Muhammad Shamrooz ASLAM, Zhenhua MA

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

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,

PDF

___

[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.