Rapid exponential stabilization of nonlinear continuous systems via event-triggered impulsive control

• Autorzy: Dlala Mohsen

Identyfikatory

DOI

10.1515/dema-2022-0032

• Języki publikacji: EN

Abstrakty

EN

This article investigates the problem of rapid exponential stabilization for nonlinear continuous systems via event-triggered impulsive control (ETIC). First, we propose a trigger mechanism that, when triggered by a predefined event, causes the closed-loop system exponentially stable. Then, the exponential stabilization is achieved by the designed ETIC with or without data dropout. The case where there are delays in the ETIC signals is also studied, and the exponential stabilization is proved. Finally, a numerical study is presented, along with numerical illustrations of the stability results.

Słowa kluczowe

EN

impulsive control; event-triggered control; rapid exponential stabilization; time delays; data dropout

PL

impulsywność; sterowanie wyzwalane zdarzeniami; stabilizacja; opóźnienia czasowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 470--481
• Opis fizyczny: Bibliogr. 35 poz., rys., wykr.

Twórcy

autor

Dlala Mohsen

• Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia

Bibliografia

• [1] C. Prieur and E. Trélat, Robust optimal stabilization of the Brockett integrator via a hybrid feedback, Math. Control Signals Systems 17 (2005), no. 3, 201–216.
• [2] M. Donkers and M. Heemels, Output-based event-triggered control with guaranteed ∞ gain and improved and decentralized event-triggering, IEEE Trans. Automat Control 57 (2012), no. 6, 1362–1376.
• [3] W. Elmenreich, Time-triggered fieldbus networks state of the art and future applications, 2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC), 2008, pp. 436–442.
• [4] M. Heemels, K. H. Johansson, and P. Tabuada, An introduction to event-triggered and self-triggered control, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012, pp. 3270–3285.
• [5] C. Albea and A. Seuret, Time-triggered and event-triggered control of switched affine systems via a hybrid dynamical approach, Nonlinear Anal. Hybrid Syst. 41 (2021), 101039.
• [6] P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Autom. Control 52 (2007), no. 9, 1680–1685.
• [7] D. Yue, E. Tian, and Q. L. Han, A delay system method for designing event-triggered controllers of networked control systems, IEEE Trans. Autom. Control 58 (2013), no. 2, 475–481.
• [8] A. Girard, Dynamic triggering mechanisms for event-triggered controls, IEEE Trans. Autom Control 60 (2015), 1992–1997.
• [9] M. Heemels, J. Donkers, and A. R. Teel, Periodic event-triggered control for linear systems, IEEE Trans. Autom. Control 54 (2013), no. 4, 847–861.
• [10] X. M. Zhang and Q. L. Han, Network-based h∞ filtering using a logic jumping-like trigger, Automatica J. IFAC 49 (2013), 1428–1435.
• [11] B. L. Zhang, Q. L. Han, and X. M. Zhang, Event-triggered h∞ reliable control for offshore structures in network environments, J. Sound Vib. 368 (2016), 1–21.
• [12] Y. L. Wang and Q. L. Han, Network-based modelling and dynamic output feedback control for unmanned marine vehicles in network environments, Automatica J. IFAC 91 (2018), 43–53.
• [13] H. Zhang, X. Zheng, H. I. Li, Z. Wang, and H. Yan, Active suspension system control with decentralized event-triggered scheme, IEEE Trans. Ind. Electron. 67 (2020), no. 12, 10798–10808.
• [14] C. Nowzari, E. Garcia, and J. Cortes, Event-triggered communication and control of networked systems for multi-agent consensus, Automatica J. IFAC 105 (2019), 1–27.
• [15] J. Qin, Q. Ma, Y. Shi, and L. Wang, Recent advances in consensus of multi-agent systems: A brief survey, IEEE Trans. Ind. Electron. 64 (2017), no. 6, 4972–4983.
• [16] V. Dolk, D. Borgers, and W. Heemels, Output-based and decentralized dynamic event-triggered control with guaranteed lp gain performance and zeno-freeness, IEEE Trans. Autom. Control 62 (2017), no. 1, 34–94.
• [17] Y. Guan, Q. L. Han, and X. Ge, On asynchronous event-triggered control of decentralized networked systems, Inform Sci. 425 (2018), 127–139.
• [18] M. S. Mahmoud and Y. Xia, Networked Control Systems, Elsevier, New York, 2019.
• [19] Y. Q. Xia, Y. L. Gao, L. P. Yan, and M. Y. Fu, Recent progress in networked control systems - A survey, Int. J. Autom. Comput. 12 (2015), 343–367.
• [20] W. Zhu, D. Wang, and L. Liu, Event-based impulsive control of continuous-time dynamic systems and its application to synchronization of memristive neural networks, IEEE Trans. Neural Netw. Learn. Syst. 29 (2018), no. 8, 3599–3609.
• [21] X. Li, D. Peng, and J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Autom. Control 65 (2020), no. 11, 4908–4913.
• [22] B. Liu, D. J. Hill, and Z. Sun, Stabilisation to input-to-state stability for continuous-time dynamical systems via eventtriggered impulsive control with three levels of events, IET Control Theory Appl. 12 (2018), no. 9, 1167–1179.
• [23] M. Cao, Z. Ai, and L. Peng, Input-to-state stabilization of nonlinear systems via event-triggered impulsive control, IEEE Access 48 (2019), no. 5, 826–836.
• [24] M. Dlala and S. Obaid Alrashidi, Rapid exponential stabilization of Lotka-McKendrick’s equation via event-triggered impulsive control, Math. Biosci. Eng. 18 (2021), 9121.
• [25] M. Dlala and A. S. Almutairi, Rapid exponential stabilization of nonlinear wave equation derived from brain activity via event-triggered impulsive control, Mathematics 9 (2021), no. 5.
• [26] B. Liu and H. J. Marquez, Razumikhin-type stability theorems for discrete delay systems, Automatica J. IFAC 43 (2007), no. 7, 1219–1225.
• [27] G. Bitsoris and E. Gravalou, Comparison principle, positive invariance and constrained regulation of nonlinear systems, Automatica J. IFAC 31 (1995), no. 2, 217–222.
• [28] A. Loria and E. Panteley, Cascaded nonlinear time-varying systems: Analysis and design, in: Advanced Topics in Control Systems Theory, Vol. 311 of Lecture Notes in Control and Information Sciences, Springer, London, 2005, Chap. 2, pp. 23–64.
• [29] E. Panteley, E. Lefeber, A. Loria, and H. Nijmeijer, Exponential tracking control of a mobile car using a cascaded approach, vol. 31, 1998 IFAC Workshop on Motion Control (MC’98), Grenoble, France, 1998, 21–23 September, pp. 201–206.
• [30] N. O. Sedova, The global asymptotic stability and stabilization in nonlinear cascade systems with delay, Russian Math. (Iz. VUZ) 52 (2008), 60–69.
• [31] M. Dlala, Exponential stability of impulsive cascaded systems and its application in robot control, IEEE Access 10 (2022), 6319–6327.
• [32] Y. Kanayama, Y. Kimura, F. Miyazaki, and T. Noguchi, A stable tracking control method for an autonomous mobile robot, in: Proceedings of IEEE International Conference on Robotics and Automation vol. 1, 1990, pp. 384–389.
• [33] J. Jakubiak, E. Lefeber, K. Tchon, and H. Nijmeijer, Two observer-based tracking algorithms for a unicycle mobile robot, Int. J. Appl. Math. Comput. Sci. 12 (2002), no. 4, 513–522.
• [34] N. Abdellouahab, B. Tellab, and K. Zennir, Existence and stability results for the solution of neutral fractional integro-differential equation with nonlocal conditions, Tamkang J. Math. 53 (2021), no. 5, 3509–35201.
• [35] A. Naimi, B. Tellab, Y. Altayeb, and A. Moumen, Generalized Ulam-Hyers-Rassias stability results of solution for nonlinear fractional differential problem with boundary conditions, Math. Probl. Eng. 2021 (2021), 7150739.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).