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Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system

Year 2023, , 1282 - 1302, 31.10.2023

Muhammad Shamrooz Aslam , Zhenhua Ma

https://doi.org/10.15672/hujms.1017898
Cited By: 8

Abstract

This article studies $H_{\infty}$ control problem based on the event--triggered scheme with time delays for the synchronization of an chaotic system represented by delayed Takagi--Sugeno models. Firstly, this method depending on two scenarios: a) Each local subsystem integrated that the delayed T-S fuzzy model for the same value of input matrices for the networked system and b) This is near steady-state zero-error diversification has to all be the same local subsystems. Generally, in the case of fuzzy regulation, these in lieu of generating the fuzzy regulator as a result of linear local controllers, circumstances were adjusted by addressing the issue of fuzzy regulation for the delayed Takagi--Sugeno models fuzzy model. Then, a delayed Takagi--Sugeno uses a fuzzy system to model the non--linear regulator. On the other hand, communication delays are a vital factor that cannot be ignored. To tackle the networked induced delay initially, author attempt to implement the event--triggered scheme for output regulation which reduce the cost of network transmission. By constructing a Lyapunov functional and making use of event--triggered method, some suitable circumstances that ensure asymptotic stability of $H_{\infty}$ performance index for the resulting model were derived. Additionally, as the variations of the aforementioned results, two scenarios were presented. Our developed approaches are demonstrated by a final example illustrating their superiority, usefulness and reliability.

Keywords

Event-triggered scheme fuzzy output regulation delayed T–S fuzzy system Francis equations

Supporting Institution

Starting PhD fund

Project Number

20z14

References

  • [1] M. Abdelrahim, R. Postoyan, J. Daafouz and D. Nesic, Robust event–triggered output feedback controllers for nonlinear systems, Automatica 75, 96–108, 2017.
  • [2] R.J. Anderson and M.W. Spong, Bilateral control of teleoperators with time delay, IEEE Trans. Automat. Contr. 34 (5), 494–501, 1989.
  • [3] P. Antsaklis and J. Baillieul, Special issue on technology of networked control systems, Proc. IEEE 95 (1), 5–8, 2007.
  • [4] K. Astrom and B. Bernhardsson, Comparison of periodic and event based sampling for first–order stochastic systems, IFAC Proc. 32 (2) 5006–5011, 1999.
  • [5] C.I. Byrnes and A. Isidori, Output regulation for nonlinear systems: An overview, Int. J. Robust Nonlinear Control. 10 (5), 323–337, 2000.
  • [6] R. Caponetto, A. Pisano and E. Usai, Second order sliding mode approaches to fault detection and control of infinite dimensional systems, Proc. ECC in Strasbourg, 2297–2303, France, 2014.
  • [7] X. Chen and Z. Chen, Robust sampled–data output synchronization of nonlinear heterogeneous multi–agents, IEEE Trans. Automat. Contr. 62 (3), 1458–1464, 2016.
  • [8] W. Chen, Z. Fei, X. Zhao and S. Ren, Event–triggered asynchronous control for switched T–S fuzzy systems based on looped functionals,J Franklin Inst 359 (12), 6311–6335 2022.
  • [9] T.S. Chiang, C.S. Chiu and P. Liu, Robust fuzzy integral regulator design for a class of affine nonlinear systems, IEICE T FUND ELECTR E89–A (4), 1100–1107, 2006.
  • [10] J. Dai and G. Guo, Event-triggered leader–following consensus for multi-agent systems with semi–Markov switching topologies, Inf. Sci. 459, 290–301, 2018.
  • [11] S. Ding and Z. Wang, Event–triggered synchronization of discrete–time neural networks: A switching approach, Neural Netw 125, 31–40, 2020.
  • [12] B.A. Francis, The linear multivariable regulator problem, SIAM J Control Optim 15, 486–505, 1977.
  • [13] W. Gao, Z. Jiang, F.L. Lewis and Y. Wang, Leader-to-formation stability of multiagent systems: An adaptive optimal control approach, IEEE Trans. Automat. Contr. 63 (10), 3581–3587, 2018.
  • [14] N. Gnaneswaran and Y.H. Joo, Event–triggered stabilisation for T–S fuzzy systems with asynchronous premise constraints and its application to wind turbine system, IET Control. Theory Appl. 13 (10), 1532–1542 2019.
  • [15] W. Gong, J. Liang and J. Cao, Matrix measure method for global exponential stability of complex–valued recurrent neural networks with time–varying delays, Neural Netw 70, 81–89, 2015.
  • [16] J. Hespanha, P. Naghshtabrizi and Y. Xu, A survey of recent results in networked control systems,Proc. IEEE 95 (1), 138–162, 2007.
  • [17] A. Hirose, Continuous complex-valued back–propagation learning, Electronics Letter 28 (20), 1854–1855, 1992.
  • [18] A. Isidori, Nonlinear Control Systems, Berlin, Germany: Springer-Verlag, 1995.
  • [19] A. Isidori and C.I. Byrnes, Output regulation of nonlinear systems, IEEE Trans. Automat. Contr. 35 (2), 131–140, 1990.
  • [20] S. Jankowski, A. Lozowski and J.M. Zurada, Complex–valued multistate neural associative memory, IEEE trans. neural netw. 7 (6), 1491–1496, 1996.
  • [21] I. Karafyllis and M. Krstic, Nonlinear stabilization under sampled and delayed measurements, and with inputs subject to delay and zero-order hold, IEEE Trans. Automat. Contr. 57 (5), 1141–1154, 2012.
  • [22] M. Kobayashi, Singularities of three–layered complex–valued neural networks with split activation function, IEEE Transactions on Neural Networks and Learning Systems, 29 (5), 1900–1907, 2018.
  • [23] J. K¨ohler, M.A. M¨uller and F. Allg¨ower, Constrained nonlinear output regulation using model predictive control, IEEE Trans. Automat. Contr. 67 (5), 2419–2434, 2022.
  • [24] K. Lian and J. Liou, Output tracking control for fuzzy systems via output feedback design, IEEE Trans Fuzzy Syst 14 (5), 28–639, 2006.
  • [25] Y. Liang and H. Zhang, Cooperative tracking control and regulation for a class of multi-agent systems, Singapore: Springer-Verlag. Lunze, 2019.
  • [26] X. Liu and Z. Li, Finite time anti–synchronization of complex–valued neural networks with bounded asynchronous time–varying delays, Neurocomputing 387, 129–138, 2020.
  • [27] W. Liu, C.C. Lim, P. Shi and S. Xu, Backstepping fuzzy adaptive control for a class of quantized nonlinear systems, IEEE Trans Fuzzy Syst 25 (5), 2017.
  • [28] D. Liu, S. Xue, B. Zhao, B. Luo and Q. Wei, Adaptive dynamic programming for control: A survey and recent advances, IEEE Trans. Syst. Man Cybern. Syst. 51 (1), 142–160, 2021.
  • [29] V. Loia, S. Tomasiello, A. Vaccaro and J. Gao, Using local learning with fuzzy transform: application to short term forecasting problems, Fuzzy Optim. Decis. Mak. 19, 13–32, 2020.
  • [30] S. Lu, J. Pei, X. Liu and P. Pardalos, Robust parallel–batching scheduling with fuzzy deteriorating processing time and variable delivery time in smart manufacturing, Fuzzy Optim. Decis. Mak. 19, 333–357, 2020.
  • [31] K. Mathiyalagan and G. Sangeetha, Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control, J Franklin Inst 356 (7), 3948–3964, 2019.
  • [32] J.A. Meda-Campana and B. Castillo–Toledo, The optimal fuzzy robust regulator for T–S discrete–time systems: An LMI approach, Int J Adapt Control Signal Process 23, 837–862, 2009.
  • [33] J.A. Meda-Campana, B. Castillo-Toledo and G. Chen, Synchronization of chaotic systems from a fuzzy regulation approach, Fuzzy Sets Syst 160, 860–2875, 2009.
  • [34] J.A. Meda-Campana, B. Castillo–Toledo and V. Zuniga, On the nonlinear fuzzy regulation for under–actuated systems, Proc. IEEE Int. Conf. Fuzzy Syst. Vancouver, BC, Canada, Jul. 16–21, 2195–2202, 2016.
  • [35] J.A. Meda–Campana, J.C. Gomez–Mancilla and B. Castillo-Toledo, Exact output regulation for nonlinear systems described by Takagi-Sugeno fuzzy models, IEEE Trans Fuzzy Syst 20 (2), 235–247, 2012.
  • [36] Y. Pan and G.H. Yang, Event–triggered fuzzy control for nonlinear networked control systems, Fuzzy Sets Syst 15 (329),91–107, 2017.
  • [37] K.S. Phogat and D.E. Chang, Model predictive regulation on manifolds in Euclidean space, Sensors 22 (14), 5170, 2022.
  • [38] R. Sakthivel, S. Selvi, K. Mathiyalagan and P. Shi, Reliable mixed H1 and passivity– based control for fuzzy Markovian switching systems with probabilistic time delays and actuator failures, IEEE Trans Cybern 45 (12), 2720–2731, 2015.
  • [39] X. Shi, A. Emrouznejad, M. Jin and F. Yang, A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory, Fuzzy Optim. Decis. Mak. 19, 311–332, 2020.
  • [40] Y. Shu, B. Li and Y. Zhu, Optimal control for uncertain discrete–time singular systems under expected value criterion, Fuzzy Optim. Decis. Mak. 20, 331–364, 2021.
  • [41] R. Sriraman, Y. Cao and R. Samidurai, Global asymptotic stability of stochastic complex–valued neural networks with probabilistic time–varying delays, Math Comput Simul 171, 103–118, 2020.
  • [42] Z. Su, C. Qian and Y. Hao, Global stabilization via sampled–data output feedback for large–scale systems interconnected by inherent nonlinearities, Automatica 92 (92), 254–258, 2018.
  • [43] Y. Sunaga, R. Natsuaki and A. Hirose, Land form classification and similar land– shape discovery by using complex–valued convolutional neural networks, IEEE Trans Neural Netw Learn Syst 57 (10), 907–7917, 2019.
  • [44] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern. Syst. 15 (1), 116–132, 1985.
  • [45] K. Tanaka and H.O. Wang, Fuzzy Control Systems Design and Analysis, A Linear Matrix Inequality Approach, New York: Wiley, 2001.
  • [46] E. Tian, D. Yue, T. Cheng Yang, Z. Gu and G. Lu, T–S fuzzy model-based robust stabilization for networked control systems with probabilistic sensor and actuator failure, IEEE Trans Fuzzy Syst 19 (3), 553–561, 2011.
  • [47] W. Yang, J. Xia, X. Guo, M. Yu and N. Zhang, Adaptive decentralized event-triggered tracking control for large–scale strongly interconnected nonlinear system with global performance, Int J Control Autom Syst, Doi: 10.1007/s12555-022-0134-4, 1–13, 2022.
  • [48] X.M. Zhang and Q.L. Han, Event–triggered mixed H1 and passive control of linear systems via dynamic output feedback, IECON 2013–39-th Annual Conference of the IEEE Industrial Electronics Society, 5080–5085, 2013.
  • [49] J. Zhang, C. Peng, D. Du and M. Zheng, Adaptive event–triggered communication scheme for networked control systems with randomly occurring nonlinearities and uncertainties, Neurocomputing 174, 475–482, 2016.

Year 2023, , 1282 - 1302, 31.10.2023

Muhammad Shamrooz Aslam , Zhenhua Ma

https://doi.org/10.15672/hujms.1017898
Cited By: 8

Abstract

Project Number

20z14

References

  • [1] M. Abdelrahim, R. Postoyan, J. Daafouz and D. Nesic, Robust event–triggered output feedback controllers for nonlinear systems, Automatica 75, 96–108, 2017.
  • [2] R.J. Anderson and M.W. Spong, Bilateral control of teleoperators with time delay, IEEE Trans. Automat. Contr. 34 (5), 494–501, 1989.
  • [3] P. Antsaklis and J. Baillieul, Special issue on technology of networked control systems, Proc. IEEE 95 (1), 5–8, 2007.
  • [4] K. Astrom and B. Bernhardsson, Comparison of periodic and event based sampling for first–order stochastic systems, IFAC Proc. 32 (2) 5006–5011, 1999.
  • [5] C.I. Byrnes and A. Isidori, Output regulation for nonlinear systems: An overview, Int. J. Robust Nonlinear Control. 10 (5), 323–337, 2000.
  • [6] R. Caponetto, A. Pisano and E. Usai, Second order sliding mode approaches to fault detection and control of infinite dimensional systems, Proc. ECC in Strasbourg, 2297–2303, France, 2014.
  • [7] X. Chen and Z. Chen, Robust sampled–data output synchronization of nonlinear heterogeneous multi–agents, IEEE Trans. Automat. Contr. 62 (3), 1458–1464, 2016.
  • [8] W. Chen, Z. Fei, X. Zhao and S. Ren, Event–triggered asynchronous control for switched T–S fuzzy systems based on looped functionals,J Franklin Inst 359 (12), 6311–6335 2022.
  • [9] T.S. Chiang, C.S. Chiu and P. Liu, Robust fuzzy integral regulator design for a class of affine nonlinear systems, IEICE T FUND ELECTR E89–A (4), 1100–1107, 2006.
  • [10] J. Dai and G. Guo, Event-triggered leader–following consensus for multi-agent systems with semi–Markov switching topologies, Inf. Sci. 459, 290–301, 2018.
  • [11] S. Ding and Z. Wang, Event–triggered synchronization of discrete–time neural networks: A switching approach, Neural Netw 125, 31–40, 2020.
  • [12] B.A. Francis, The linear multivariable regulator problem, SIAM J Control Optim 15, 486–505, 1977.
  • [13] W. Gao, Z. Jiang, F.L. Lewis and Y. Wang, Leader-to-formation stability of multiagent systems: An adaptive optimal control approach, IEEE Trans. Automat. Contr. 63 (10), 3581–3587, 2018.
  • [14] N. Gnaneswaran and Y.H. Joo, Event–triggered stabilisation for T–S fuzzy systems with asynchronous premise constraints and its application to wind turbine system, IET Control. Theory Appl. 13 (10), 1532–1542 2019.
  • [15] W. Gong, J. Liang and J. Cao, Matrix measure method for global exponential stability of complex–valued recurrent neural networks with time–varying delays, Neural Netw 70, 81–89, 2015.
  • [16] J. Hespanha, P. Naghshtabrizi and Y. Xu, A survey of recent results in networked control systems,Proc. IEEE 95 (1), 138–162, 2007.
  • [17] A. Hirose, Continuous complex-valued back–propagation learning, Electronics Letter 28 (20), 1854–1855, 1992.
  • [18] A. Isidori, Nonlinear Control Systems, Berlin, Germany: Springer-Verlag, 1995.
  • [19] A. Isidori and C.I. Byrnes, Output regulation of nonlinear systems, IEEE Trans. Automat. Contr. 35 (2), 131–140, 1990.
  • [20] S. Jankowski, A. Lozowski and J.M. Zurada, Complex–valued multistate neural associative memory, IEEE trans. neural netw. 7 (6), 1491–1496, 1996.
  • [21] I. Karafyllis and M. Krstic, Nonlinear stabilization under sampled and delayed measurements, and with inputs subject to delay and zero-order hold, IEEE Trans. Automat. Contr. 57 (5), 1141–1154, 2012.
  • [22] M. Kobayashi, Singularities of three–layered complex–valued neural networks with split activation function, IEEE Transactions on Neural Networks and Learning Systems, 29 (5), 1900–1907, 2018.
  • [23] J. K¨ohler, M.A. M¨uller and F. Allg¨ower, Constrained nonlinear output regulation using model predictive control, IEEE Trans. Automat. Contr. 67 (5), 2419–2434, 2022.
  • [24] K. Lian and J. Liou, Output tracking control for fuzzy systems via output feedback design, IEEE Trans Fuzzy Syst 14 (5), 28–639, 2006.
  • [25] Y. Liang and H. Zhang, Cooperative tracking control and regulation for a class of multi-agent systems, Singapore: Springer-Verlag. Lunze, 2019.
  • [26] X. Liu and Z. Li, Finite time anti–synchronization of complex–valued neural networks with bounded asynchronous time–varying delays, Neurocomputing 387, 129–138, 2020.
  • [27] W. Liu, C.C. Lim, P. Shi and S. Xu, Backstepping fuzzy adaptive control for a class of quantized nonlinear systems, IEEE Trans Fuzzy Syst 25 (5), 2017.
  • [28] D. Liu, S. Xue, B. Zhao, B. Luo and Q. Wei, Adaptive dynamic programming for control: A survey and recent advances, IEEE Trans. Syst. Man Cybern. Syst. 51 (1), 142–160, 2021.
  • [29] V. Loia, S. Tomasiello, A. Vaccaro and J. Gao, Using local learning with fuzzy transform: application to short term forecasting problems, Fuzzy Optim. Decis. Mak. 19, 13–32, 2020.
  • [30] S. Lu, J. Pei, X. Liu and P. Pardalos, Robust parallel–batching scheduling with fuzzy deteriorating processing time and variable delivery time in smart manufacturing, Fuzzy Optim. Decis. Mak. 19, 333–357, 2020.
  • [31] K. Mathiyalagan and G. Sangeetha, Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control, J Franklin Inst 356 (7), 3948–3964, 2019.
  • [32] J.A. Meda-Campana and B. Castillo–Toledo, The optimal fuzzy robust regulator for T–S discrete–time systems: An LMI approach, Int J Adapt Control Signal Process 23, 837–862, 2009.
  • [33] J.A. Meda-Campana, B. Castillo-Toledo and G. Chen, Synchronization of chaotic systems from a fuzzy regulation approach, Fuzzy Sets Syst 160, 860–2875, 2009.
  • [34] J.A. Meda-Campana, B. Castillo–Toledo and V. Zuniga, On the nonlinear fuzzy regulation for under–actuated systems, Proc. IEEE Int. Conf. Fuzzy Syst. Vancouver, BC, Canada, Jul. 16–21, 2195–2202, 2016.
  • [35] J.A. Meda–Campana, J.C. Gomez–Mancilla and B. Castillo-Toledo, Exact output regulation for nonlinear systems described by Takagi-Sugeno fuzzy models, IEEE Trans Fuzzy Syst 20 (2), 235–247, 2012.
  • [36] Y. Pan and G.H. Yang, Event–triggered fuzzy control for nonlinear networked control systems, Fuzzy Sets Syst 15 (329),91–107, 2017.
  • [37] K.S. Phogat and D.E. Chang, Model predictive regulation on manifolds in Euclidean space, Sensors 22 (14), 5170, 2022.
  • [38] R. Sakthivel, S. Selvi, K. Mathiyalagan and P. Shi, Reliable mixed H1 and passivity– based control for fuzzy Markovian switching systems with probabilistic time delays and actuator failures, IEEE Trans Cybern 45 (12), 2720–2731, 2015.
  • [39] X. Shi, A. Emrouznejad, M. Jin and F. Yang, A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory, Fuzzy Optim. Decis. Mak. 19, 311–332, 2020.
  • [40] Y. Shu, B. Li and Y. Zhu, Optimal control for uncertain discrete–time singular systems under expected value criterion, Fuzzy Optim. Decis. Mak. 20, 331–364, 2021.
  • [41] R. Sriraman, Y. Cao and R. Samidurai, Global asymptotic stability of stochastic complex–valued neural networks with probabilistic time–varying delays, Math Comput Simul 171, 103–118, 2020.
  • [42] Z. Su, C. Qian and Y. Hao, Global stabilization via sampled–data output feedback for large–scale systems interconnected by inherent nonlinearities, Automatica 92 (92), 254–258, 2018.
  • [43] Y. Sunaga, R. Natsuaki and A. Hirose, Land form classification and similar land– shape discovery by using complex–valued convolutional neural networks, IEEE Trans Neural Netw Learn Syst 57 (10), 907–7917, 2019.
  • [44] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern. Syst. 15 (1), 116–132, 1985.
  • [45] K. Tanaka and H.O. Wang, Fuzzy Control Systems Design and Analysis, A Linear Matrix Inequality Approach, New York: Wiley, 2001.
  • [46] E. Tian, D. Yue, T. Cheng Yang, Z. Gu and G. Lu, T–S fuzzy model-based robust stabilization for networked control systems with probabilistic sensor and actuator failure, IEEE Trans Fuzzy Syst 19 (3), 553–561, 2011.
  • [47] W. Yang, J. Xia, X. Guo, M. Yu and N. Zhang, Adaptive decentralized event-triggered tracking control for large–scale strongly interconnected nonlinear system with global performance, Int J Control Autom Syst, Doi: 10.1007/s12555-022-0134-4, 1–13, 2022.
  • [48] X.M. Zhang and Q.L. Han, Event–triggered mixed H1 and passive control of linear systems via dynamic output feedback, IECON 2013–39-th Annual Conference of the IEEE Industrial Electronics Society, 5080–5085, 2013.
  • [49] J. Zhang, C. Peng, D. Du and M. Zheng, Adaptive event–triggered communication scheme for networked control systems with randomly occurring nonlinearities and uncertainties, Neurocomputing 174, 475–482, 2016.
There are 49 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Muhammad Shamrooz Aslam 0000-0002-7622-1788

Zhenhua Ma This is me 0000-0002-4436-4151

Project Number 20z14
Early Pub Date June 11, 2023
Publication Date October 31, 2023
Published in Issue Year 2023

Cite

APA Aslam, M. S., & Ma, Z. (2023). Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system. Hacettepe Journal of Mathematics and Statistics, 52(5), 1282-1302. https://doi.org/10.15672/hujms.1017898
AMA Aslam MS, Ma Z. Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system. Hacettepe Journal of Mathematics and Statistics. October 2023;52(5):1282-1302. doi:10.15672/hujms.1017898
Chicago Aslam, Muhammad Shamrooz, and Zhenhua Ma. “Output Regulation for time–delayed Takagi–Sugeno Fuzzy Model With Networked Control System”. Hacettepe Journal of Mathematics and Statistics 52, no. 5 (October 2023): 1282-1302. https://doi.org/10.15672/hujms.1017898.
EndNote Aslam MS, Ma Z (October 1, 2023) Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system. Hacettepe Journal of Mathematics and Statistics 52 5 1282–1302.
IEEE M. S. Aslam and Z. Ma, “Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 5, pp. 1282–1302, 2023, doi: 10.15672/hujms.1017898.
ISNAD Aslam, Muhammad Shamrooz - Ma, Zhenhua. “Output Regulation for time–delayed Takagi–Sugeno Fuzzy Model With Networked Control System”. Hacettepe Journal of Mathematics and Statistics 52/5 (October 2023), 1282-1302. https://doi.org/10.15672/hujms.1017898.
JAMA Aslam MS, Ma Z. Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system. Hacettepe Journal of Mathematics and Statistics. 2023;52:1282–1302.
MLA Aslam, Muhammad Shamrooz and Zhenhua Ma. “Output Regulation for time–delayed Takagi–Sugeno Fuzzy Model With Networked Control System”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 5, 2023, pp. 1282-0, doi:10.15672/hujms.1017898.
Vancouver Aslam MS, Ma Z. Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system. Hacettepe Journal of Mathematics and Statistics. 2023;52(5):1282-30.

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