, vol. 377, p. 125138, 2020.
K. Lu, Z. Liu, G. Lai, Y. Zhang, and C. L. P. Chen, “Adaptive fuzzy tracking control of uncertain nonlinear systems subject to actuator dead zone with piecewise time-varying parameters,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 7, pp. 1493–1505, July 2019.
Z. Ma and H. Ma, “Improved adaptive fuzzy output-feedback dynamic surface control of nonlinear systems with unknown dead-zone output,” IEEE Transactions on Fuzzy Systems, pp. 1–1, 2020.
E. M., T. H. A., and M. M. B., “Robust adaptive dynamic surface control of nonlinear time-varying systems in strict-feedback form,” Int. J. Control Autom. Syst., vol. 17, pp. 1432-1444, 2019.
H. Ma, H. Liang, Q. Zhou, and C. K. Ahn, “Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 3, pp. 506–515, 2019.
X. Shi and et al., “Design of adaptive backstepping dynamic surface control method with rbf neural network for uncertain nonlinear system,” Neurocomputing, vol. 330, pp. 490–503, 2019.
W. Shi, M. Hou, and M. Hao, “Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown control direction,” ISA transactions, vol. 121, pp. 95–104, 2022.
Z. Ma and H. Ma, “Improved adaptive fuzzy output-feedback dynamic surface control of nonlinear systems with unknown dead-zone output,” IEEE Transactions on Fuzzy Systems, pp. 1–1, 2020.
Z. J., “State observer-based adaptive neural dynamic surface control for a class of uncertain nonlinear systems with input saturation using disturbance observer,” Neural Comput & Applic, vol. 31, pp. 4993–5004, 2019.
Y. Cui, H. Zhang, Y. Wang, and Z. Zhang, “Adaptive neural dynamic surface control for a class of uncertain nonlinear systems with disturbances,” Neurocomputing, vol. 165, pp. 152–158, 2015.
L. Wu and G. Yang, “Adaptive output neural network control for a class of stochastic nonlinear systems with dead-zone nonlinearities,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 3, pp. 726–739, March 2017.
Z. Yang and H. Zhang, “A fuzzy adaptive tracking control for a class of uncertain strick-feedback nonlinear systems with dead-zone input,” Neurocomputing, vol. 272, pp. 130–135, 2018.
H. Li, S. Zhao, W. He, and R. Lu, “Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone,” Automatica, vol. 100, pp. 99–107, 2019.
N.-N. Zhao, L.-B. Wu, X.-Y. Ouyang, Y. Yan, and R.-Y. Zhang, “Finite time adaptive fuzzy tracking control for nonlinear systems with disturbances and dead-zone nonlinearities,” Applied Mathematics and Computation, vol. 362, p. 124494, 2019.
J. Ni, Z. Wu, L. Liu, and C. Liu, “Fixed-time adaptive neural network control for nonstrict-feedback nonlinear systems with deadzone and output constraint,” ISA Transactions, 2019.
F. Wang, B. Chen, C. Lin, J. Zhang, and X. Meng, “Adaptive neural network finite-time output feedback control of quantized nonlinear systems,” IEEE Transactions on Cybernetics, vol. 48, no. 6, pp. 1839–1848, June 2018.
Z. Zhang, X. Liu, Y. Liu, C. Lin, and B. Chen, “Fixed-time almost disturbance decoupling of nonlinear time-varying systems with multiple disturbances and dead-zone input,” Information Sciences, vol. 450, pp. 267–283, 2018.
H. Wang, H. R. Karimi, P. X. Liu, and H. Yang, “Adaptive neural control of nonlinear systems with unknown control directions and input deadzone,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 11, pp. 1897–1907, 2018.
X. Zhou, C. Gao, Z.-g. Li, X.-y. Ouyang, and L.-b. Wu, “Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation,” Nonlinear Dynamics, vol. 103, no. 2, pp. 1645–1661, 2021.
B. Tian, Y. Ma, and Q. Zong, “A continuous finite-time output feedback control scheme and its application in quadrotor uavs,” IEEE Access, vol. 6, pp. 19 807–19 813, 2018.
M. S. Mahmoud and M. Maaruf, “Robust adaptive multilevel control of a quadrotor,” IEEE Access, vol. 8, pp. 167 684–167 692, 2020.
N. Wang, Q. Deng, G. Xie, and X. Pan, “Hybrid finite-time trajectory tracking control of a quadrotor,” ISA transactions, vol. 90, pp. 278–286, 2019.
DOI: https://doi.org/10.18196/jrc.v3i6.15355
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