Dissipative control for singular Takagi-Sugeno fuzzy systems with random actuator failures

Xiaoqing Zhang; Lanlan He; Haohan Ni; Yebin Chen; Jianping Zhou

doi:10.3934/mfc.2024028

Article Contents

2025, Volume 8, Issue 5: 756-774. Doi: 10.3934/mfc.2024028

This issue Previous Article Total stability of outcome weighted learning Next Article A trainable variational Chan-Vese network based on algorithm unfolding for image segmentation

Dissipative control for singular Takagi-Sugeno fuzzy systems with random actuator failures

School of Computer Science & Technology, Anhui University of Technology, Ma'anshan 243032, China

^*Corresponding author: Jianping Zhou
^*Corresponding author: Jianping Zhou

Received: March 2024

Revised: June 2024

Early access: June 2024

Published: October 2025

Abstract / Introduction Full Text(HTML) Figure(5) / Table(2) Related Papers Cited by

Abstract

This paper addresses the dissipative control issue of the singular Takagi-Sugeno fuzzy system. The aim is to develop a fuzzy controller to handle random actuator failures, which ensures the closed-loop system is admissible and dissipative. A Bernoulli-distributed random variable is introduced to characterize the random occurrence of actuator failures. A sufficient condition that guarantees the admissibility and dissipativity of the closed-loop system is established by using the Lyapunov functional, free-weight matrix method, and inequality method. Subsequently, a design approach for fuzzy controller gains with an adjustable parameter is provided, where the adjustable parameter plays a crucial role in expanding the solution space. On this basis, an improved iterative algorithm for determining the fuzzy controller gains is given, which fully leverages the adjustable parameter. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

Keywords:

Mathematics Subject Classification: Primary: 93C42, 34K20; Secondary: 93D05.

Citation:

Full Text(HTML)

Figure 1. The trajectories of the STSFS states with $ u^{F} (t) = 0 $

Download: Full-size image PowerPoint slide

Figure 2. The trajectories of CLS states

Download: Full-size image PowerPoint slide

Figure 3. The trajectory of $ \delta(t) $

Download: Full-size image PowerPoint slide

Figure 4. The trajectories of CLS states

Download: Full-size image PowerPoint slide

Figure 5. The trajectory of $ \delta(t) $

Download: Full-size image PowerPoint slide

Table 1. List of abbreviations

Abbreviation	Description
SS	Singular system
T-S	Takagi-Sugeno
STSFS	Singular T-S fuzzy system
MF	Membership function
AF	Actuator failure
DC	Dissipative control
IA	Iterative algorithm
LF	Lyapunov functional
CLS	Closed-loop system
FCG	Fuzzy controller gain
SD	Strictly $ (W_{1}, W_{2}, W_{3}) $ - $ \delta $ - dissipative

| Show Table

DownLoad: CSV

Table 2. FCGs calculated by different algorithms in [5]

Algorithms	FCGs
Algorithms	$ \delta=3.7 $	$ \delta=3.8 $	$ \delta=3.9 $	$ \delta=4.0 $	$ \delta=4.1 $
Algorithm 1 in [5]	√	√	√	×	×
Algorithm 1	√	√	√	√	√

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

[1]	K. Badie, Z. Chalh and M. Alfidi, Output tracking control for 2-D discrete systems with actuator failures, Optimal Control Applications and Methods, 44 (2023), 2517-2531. doi: 10.1002/oca.2990.
[2]	W.-J. Chang, M.-H. Tsai and C.-L. Pen, Observer-based fuzzy controller design for nonlinear discrete-time singular systems via proportional derivative feedback scheme, Applied Sciences, 11 (2021), 2833. doi: 10.3390/app11062833.
[3]	X.-H. Chang, J. Wang and X. Zhao, Peak-to-peak filtering for discrete-time singular systems, IEEE Transactions on Circuits and Systems II: Express Briefs, 68 (2021), 2543-2547. doi: 10.1109/TCSII.2021.3049840.
[4]	J. Chen, J. Yu and H.-K. Lam, New admissibility and admissibilization criteria for nonlinear discrete-time singular systems by switched fuzzy models, IEEE Transactions on Cybernetics, 52 (2022), 9240-9250. doi: 10.1109/TCYB.2021.3057127.
[5]	Z. Feng, H. Zhang and H.-K. Lam, New results on dissipative control for a class of singular Takagi–Sugeno fuzzy systems with time delay, IEEE Transactions on Fuzzy Systems, 30 (2022), 2466-2475. doi: 10.1109/TFUZZ.2021.3086227.
[6]	C. Ge, Z. Zhang, L. Wang and Y. Liu, Novel stability criteria for sampled-data T-S fuzzy systems with actuator failures, International Journal of Fuzzy Systems, 25 (2023), 940-949. doi: 10.1007/s40815-022-01380-2.
[7]	Y. Han and S. Zhou, Novel criteria of stochastic stability for discrete-time Markovian jump singular systems via supermartingale approach, IEEE Transactions on Automatic Control, 67 (2022), 6940-6947. doi: 10.1109/TAC.2022.3200949.
[8]	J. Hu, J. Liang and D. Chen, Reliable guaranteed-cost control for networked systems with randomly occurring actuator failures and fading performance output, International Journal of General Systems, 44 (2015), 129-141. doi: 10.1080/03081079.2014.973724.
[9]	R. Kavikumar, R. Sakthivel, B. Kaviarasan, O. M. Kwon and S. Marshal Anthoni, Non-fragile control design for interval-valued fuzzy systems against nonlinear actuator faults, Fuzzy Sets and Systems, 365 (2019), 40-59. doi: 10.1016/j.fss.2018.04.004.
[10]	M. Li, X. Chen, M. Liu, Y. Zhang and H. Zhang, Asynchronous adaptive fault-tolerant sliding-mode control for T-S fuzzy singular Markovian jump systems with uncertain transition rates, IEEE Transactions on Cybernetics, 52 (2022), 544-555. doi: 10.1109/TCYB.2020.2981158.
[11]	R. Li and Y. Yang, Fault-tolerant control for TS fuzzy stochastic singular systems, IEEE Transactions on Fuzzy Systems, 29 (2021), 3925-3935. doi: 10.1109/TFUZZ.2020.3029303.
[12]	Y. Li and Y. He, Improved admissibility analysis of Takagi–Sugeno fuzzy singular systems with time-varying delays, IEEE Transactions on Fuzzy Systems, 30 (2022), 4766-4774. doi: 10.1109/TFUZZ.2022.3159957.
[13]	Z. Li, H. Yan, H. Zhang, X. Zhan and C. Huang, Improved inequality-based functions approach for stability analysis of time delay system, Automatica, 108 (2019), 108416. doi: 10.1016/j.automatica.2019.05.033.
[14]	R.-R. Liu, X.-H. Chang, Z. Chen, Z.-M. Li, W.-H. Huang and J. Xiong, Dissipative control for switched nonlinear singular systems with dynamic quantization, Communications in Nonlinear Science and Numerical Simulation, 127 (2023), 107551. doi: 10.1016/j.cnsns.2023.107551.
[15]	Y. Ma and C. Kong, Dissipative asynchronous T-S fuzzy control for singular semi-Markovian jump systems, IEEE Transactions on Cybernetics, 52 (2022), 5454-5463. doi: 10.1109/TCYB.2020.3032398.
[16]	K. Ouarid, M. Essabre, A. E. Assoudi and E. H. E. Yaagoubi, State and fault estimation based on fuzzy observer for a class of Takagi-Sugeno singular models, Indonesian Journal of Electrical Engineering and Computer Science, 25 (2022), 172-182. doi: 10.11591/ijeecs.v25.i1.pp172-182.
[17]	P. Park, W. I. Lee and S. Y. Lee, Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, Journal of the Franklin Institute, 352 (2015), 1378-1396. doi: 10.1016/j.jfranklin.2015.01.004.
[18]	M.-Y. Qiao and X.-H. Chang, Quantified guaranteed cost fault-tolerant control for continuous-time fuzzy singular systems with sensor and actuator faults, IEEE Transactions on Fuzzy Systems, 32 (2024), 660-670. doi: 10.1109/TFUZZ.2023.3303624.
[19]	S. Rathinasamy, M. Rathika, B. Kaviarasan and H. Shen, Stabilization criteria for singular fuzzy systems with random delay and mixed actuator failures, Asian Journal of Control, 20 (2018), 829-838. doi: 10.1002/asjc.1600.
[20]	J. Ren, G. He and J. Fu, Robust $H_{\infty}$ sliding mode control for nonlinear stochastic T-S fuzzy singular Markovian jump systems with time-varying delays, Information Sciences, 535 (2020), 42-63. doi: 10.1016/j.ins.2020.05.029.
[21]	R. Saravanakumar, A. Amini, R. Datta and Y. Cao, Reliable memory sampled-data consensus of multi-agent systems with nonlinear actuator faults, IEEE Transactions on Circuits and Systems II: Express Briefs, 69 (2022), 2201-2205. doi: 10.1109/TCSII.2021.3124043.
[22]	H. Shen, M. Xing, Z.-G. Wu and J. H. Park, Fault-tolerant control for fuzzy switched singular systems with persistent dwell-time subject to actuator fault, Fuzzy Sets and Systems, 392 (2020), 60-76. doi: 10.1016/j.fss.2019.08.011.
[23]	R. Suresh, S. Saravanan, H. Dutta, R. Vadivel and N. Gunasekaran, Extended dissipativity-based sampled-data controller design for fuzzy distributed parameter systems, Mathematical Foundations of Computing, 2024. doi: 10.3934/mfc.2024006.
[24]	G. Tan and Z. Wang, Reachable set estimation of delayed Markovian jump neural networks based on an improved reciprocally convex inequality, IEEE Transactions on Neural Networks and Learning Systems, 33 (2022), 2737-2742. doi: 10.1109/TNNLS.2020.3045599.
[25]	G. Tao, S. Chen, X. Tang and S. M. Joshi, Adaptive Control of Systems with Actuator Failures, 1$^{nd}$ edition, Springer, London, 2004. doi: 10.1007/978-1-4471-3758-0.
[26]	J. Wang, Q. Gong, K. Huang, Z. Liu, C. L. Philip Chen and J. Liu, Event-triggered prescribed settling time consensus compensation control for a class of uncertain nonlinear systems with actuator failures, IEEE Transactions on Neural Networks and Learning Systems, 34 (2023), 5590-5600. doi: 10.1109/TNNLS.2021.3129816.
[27]	J. Wang, Y. Yan, Z. Liu, C. L. Philip Chen, C. Zhang and K. Chen, Finite-time consensus control for multi-agent systems with full-state constraints and actuator failures, Neural Networks, 157 (2023), 350-363. doi: 10.1016/j.neunet.2022.10.028.
[28]	J. C. Willems, Dissipative dynamical systems, European Journal of Control, 13 (2007), 134-151. doi: 10.3166/ejc.13.134-151.
[29]	Z.-G. Wu, H. Su, P. Shi and J. Chu, Analysis and Synthesis of Singular Systems with Time-delays, 1$^{nd}$ edition, Springer, Berlin, 2013. doi: 10.1007/978-3-642-37497-5.
[30]	L. Xie, M. Fu, C. E. de Souza, et al. $H_{\infty}$ control and quadratic stabilization of systems with parameter uncertainty via output feedback, IEEE Transactions on Automatic Control, 37 (1992), 1253-1256. doi: 10.1109/9.151120.
[31]	S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, 1$^{nd}$ edition, Springer, Berlin, 2006. doi: 10.1007/11375753.
[32]	X. Yao, L. Wu and W. X. Zheng, Fault detection filter design for Markovian jump singular systems with intermittent measurements, IEEE Transactions on Signal Processing, 59 (2011), 3099-3109. doi: 10.1109/TSP.2011.2141666.
[33]	C.-K. Zhang, Y. He, L. Jiang and M. Wu, Notes on stability of time-delay systems: Bounding inequalities and augmented Lyapunov-Krasovskii functionals, IEEE Transactions on Automatic Control, 62 (2017), 5331-5336. doi: 10.1109/TAC.2016.2635381.
[34]	J. Zhang, D. Liu and Y. Ma, Finite-time dissipative control of uncertain singular T–S fuzzy time-varying delay systems subject to actuator saturation, Computational and Applied Mathematics, 39 (2020), 1-22. doi: 10.1007/s40314-019-0964-8.
[35]	L. Zhang, X. Zhao and N. Zhao, Real-time reachable set control for neutral singular Markov jump systems with mixed delays, IEEE Transactions on Circuits and Systems II: Express Briefs, 69 (2022), 1367-1371. doi: 10.1109/TCSII.2021.3118075.
[36]	X. Zhang and Z. Wang, Alternative criteria for admissibility and stabilization of singular fractional order systems, Mathematical Foundations of Computing, 2 (2019), 267-277. doi: 10.3934/mfc.2019017.
[37]	Y. Zhang, Z. Jin and Q. Zhang, Impulse elimination of the Takagi–Sugeno fuzzy singular system via sliding-mode control, IEEE Transactions on Fuzzy Systems, 30 (2022), 1164-1174. doi: 10.1109/TFUZZ.2021.3053325.
[38]	J. Zhou, J. Dong and S. Xu, Asynchronous dissipative control of discrete-time fuzzy Markov jump systems with dynamic state and input quantization, IEEE Transactions on Fuzzy Systems, 31 (2023), 3906-3920. doi: 10.1109/TFUZZ.2023.3271348.
[39]	J. Zhou, J. Dong, S. Xu and C. K. Ahn, Input-to-state stabilization for Markov jump systems with dynamic quantization and multimode injection attacks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 54 (2024), 2517-2529. doi: 10.1109/TSMC.2023.3344869.