$H_{\infty}$ control for discrete-time IT2 fuzzy system with infinite distributed-delay via Adaptive event-triggered scheme and its application

Document Type : Research Paper

Authors

1 Department of Mathematics, Thiruvalluvar University, Vellore - 632 106, Tamilnadu, India

2 Complex systems and Networked Science Lab, Department of Mathematics, Thiruvalluvar University, Vellore-632 115, Tamil Nadu, India.

3 Maejo university, Thailand.

4 Department of Mathematics, Faculty of Science and Technology, Rajabhat Phuket University, Phuket, Thailand

Abstract

This article investigates the $H_{\infty}$ control problem for discrete-time interval type-2 (IT2) fuzzy systems with infinite distributed delay via an adaptive event-triggered scheme. The IT2 T-S fuzzy system, which is a development over the (type-1) T-S fuzzy system, has greater effectiveness for the expression of system uncertainty, which will improve the difficulty of analysis. Our main goal is to make more efficient use of network resources by developing an adaptive event-triggered controller for interval type-2 fuzzy systems. In contrast to the traditional triggering method, an adaptive event-triggered technique is proposed to improve bandwidth consumption and network control performance. The triggering function's parameters are based on an adaptive law. Moreover, employing the Lyapunov functional method, the resultant criterion gives sufficient conditions to guarantee that discrete time IT2 fuzzy systems are mean-square exponentially stable with a $H_{\infty}$ performance. Finally, a single-link robot arm model and a DC motor are employed to show the usefulness and efficiency of the obtained theoretical results.

Keywords

Main Subjects

References

[1] M. S. Ali, Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters
and time-varying delays, International Journal of Machine Learning and Cybernetics, 5(1) (2014), 13-22.
[2] M. S. Aslam, X. Dai, T. Zhao, Stability and stabilization of network T-S fuzzy systems with random packet-loss for
synchronous machine, Iranian Journal of Fuzzy Systems, 18(1) (2021), 35-51.
[3] P. Balasubramaniam, L. J. Banu, Robust stability criterion for discrete-time nonlinear switched systems with
randomly occurring delays via T-S fuzzy approach, Information Sciences, 20(6) (2015), 49-61.
[4] B. Ding, B. Wang, R. Zhang, Event-triggered control for hybrid power supply of fuel-cell heavy-duty truck, Journal
of Energy Storage, 41 (2021), 102985.
[5] L. Fan, Q. Zhu, Mean square exponential stability of discrete-time Markov switched stochastic neural networks with
partially unstable subsystems and mixed delays, Information Sciences, 580 (2021), 243-259.
[6] M. Gao, L. Zhang, W. Qi, J. Cao, Security control for T-S fuzzy systems with multi-sensor saturations and
distributed event-triggered mechanism, Journal of the Franklin Institute, 357(5) (2020), 2851-2867.
[7] H. Gao, Y. Zhao, T. Chen, H1 fuzzy control of nonlinear systems under unreliable communication links, ISA
Transactions, 17(2) (2009), 96-104.
[8] A. Kazemy, J. Lam, Z. Chang, Adaptive event-triggered mechanism for networked control systems under deception
attacks with uncertain occurring probability, International Journal of Systems Science, 52(7) (2021), 1426-1439.
[9] B. A. Khashooei, D. J. Antunes, W. P. M. H. Heemels, Output-based event-triggered control with performance
guarantees, IEEE Transactions on Automatic Control, 62(7) (2017), 3646-3652.
[10] Q. Li, Y. Pan, Z. Zhang, H. K. Lam, Reliable dissipative interval type-2 fuzzy control for nonlinear systems with
stochastic incomplete communication route and actuator failure, International Journal of Fuzzy Systems, 22 (2020),
368-379.
[11] Z. Lian, P. Shi, C. C. Lim, Hybrid-triggered interval type-2 fuzzy control for networked systems under attacks,
Information Science, 567 (2021), 332-347.
[12] J. Liu, Q. Liu, J. Cao, Y. Zhang, Adaptive event-triggered H1  ltering for T-S fuzzy system with time delay,
Neurocomputing, 189 (2015), 86-94.
[13] Y. Liu, Z. Wang, J. Liang, X. Liu, Synchronization and state estimation for discrete-time complex networks with
distributed delays, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 38(5) (2008), 1314-1325.
[14] K. Mathiyalagan, R. Sakthivel, Robust stabilization and H1 control for discrete-time stochastic genetic regulatory
networks with time delays, Canadian Journal of Physics, 90(10) (2012), 939-953.
[15] M. Mubeen Tajudeen, M. S. Ali, S. A. Kauser, K. Subkrajang, A. Jirawattanapanit, G. Rajchakit, Adaptive event-
triggered control for complex dynamical network with random coupling delay under stochastic deception attacks,
Hindawi Complexity, (2022). DOI: 10.1155/2022/8761612.
[16] R. Pan, Y. Tana, D. Du, S. Fei, Adaptive event-triggered synchronization control for complex networks with quan-
tization and cyber-attacks, Neurocomputing, 382 (2020), 249-258.
[17] B. Priya, M. Mubeen Tajudeen, M. Syed Ali, G. Rajchakit, G. Kumar Thakur, Event-triggered H1 control of
complex dynamical networks subject to stochastic cyber-attacks by new two-sided delay-dependent LKF functional,
Journal of Control and Decision, (2023). DOI: 10.1080/23307706.2023.2240338.
[18] Z. Qu, Z. Du, G. Zhang, Sampled-data H1 control for nonlinear dynamical intelligent fuzzy systems with time-
varying delay, 2022 34th Chinese Control and Decision Conference (CCDC), (2022), 4077-4084.
[19] N. Rong, Z. Wang, State-dependent asynchronous intermittent control for IT2 T-S fuzzy interconnected systems
under deception attacks, Nonlinear Dynamics, 100 (2020), 3433-3448.
[20] A. W. A. Saif, M. Mudasar, M. Mysorewala, M. Elshafei, Observer-based interval type-2 fuzzy logic control for
nonlinear networked control systems with delays, International Journal of Fuzzy Systems, 22 (2020), 380-399.
[21] J. Sun, H. Zhang, Y. Wang, S. Sun, Fault-tolerant control for stochastic switched IT2 fuzzy uncertain time-delayed
nonlinear systems, IEEE Transactions on Cybernetics, 52(2) (2022), 1335-1346.
[22] J. Suo, Z. Wang, B. Shen, Pinning synchronization control for a class of discrete-time switched stochastic complex
networks under event-triggered mechanism, Nonlinear Analysis: Hybrid Systems, 37 (2020), 100886.
[23] M. Syed Ali, M. Mubeen Tajudeen, G. Rajchakit, B. Priya, G. Kumar Thakur, Adaptive event-triggered pinning
synchronization control for complex networks with random saturation subject to hybrid cyber-attacks, International
Journal of Adaptive Control and Signal Processing, 37(8) (2023), 2041-2062.
[24] J. Tao, R. Lu, P. Shi, H. Su, Z. G. Wu, Dissipativity-based reliable control for fuzzy Markov jump systems with
actuator faults, IEEE Transactions on Cybernetics, 47(9) (2017), 2377-2388.
[25] X. Wang, J. H. Park, H. Yang, Z. Yu, Sampled-data-based H1 fuzzy pinning synchronization of complex networked
systems with adaptive event-triggered communications, IEEE Transactions on Fuzzy Systems, 30(7) (2022), 2254-
2265.
[26] G. Wei, G. Feng, Z. Wang, Robust H1 control for discrete-time fuzzy systems with in nite-distributed delays, IEEE
Transactions on Fuzzy Systems, 17(1) (2009). DOI:10.1109/TFUZZ.2008.2006621.
[27] Y. Yan, C. Yang, X. Ma, L. Zhou, Observer-based event-triggered control for singularly perturbed systems with
saturating actuator, International Journal of Robust and Nonlinear Control, 29(12) (2019), 3954-3970.
[28] L. Yang, C. Guan, Z. Fei, Finite-time asynchronous  ltering for switched linear systems with an event-triggered
mechanism, Journal of the Franklin Institute, 356(10) (2015), 5503-5520.
[29] X. Yang, H. Wang, Q. Zhu, Event-triggered predictive control of nonlinear stochastic systems with output delay,
Automatica, 140 (2022), 110230.
[30] X. Yang, Q. Zhu, Stabilization of stochastic retarded systems based on sampled-data feedback control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(9) (2021), 5895-5904.
[31] Y. Zeng, H. K. Lam, B. Xiao, L. Wu, l2 - l∞ control of discrete-time state-delay interval type-2 fuzzy systems via
dynamic output feedback, IEEE Transactions on Cybernetics, 52(6) (2022), 4198-4208.
[32] H. Zhang, Q. Ma, J. Lu, Y. Chu, Y. Li, Synchronization control of neutralty neural networks with sampled-data
via adaptive event-triggered communication scheme, Journal of the Franklin Institute, 358(3) (2021), 1999-2014.
[33] S. Zhang, J. Zhao, Dwell-time-dependent H1 bumpless transfer control for discrete-time switched interval type-2
fuzzy systems, IEEE Transactions on Fuzzy Systems, 30(7) (2022), 2426-2437.
[34] D. Zhang, Z. Zhou, X. Ji, Networked fuzzy output feedback control for discrete-time Takagi-Sugeno fuzzy systems
with sensor saturation and measurement noise, Information Sciences, 457(8) (2018), 182-194.
[35] N. Zhao, P. Shi, W. Xing, C. P. Lim, Resilient adaptive event-triggered fuzzy tracking control and  ltering for
nonlinear networked systems under denial-of-service attacks, IEEE Transactions on Fuzzy Systems, 30(8) (2022),
3191-3201.
[36] Q. Zhu, Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered
feedback control, IEEE Transactions on Automatic Control, 64(9) (2019), 3764-3771.
Iranian Journal of Fuzzy Systems
Volume 21, Issue 1
January and February 2024
Pages 83-101

Files

Share

How to cite

Statistics