Journal of Applied Science and Engineering

Published by Tamkang University Press

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Weiwei Tong and Shaohui WangThis email address is being protected from spambots. You need JavaScript enabled to view it.

College of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454003


Received: January 17, 2023
Accepted: August 12, 2023
Publication Date: November 4, 2023

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.


Download Citation: ||https://doi.org/10.6180/jase.202407_27(7).0005  


An important research gap in the field of switched systems is the design of fault tolerant control for Lipschitz non-linear delayed switched systems using a model predictive method. This study addresses this gap by taking into account the failure of the actuators and develops a fault-tolerant model predictive control technique for the non-linear delayed Lipschitz switched systems with arbitrary switching signal to asymptotically stabilize the closed-loop system. The non-convex optimization issue is phrased as a linear matrix inequality optimization problem and a set of novel stability criteria are derived by taking into account the cost function with infinite predictive horizon and input limitation and employing switched Lyapunov-Krasovskii functional. The success of the suggested scheme is then evaluated using a computer simulation of a system that causes water pollution. The results support the proposed scheme’s successful execution.


Keywords: Lipschitz non-linear delayed switched systems, fault tolerant control, model predictive control, switched Lyapunov-Krasovskii functional, arbitrary switching signal, linear matrix inequality


  1. [1] Z. Sun. Switched linear systems: control and design. Springer Science & Business Media, 2006.
  2. [2] Z. Sun and S. S. Ge, (2011) “Stability theory of switched dynamical systems": DOI: 10.1007/978-0-85729-256-8.
  3. [3] H. Yang, B. Jiang, and V. Cocquempot, (2014) “A survey of results and perspectives on stabilization of switched nonlinear systems with unstable modes" Nonlinear Analysis: Hybrid Systems 13: 45–60. DOI: 10.1016/j.nahs.2013.12.005.
  4. [4] S. Saki and H. Bolandi, (2018) “Optimal direct adaptive soft switching multi-model predictive control using the gap metric for spacecraft attitude control in a wide range of operating points" Aerospace science and technology 77: 235–243. DOI: 10.1016/j.ast.2018.03.001.
  5. [5] M. J. Park, O. M. Kwon, and S. G. Choi, (2017) “Stability analysis of discrete-time switched systems with time-varying delays via a new summation inequality" Nonlinear Analysis: Hybrid Systems 23: 76–90. DOI: 10.1016/j.nahs.2016.08.001.
  6. [6] N. A. Baleghi and M. H. Shafiei, (2018) “Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties" Transactions of the Institute of Measurement and Control 40(4): 1150–1157. DOI: 10.1177/014233121667806.
  7. [7] M. Kermani and A. Sakly, (2018) “On robust stability analysis of uncertain discrete-time switched nonlinear systems with time varying delays" Mathematical Problems in Engineering 2018: 1–14. DOI: 10.1155/2018/6354979.
  8. [8] D. Wang, P. Shi, J. Wang, and W. Wang, (2012) “Delay-dependent exponential H∞ filtering for discretetime switched delay systems" International Journal of Robust and Nonlinear Control 22(13): 1522–1536. DOI: 10.1109/TCYB.2014.2332356.
  9. [9] E. Tian, W. K. Wong, D. Yue, and T.-C. Yang, (2015) “H∞ Filtering for Discrete-Time Switched Systems With Known Sojourn Probabilities" IEEE Transactions on Automatic Control 60(9): 2446–2451. DOI: 10.1109/TAC.2015.2409909.
  10. [10] Y. Dong, S. Liang, and H. Wang, (2019) “Robust stability and H∞ control for nonlinear discrete-time switched systems with interval time-varying delay" Mathematical Methods in the Applied Sciences 42(6): 1999–2015. DOI: 10.1002/mma.5493.
  11. [11] L. Zhang, P. Shi, and E.-K. Boukas, (2007) “H∞ outputfeedback control for switched linear discrete-time systems with time-varying delays" International Journal of Control 80(8): 1354–1365. DOI: 10.1080/00207170701377113.
  12. [12] L. Zhang, H. Li, and Y. Chen, (2010) “Robust stability analysis and synthesis for switched discrete-time systems with time delay" Discrete Dynamics in Nature and Society 2010: DOI: 10.1155/2010/408105.
  13. [13] D. Du, B. Jiang, and S. Zhou, (2008) “Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay" International Journal of Systems Science 39(3): 305–313. DOI: 10.1080/00207720701805982.
  14. [14] L. Zhang, P. Shi, and M. Basin, (2008) “Robust stability and stabilisation of uncertain switched linear discrete timedelay systems" IET Control Theory & Applications 2(7): 606–614. DOI: 10.1049/iet-cta:20070327.
  15. [15] Z. Xiang and R. Wang, (2011) “Robust stabilization of discrete time switched non-linear systems with time delay under asynchronous switching" Transactions of the Institute of Measurement and Control 33(5): 591– 609. DOI: 10.1177/0142331210371815.
  16. [16] N. A. Baleghi and M. H. Shafiei, (2018) “Design of static and dynamic output feedback controllers for a discrete-time switched non-linear system with timevarying delay and parametric uncertainty" IET Control Theory & Applications 12(11): 1635–1643. DOI: 10.1049/iet-cta.2017.1203.
  17. [17] X. Yu-Geng, L. De-Wei, and L. Shu, (2013) “Model predictive control—status and challenges" Acta Automatica Sinica 39(3): 222–236. DOI: 10.1016/S1874- 1029(13)60024-5.
  18. [18] M. Benallouch, G. Schutz, D. Fiorelli, and M. Boutayeb, (2014) “H∞ model predictive control for discrete-time switched linear systems with application to drinking water supply network" Journal of Process Control 24(6): 924–938. DOI: 10.1016/j.jprocont.2014.04.008.
  19. [19] X. Song and X. Liu. “Mixed H2/H∞ model predictive control for a class of switched singular systems”. In: 2016 Chinese Control and Decision Conference (CCDC). IEEE, 2016, 2236–2241. DOI: 10.1109/CCDC.2016.7531357.
  20. [20] L. Zhang, S. Zhuang, and R. D. Braatz, (2016) “Switched model predictive control of switched linear systems: Feasibility, stability and robustness" Automatica 67: 8–21. DOI: 10.1016/j.automatica.2016.01.010.
  21. [21] M. Aminsafaee and M. H. Shafiei, (2019) “Stabilization of uncertain nonlinear discrete-time switched systems with state delays: A constrained robust model predictive control approach" Journal of Vibration and Control 25(14): 2079–2090. DOI: 10.1177/1077546319849285.
  22. [22] A. Taghieh and M. H. Shafiei, (2021) “Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties" Journal of Vibration and Control 27(17-18): 1939–1955. DOI: 10.1177/1077546320950523.
  23. [23] A. Shokrollahi and S. Shamaghdari, (2021) “Robust H∞ model predictive control for constrained Lipschitz nonlinear systems" journal of process control 104: 101–111. DOI: 10.1016/j.jprocont.2021.06.007.
  24. [24] I. Nodozi and M. Rahmani, (2017) “LMI-based model predictive control for switched nonlinear systems" Journal of Process Control 59: 49–58. DOI: 10.1016/j.jprocont.2017.09.001.


    



 

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