Transactions on Machine Intelligence

Transactions on Machine Intelligence

Type 2 Neuro-Fuzzy Controller for a Class of Delayed Nonlinear Systems

Document Type : Original Article

Author
K. Sabahi
Assistant Professor, Department of Engineering Sciences, Faculty of New Technologies, University of Mohaghegh Ardabili, Namin, Iran
10.47176/TMI.2022.139
Abstract
This article explores the design of a type 2 neuro-fuzzy controller specifically for managing delayed nonlinear systems through feedback error training. The feedback error training framework incorporates a traditional controller in the feedback loop to stabilize the system. Meanwhile, the forward loop employs a type 2 neuro-fuzzy controller, which serves as an intelligent controller to address system nonlinearity and time delay issues. The parameters of the type 2 neuro-fuzzy controller are fine-tuned using the gradient descent method within this framework. To assess the stability of both the closed-loop system and the parameter adjustment algorithm, a Lyapunov-Krasowski function is utilized. This function demonstrates that the tracking error can be reduced to zero, even with the presence of delay in the control system input. Furthermore, the regulation rules for the intelligent controller's parameters can be derived without needing the exact mathematical model or parameters of the system being controlled, thus simplifying the calculations. The proposed method has been applied to control an inverse pendulum system characterized by nonlinear behavior and time-varying delays in its input due to network-based control. Additionally, sensor measurements are assumed to be noisy. Simulation results validate the effectiveness of the designed controller across various time delay scenarios and noise levels.
Keywords
Delayed Nonlinear Systems
Type 2 Neuro-Fuzzy Controller
Lyapunov-Krasovski Function
Measurement Noise
Stability
  • Tuli, S., Casale, G., & Jennings, N. (2022). TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data. Proceedings of the VLDB Endowment, 15, 1201-1214. https://doi.org/10.14778/3514061.3514067
  • Adel, A. (2022). Future of industry 5.0 in society: Human-centric solutions, challenges, and prospective research areas. Journal of Cloud Computing, 11. https://doi.org/10.1186/s13677-022-00314-5
  • Sathya, K., Nagarajan, K., Malar, G. C. G., Rajalakshmi, S., & Lakshmi, P. R. (2022). A comprehensive review on comparison among effluent treatment methods and modern methods of treatment of industrial wastewater effluent from different sources. Applied Water Science, 12. https://doi.org/10.1007/s13201-022-01594-7
  • Zhou, X., Xu, X., Liang, W., Zeng, Z., Shimizu, S., Yang, L., & Jin, Q. (2021). Intelligent small object detection for digital twin in smart manufacturing with industrial cyber-physical systems. IEEE Transactions on Industrial Informatics, 18, 1377-1386. https://doi.org/10.1109/TII.2021.3061419
  • Yao, J., & Capmany, J. (2022). Microwave photonics. Science China Information Sciences, 65. https://doi.org/10.1007/s11432-021-3524-0
  • Duo, W., Zhou, M., & Abusorrah, A. (2022). A survey of cyber attacks on cyber-physical systems: Recent advances and challenges. IEEE/CAA Journal of Automatica Sinica, 9, 784-800. https://doi.org/10.1109/JAS.2022.105548
  • Abuhasel, K., Kchaou, M., Alquraish, M., Munusamy, Y., & Jeng, Y. T. (2021). Oily wastewater treatment: Overview of conventional and modern methods, challenges, and future opportunities. Water, 13, 980. https://doi.org/10.3390/w13070980
  • Wang, J., Tian, J., Zhang, X., Yang, B., Liu, S., Yin, L., & Zheng, W. (2022). Control of time delay force feedback teleoperation system with finite time convergence. Frontiers in Neurorobotics, 16. https://doi.org/10.3389/fnbot.2022.877069
  • Yang, T., Sun, N., & Fang, Y. (2021). Adaptive fuzzy control for a class of MIMO underactuated systems with plant uncertainties and actuator deadzones: Design and experiments. IEEE Transactions on Cybernetics, 52, 8213-8226. https://doi.org/10.1109/TCYB.2021.3050475
  • Bhatia, N. P., & Szegö, G. P. (1970). Stability theory of dynamical systems. Springer-Verlag. https://doi.org/10.1007/978-3-642-62006-5
  • LaSalle, J. P. (1976). The stability of dynamical systems. SIAM. https://doi.org/10.21236/ADA031020
  • Ziegler, J. G., & Nichols, N. B. (1942). Optimum settings for automatic controllers. Transactions of the ASME, 64, 759-768. https://doi.org/10.1115/1.4019264
  • Smith, O. J. M. (1959). A controller to overcome dead time. ISA Journal, 6, 28-33.
  • Hale, J. K., & Verduyn Lunel, S. M. (1993). Introduction to functional differential equations. Springer-Verlag. https://doi.org/10.1007/978-1-4612-4342-7
  • Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. SIAM. https://doi.org/10.1137/1.9781611970777
  • Richard, P. (2003). Time-delay systems: An overview of some recent advances and open problems. Automatica, 39(10), 1667-1694. https://doi.org/10.1016/S0005-1098(03)00167-5
  • Shen, C. C., & Zhong, S. M. (2009). New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties. Chaos, Solitons & Fractals, 40, 2277-2285. https://doi.org/10.1016/j.chaos.2007.10.020
  • Guo, L. D., Gu, H., & Zhang, D. (2010). Robust stability criteria for uncertain neutral system with interval time-varying discrete delay. Asian Journal of Control, 12(6), 739-745. https://doi.org/10.1002/asjc.251
  • Suplin, V., & Shaked, U. (2008). Robust H∞ output-feedback control of systems with time-delay. Systems & Control Letters, 57, 193-199. https://doi.org/10.1016/j.sysconle.2007.08.007
  • Arefi, M. M., Zarei, J., & Karimi, H. R. (2014). Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction. Journal of the Franklin Institute, 351(8), 4302-4316. https://doi.org/10.1016/j.jfranklin.2014.05.006
  • Yu, Z., & Li, S. (2014). Neural-network-based output-feedback adaptive dynamic surface control for a class of stochastic nonlinear time-delay systems with unknown control directions. Neurocomputing, 129, 540-547. https://doi.org/10.1016/j.neucom.2013.09.005
  • Koo, G. B., Park, J. B., & Joo, Y. H. (2014). Decentralized fuzzy observer-based output-feedback control for nonlinear large-scale systems: An LMI approach. IEEE Transactions on Fuzzy Systems, 22(2), 406-419. https://doi.org/10.1109/TFUZZ.2013.2259497
  • Gao, Q., Feng, G., Xi, Z., Wang, Y., & Jian, B. (2014). Robust H∞ control of T-S fuzzy time-delay systems via a new sliding mode control scheme. IEEE Transactions on Fuzzy Systems, 22(2), 459-465. https://doi.org/10.1109/TFUZZ.2013.2256914
  • Sheng, L., & Ma, X. (2014). Stability analysis and controller design of interval type-2 fuzzy systems with time delay. International Journal of Systems Science, 45(5), 977-993. https://doi.org/10.1080/00207721.2012.743056
  • Ganjefar, S., & Solgi, Y. (2015). A Lyapunov stable type-2 fuzzy wavelet network controller design for a bilateral teleoperation system. Information Sciences, 311, 1-17. https://doi.org/10.1016/j.ins.2015.03.036
  • Ruan, X., Ding, M., Gong, D., & Qiao, J. (2007). On-line adaptive control for inverted pendulum balancing based on feedback-error-learning. Neurocomputing, 70, 770-776. https://doi.org/10.1016/j.neucom.2006.10.012
  • Ideta, A. M. (2006). Stability of feedback error learning method with time delay. Neurocomputing, 69(13-15), 1645-1654. https://doi.org/10.1016/j.neucom.2005.04.011
  • Sabahi, K., Ghaemi, S., & Pezeshki, S. (2014). Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches. Applied Soft Computing, 21, 1-11. https://doi.org/10.1016/j.asoc.2014.02.022
  • Khanesar, M. A., Kaynak, O., Yin, S., & Gao, H. (2015). Adaptive indirect fuzzy sliding mode controller for networked control systems. IEEE Transactions on Fuzzy Systems, 23(1), 240-254. https://doi.org/10.1109/TFUZZ.2014.2362549
  • Biglarbegian, M., Melek, W., & Mendel, J. (2011). Design of novel interval type-2 fuzzy controllers for modular and reconfigurable robots. IEEE Transactions on Industrial Electronics, 58(4), 1371-1384. https://doi.org/10.1109/TIE.2010.2049718
  •  
Transactions on Machine Intelligence
Volume 5, Issue 3
Summer 2022
Pages 139-151

  • Receive Date 03 May 2022
  • Revise Date 11 July 2022
  • Accept Date 03 September 2022