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04.07.2022

Hybrid Neural Network Control for Uncertain Nonlinear Discrete-Time Systems with Bounded Disturbance

verfasst von: Rahul Kumar, Uday Pratap Singh, Arun Bali, Kuldip Raj

Erschienen in: Wireless Personal Communications

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Abstract

This paper has proposed an adaptive control scheme based on a hybrid neural network (HNN) to address the problem of uncertain nonlinear systems with discrete-time having bounded disturbances. This proposed control scheme is composed of a neural network (NN) and differential evolution (DE) technique which is used to initialize the weights of the NN and the controller is designed in such a manner so that the stability can be ensured and the desired trajectory can be achieved. The designed HNN is employed to approximate unknown functions present in the system. By using the concept of system transformation, the adaptive law and controller are designed and the whole system is proved to be stable in the sense of semi-globally uniformly ultimately boundedness (SGUUB) with the assistance of Lyapunov theory. Finally, the validity and effectiveness of the results are proved through two simulation examples.
Literatur
1.
Zurück zum Zitat Lian, Y., Zhou, Y., Zhang, J., Ma, S., & Wu, S. (2022). An Intelligent Nonlinear Control Method for the Multistage Electromechanical Servo System. Applied Sciences, 12(10), 5053. CrossRef Lian, Y., Zhou, Y., Zhang, J., Ma, S., & Wu, S. (2022). An Intelligent Nonlinear Control Method for the Multistage Electromechanical Servo System. Applied Sciences, 12(10), 5053. CrossRef
2.
Zurück zum Zitat Cruz-Zavala, E., Nuño, E., & Moreno, J. A. (2021). Robust trajectory-tracking in finite-time for robot manipulators using nonlinear proportional-derivative control plus feed-forward compensation. International Journal of Robust and Nonlinear Control, 31(9), 3878–3907. MathSciNetCrossRef Cruz-Zavala, E., Nuño, E., & Moreno, J. A. (2021). Robust trajectory-tracking in finite-time for robot manipulators using nonlinear proportional-derivative control plus feed-forward compensation. International Journal of Robust and Nonlinear Control, 31(9), 3878–3907. MathSciNetCrossRef
3.
Zurück zum Zitat Gong, P., Yan, Z., Zhang, W., & Tang, J. (2021). Lyapunov-based model predictive control trajectory tracking for an autonomous underwater vehicle with external disturbances. Ocean Engineering, 232, 109010. CrossRef Gong, P., Yan, Z., Zhang, W., & Tang, J. (2021). Lyapunov-based model predictive control trajectory tracking for an autonomous underwater vehicle with external disturbances. Ocean Engineering, 232, 109010. CrossRef
4.
Zurück zum Zitat Bacciotti, A., & Rosier, L. (2005). Liapunov functions and stability in control theory. Heidelberg: Springer Science & Business Media. CrossRef Bacciotti, A., & Rosier, L. (2005). Liapunov functions and stability in control theory. Heidelberg: Springer Science & Business Media. CrossRef
5.
Zurück zum Zitat Esfandiari, F., & Khalil, H. K. (1992). Output feedback stabilization of fully linearizable systems. International Journal of control, 56(5), 1007–1037. MathSciNetCrossRef Esfandiari, F., & Khalil, H. K. (1992). Output feedback stabilization of fully linearizable systems. International Journal of control, 56(5), 1007–1037. MathSciNetCrossRef
6.
Zurück zum Zitat Jiang, B., Karimi, H. R., Kao, Y., & Gao, C. (2019). Reduced-order adaptive sliding mode control for nonlinear switching semi-Markovian jump delayed systems. Information Sciences, 477, 334–348. MathSciNetCrossRef Jiang, B., Karimi, H. R., Kao, Y., & Gao, C. (2019). Reduced-order adaptive sliding mode control for nonlinear switching semi-Markovian jump delayed systems. Information Sciences, 477, 334–348. MathSciNetCrossRef
7.
Zurück zum Zitat Lei, H., & Lin, W. (2005). Universal output feedback control of nonlinear systems with unknown growth rate. IFAC Proceedings Volumes, 38(1), 1073–1078. CrossRef Lei, H., & Lin, W. (2005). Universal output feedback control of nonlinear systems with unknown growth rate. IFAC Proceedings Volumes, 38(1), 1073–1078. CrossRef
8.
Zurück zum Zitat Li, F., & Liu, Y. (2017). Global finite-time stabilization via time-varying output-feedback for uncertain nonlinear systems with unknown growth rate. International Journal of Robust and Nonlinear Control, 27(17), 4050–4070. MathSciNetMATH Li, F., & Liu, Y. (2017). Global finite-time stabilization via time-varying output-feedback for uncertain nonlinear systems with unknown growth rate. International Journal of Robust and Nonlinear Control, 27(17), 4050–4070. MathSciNetMATH
9.
Zurück zum Zitat Li, Y., Li, K., & Tong, S. (2018). Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems. IEEE Transactions on Fuzzy Systems, 27(1), 96–110. CrossRef Li, Y., Li, K., & Tong, S. (2018). Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems. IEEE Transactions on Fuzzy Systems, 27(1), 96–110. CrossRef
10.
Zurück zum Zitat Miao, P., Shen, Y., Li, Y., & Bao, L. (2016). Finite-time recurrent neural networks for solving nonlinear optimization problems and their application. Neurocomputing, 177, 120–129. CrossRef Miao, P., Shen, Y., Li, Y., & Bao, L. (2016). Finite-time recurrent neural networks for solving nonlinear optimization problems and their application. Neurocomputing, 177, 120–129. CrossRef
11.
Zurück zum Zitat Singh, U. P., & Jain, S. (2016). Modified chaotic bat algorithm based counter propagation neural network for uncertain nonlinear discrete time system. International Journal of Computational Intelligence and Applications, 15(03), 1650016. CrossRef Singh, U. P., & Jain, S. (2016). Modified chaotic bat algorithm based counter propagation neural network for uncertain nonlinear discrete time system. International Journal of Computational Intelligence and Applications, 15(03), 1650016. CrossRef
12.
Zurück zum Zitat Chen, B., Liu, X., Liu, K., & Lin, C. (2009). Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica, 45(6), 1530–1535. MathSciNetCrossRef Chen, B., Liu, X., Liu, K., & Lin, C. (2009). Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica, 45(6), 1530–1535. MathSciNetCrossRef
13.
Zurück zum Zitat Chen, B., Liu, X., Liu, K., & Lin, C. (2010). Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Transactions on Fuzzy Systems, 18(5), 883–892. CrossRef Chen, B., Liu, X., Liu, K., & Lin, C. (2010). Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Transactions on Fuzzy Systems, 18(5), 883–892. CrossRef
14.
Zurück zum Zitat Singh, U. P., Jain, S., Gupta, R. K., & Tiwari, A. (2019). AFMBC for a class of nonlinear discrete-time systems with dead zone. International Journal of Fuzzy Systems, 21(4), 1073–1084. MathSciNetCrossRef Singh, U. P., Jain, S., Gupta, R. K., & Tiwari, A. (2019). AFMBC for a class of nonlinear discrete-time systems with dead zone. International Journal of Fuzzy Systems, 21(4), 1073–1084. MathSciNetCrossRef
15.
Zurück zum Zitat Tong, S., Min, X., & Li, Y. (2020). Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Transactions on Cybernetics, 50(9), 3903–3913. CrossRef Tong, S., Min, X., & Li, Y. (2020). Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Transactions on Cybernetics, 50(9), 3903–3913. CrossRef
16.
Zurück zum Zitat Das, M., & Mahanta, C. (2014). Optimal second order sliding mode control for linear uncertain systems. ISA transactions, 53(6), 1807–1815. CrossRef Das, M., & Mahanta, C. (2014). Optimal second order sliding mode control for linear uncertain systems. ISA transactions, 53(6), 1807–1815. CrossRef
17.
Zurück zum Zitat Shaocheng, T., Changying, L., & Yongming, L. (2009). Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy sets and systems, 160(19), 2755–2775. MathSciNetCrossRef Shaocheng, T., Changying, L., & Yongming, L. (2009). Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy sets and systems, 160(19), 2755–2775. MathSciNetCrossRef
18.
Zurück zum Zitat Mobayen, S., & Majd, V. J. (2012). Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dynamics, 70(1), 171–180. MathSciNetCrossRef Mobayen, S., & Majd, V. J. (2012). Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dynamics, 70(1), 171–180. MathSciNetCrossRef
19.
Zurück zum Zitat Ho, H. F., Wong, Y. K., & Rad, A. B. (2009). Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems. Simulation Modelling Practice and Theory, 17(7), 1199–1210. CrossRef Ho, H. F., Wong, Y. K., & Rad, A. B. (2009). Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems. Simulation Modelling Practice and Theory, 17(7), 1199–1210. CrossRef
20.
Zurück zum Zitat Lee, H. (2010). Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Transactions on Fuzzy Systems, 19(2), 265–275. CrossRef Lee, H. (2010). Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Transactions on Fuzzy Systems, 19(2), 265–275. CrossRef
21.
Zurück zum Zitat Chen, B., Liu, X., Liu, K., & Lin, C. (2009). Novel adaptive neural control design for nonlinear MIMO time-delay systems. Automatica, 45(6), 1554–1560. MathSciNetCrossRef Chen, B., Liu, X., Liu, K., & Lin, C. (2009). Novel adaptive neural control design for nonlinear MIMO time-delay systems. Automatica, 45(6), 1554–1560. MathSciNetCrossRef
22.
Zurück zum Zitat Zhou, Q., Zhao, S., Li, H., Lu, R., & Wu, C. (2018). Adaptive neural network tracking control for robotic manipulators with dead zone. IEEE Transactions on Neural Networks and Learning Systems, 30(12), 3611–3620. MathSciNetCrossRef Zhou, Q., Zhao, S., Li, H., Lu, R., & Wu, C. (2018). Adaptive neural network tracking control for robotic manipulators with dead zone. IEEE Transactions on Neural Networks and Learning Systems, 30(12), 3611–3620. MathSciNetCrossRef
23.
Zurück zum Zitat Chen, M., & Tao, G. (2015). Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone. IEEE Transactions on Cybernetics, 46(8), 1851–1862. CrossRef Chen, M., & Tao, G. (2015). Adaptive fault-tolerant control of uncertain nonlinear large-scale systems with unknown dead zone. IEEE Transactions on Cybernetics, 46(8), 1851–1862. CrossRef
24.
Zurück zum Zitat Zhao, X., Shi, P., Zheng, X., & Zhang, L. (2015). Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica, 60, 193–200. MathSciNetCrossRef Zhao, X., Shi, P., Zheng, X., & Zhang, L. (2015). Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone. Automatica, 60, 193–200. MathSciNetCrossRef
25.
Zurück zum Zitat Cao, L., Zhou, Q., Dong, G., & Li, H. (2019). Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(3), 1380–1391. CrossRef Cao, L., Zhou, Q., Dong, G., & Li, H. (2019). Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(3), 1380–1391. CrossRef
26.
Zurück zum Zitat Xu, B., Sun, F., Pan, Y., & Chen, B. (2016). Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 1854–1862. CrossRef Xu, B., Sun, F., Pan, Y., & Chen, B. (2016). Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 1854–1862. CrossRef
27.
Zurück zum Zitat Chen, B., Liu, X., Liu, K., & Lin, C. (2013). Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone. IEEE Transactions on Fuzzy Systems, 22(2), 237–248. CrossRef Chen, B., Liu, X., Liu, K., & Lin, C. (2013). Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone. IEEE Transactions on Fuzzy Systems, 22(2), 237–248. CrossRef
28.
Zurück zum Zitat Liu, Y. J., Tong, S., Li, D. J., & Gao, Y. (2015). Fuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraint. IEEE Transactions on Fuzzy Systems, 24(5), 1147–1158. CrossRef Liu, Y. J., Tong, S., Li, D. J., & Gao, Y. (2015). Fuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraint. IEEE Transactions on Fuzzy Systems, 24(5), 1147–1158. CrossRef
29.
Zurück zum Zitat Liu, Y. J., Li, S., Tong, S., & Chen, C. P. (2018). Adaptive reinforcement learning control based on neural approximation for nonlinear discrete-time systems with unknown nonaffine dead-zone input. IEEE transactions on neural networks and learning systems, 30(1), 295–305. CrossRef Liu, Y. J., Li, S., Tong, S., & Chen, C. P. (2018). Adaptive reinforcement learning control based on neural approximation for nonlinear discrete-time systems with unknown nonaffine dead-zone input. IEEE transactions on neural networks and learning systems, 30(1), 295–305. CrossRef
30.
Zurück zum Zitat Liu, Y. J., Gao, Y., Tong, S., & Chen, C. P. (2015). A unified approach to adaptive neural control for nonlinear discrete-time systems with nonlinear dead-zone input. IEEE Transactions on Neural Networks and Learning Systems, 27(1), 139–150. MathSciNetCrossRef Liu, Y. J., Gao, Y., Tong, S., & Chen, C. P. (2015). A unified approach to adaptive neural control for nonlinear discrete-time systems with nonlinear dead-zone input. IEEE Transactions on Neural Networks and Learning Systems, 27(1), 139–150. MathSciNetCrossRef
31.
Zurück zum Zitat Singh, U. P., & Jain, S. (2018). Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of Indian currency exchange rate prediction. Soft Computing, 22(8), 2667–2681. CrossRef Singh, U. P., & Jain, S. (2018). Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of Indian currency exchange rate prediction. Soft Computing, 22(8), 2667–2681. CrossRef
32.
Zurück zum Zitat Wei, Q., & Liu, D. (2015). Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors. Neurocomputing, 149, 106–115. CrossRef Wei, Q., & Liu, D. (2015). Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors. Neurocomputing, 149, 106–115. CrossRef
33.
Zurück zum Zitat Na, J., Lv, Y., Wu, X., Guo, Y., & Chen, Q. (2014). Approximate optimal tracking control for continuous-time unknown nonlinear systems. In  Proceedings of the 33rd chinese control conference (pp. 8990–8995). IEEE Na, J., Lv, Y., Wu, X., Guo, Y., & Chen, Q. (2014). Approximate optimal tracking control for continuous-time unknown nonlinear systems. In  Proceedings of the 33rd chinese control conference (pp. 8990–8995). IEEE
34.
Zurück zum Zitat Zhou, Q., Shi, P., Lu, J., & Xu, S. (2011). Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems, 19(5), 972–982. CrossRef Zhou, Q., Shi, P., Lu, J., & Xu, S. (2011). Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems, 19(5), 972–982. CrossRef
35.
Zurück zum Zitat Mehraeen, S., Jagannathan, S., & Crow, M. L. (2011). Decentralized dynamic surface control of large-scale interconnected systems in strict-feedback form using neural networks with asymptotic stabilization. IEEE Transactions on Neural Networks, 22(11), 1709–1722. CrossRef Mehraeen, S., Jagannathan, S., & Crow, M. L. (2011). Decentralized dynamic surface control of large-scale interconnected systems in strict-feedback form using neural networks with asymptotic stabilization. IEEE Transactions on Neural Networks, 22(11), 1709–1722. CrossRef
36.
Zurück zum Zitat Chen, W., & Li, J. (2008). Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(1), 258–266. CrossRef Chen, W., & Li, J. (2008). Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(1), 258–266. CrossRef
37.
Zurück zum Zitat Lee, T. H., & Narendra, K. (1986). Stable discrete adaptive control with unknown high-frequency gain. IEEE Transactions on Automatic Control, 31(5), 477–479. CrossRef Lee, T. H., & Narendra, K. (1986). Stable discrete adaptive control with unknown high-frequency gain. IEEE Transactions on Automatic Control, 31(5), 477–479. CrossRef
Metadaten
Titel
Hybrid Neural Network Control for Uncertain Nonlinear Discrete-Time Systems with Bounded Disturbance
verfasst von
Rahul Kumar
Uday Pratap Singh
Arun Bali
Kuldip Raj
Publikationsdatum
04.07.2022
Verlag
Springer US
Erschienen in
Wireless Personal Communications
Print ISSN: 0929-6212
Elektronische ISSN: 1572-834X
DOI
https://doi.org/10.1007/s11277-022-09875-9