×

zbMATH — the first resource for mathematics

Event-triggered \(H_{\infty}\) control for a class of nonlinear networked control systems using novel integral inequalities. (English) Zbl 1356.93058
Summary: This paper is concerned with event-triggered \(H_{\infty}\) control for a class of nonlinear networked control systems. An event-triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event-triggered transmission scheme, the closed-loop system is modeled as a system with an interval time-varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov-Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event-triggered \(H_{\infty}\) controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality-based conditions are formulated to design both event-triggered and time-triggered \(H_{\infty}\) controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

MSC:
93C65 Discrete event control/observation systems
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93C57 Sampled-data control/observation systems
93D21 Adaptive or robust stabilization
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zames, Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverse, IEEE Transactions on Automatic Control 26 pp 301– (1981) · Zbl 0474.93025 · doi:10.1109/TAC.1981.1102603
[2] Doyle, State space solutions to the standard H2 and H control problems, IEEE Transactions on Automatic Control 34 pp 831– (1989) · Zbl 0698.93031 · doi:10.1109/9.29425
[3] Pavel, Nonlinear H control: a J-dissipative approach, IEEE Transactions on Automatic Control 42 pp 1636– (1997) · Zbl 0904.93006 · doi:10.1109/9.650014
[4] Wu, Robust H control for polytopic nonlinear control systems, IEEE Transactions on Automatic Control 58 pp 2957– (2013) · Zbl 1369.93258 · doi:10.1109/TAC.2013.2258780
[5] Jia, Fuzzy H tracking control for nonlinear networked control systems in T-S fuzzy model, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 39 pp 1073– (2009) · doi:10.1109/TSMCB.2008.2010524
[6] Jiang, Robust H control for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay, IEEE Transactions on Fuzzy Systems 15 pp 321– (2007) · Zbl 05452652 · doi:10.1109/TFUZZ.2006.878251
[7] Wang, Network-based fault detection filter and controller coordinated design for unmanned surface vehicles in network environments, IEEE Transactions on Industrial Informatics (2016) · doi:10.1109/TII.2016.2526648
[8] Zhang, Network-based output tracking control for a class of T-S fuzzy systems that can not be stabilized by non-delayed output feedback controllers, IEEE Transactions on Cybernetics 45 pp 1511– (2015) · doi:10.1109/TCYB.2014.2354421
[9] Zhang, Network-based modelling and active control for offshore steel jacket platform with TMD mechanisms, Journal of Sound and Vibration 333 pp 6796– (2014) · doi:10.1016/j.jsv.2014.08.007
[10] Zhang, Event-triggered H reliable control for offshore structures in network environments, Journal of Sound and Vibration 368 pp 1– (2016) · doi:10.1016/j.jsv.2016.01.008
[11] Gupta, Networked control system: overview and research trends, IEEE Transactions on Industrial Electronics 57 pp 2527– (2010) · doi:10.1109/TIE.2009.2035462
[12] Hespanha, A survey of recent results in networked control systems, Proceedings of the IEEE 95 pp 138– (2007) · doi:10.1109/JPROC.2006.887288
[13] Zhang XM Han QL Yu XH 2016 Survey on recent advances in networked control systems 10.1109/TII.2015.2506545
[14] Ge X Yang F Han QL 2016 Distributed networked control systems: a brief overview
[15] Zhang, On designing network-based H controllers for stochastic systems, International Journal of Robust Nonlinear Control 25 pp 52– (2015)
[16] Zeng, Absolute stability and stabilization for Lurie networked control systems, International Journal of Robust and Nonlinear Control 21 pp 1667– (2011) · Zbl 1227.93099 · doi:10.1002/rnc.1658
[17] Seiler, An H approach to networked control, IEEE Transactions on Automatic Control 50 pp 356– (2005) · Zbl 1365.93147 · doi:10.1109/TAC.2005.844177
[18] Qiu L, H control of networked control systems based on Markov jump unified model, International Journal of Robust and Nonlinear Control 25 pp 2770– (2015) · Zbl 1328.93246 · doi:10.1002/rnc.3230
[19] Jiang, A new H stabilization criterion for networked control systems, IEEE Transactions on Automatic Control 53 pp 1025– (2008) · Zbl 1367.93179 · doi:10.1109/TAC.2008.919547
[20] Zhang, A delay decomposition approach to H control of networked control systems, European Journal of Control 15 pp 523– (2009) · Zbl 1298.93155 · doi:10.3166/ejc.15.523-533
[21] Li, Observer-based H control for networked systems with bounded random delays and consecutive packet dropouts, International Journal of Robust and Nonlinear Control 24 pp 2785– (2014) · Zbl 1305.93181 · doi:10.1002/rnc.3025
[22] Zhou, A new approach to network-based H control for stochastic systems, International Journal of Robust and Nonlinear Control 22 pp 1036– (2012) · Zbl 1273.93150 · doi:10.1002/rnc.1750
[23] Yue, A delay system method for designing event-triggered controllers of networked control systems, IEEE Transactions on Automatic Control 58 pp 475– (2013) · Zbl 1369.93183 · doi:10.1109/TAC.2012.2206694
[24] Peng, A novel event-triggered transmission scheme and 2 control co-design for sampled-data control systems, IEEE Transactions on Automatic Control 58 pp 2620– (2013) · Zbl 1369.93365 · doi:10.1109/TAC.2013.2256015
[25] Wang, Self-triggered feedback control systems with finite-gain 2 stability, IEEE Transactions on Automatic Control 54 pp 452– (2009) · Zbl 1367.93354 · doi:10.1109/TAC.2009.2012973
[26] Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control 52 pp 1680– (2007) · Zbl 1366.90104 · doi:10.1109/TAC.2007.904277
[27] Jiang, A survey of recent results in quantized and event-based nonlinear control, International Journal of Automation and Computing 12 pp 455– (2015) · doi:10.1007/s11633-015-0906-x
[28] Liu, A small-gain approach to robust event-triggered control of nonlinear systems, IEEE Transactions on Automatic Control 60 pp 2072– (2015) · Zbl 1360.93297 · doi:10.1109/TAC.2015.2396645
[29] Hu, 2-gain analysis of event-triggered networked control systems: a discontinuous Lyapunov functional approach, International Journal of Robust and Nonlinear Control 23 pp 1277– (2013) · Zbl 1271.93125 · doi:10.1002/rnc.2815
[30] Zhang, Event-triggered dynamic output feedback control for networked control systems, IET Control Theory and Applications 8 pp 226– (2014) · doi:10.1049/iet-cta.2013.0253
[31] Zhang, A decentralized event-triggered dissipative control scheme for systems with multiple sensors to sample the system outputs, IEEE Transactions on Cybernetics · doi:10.1109/TCYB.2015.2487420
[32] Yin, Event-triggered tracking control for discrete-time multi-agent systems, IMA Journal of Mathematical Control and Information 38 pp 165– (2014) · Zbl 1293.93530 · doi:10.1093/imamci/dns042
[33] Tian, Decentralized control of network-based interconnected systems: a state-dependent triggering method, International Journal of Robust and Nonlinear Control 25 pp 1126– (2015) · Zbl 1317.93021 · doi:10.1002/rnc.3119
[34] Liu, Event-based fault detection for networked systems with communication delay and nonlinear perturbation, Journal of the Franklin Institute 350 pp 2791– (2013) · Zbl 1287.93053 · doi:10.1016/j.jfranklin.2013.06.021
[35] Guo, A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems, Automatica 50 pp 1489– (2014) · Zbl 1296.93108 · doi:10.1016/j.automatica.2014.03.017
[36] Yu M Wang L Chu TG Robust stabilization of nonlinear sampled-data systems Proceedings of American Control Conference Portland, OR, USA 2005 3421 3426
[37] Peng, State feedback controller design of networked control systems with interval time-varying delay and nonlinearity, International Journal of Robust and Nonlinear Control 18 pp 1285– (2008) · Zbl 1284.93111 · doi:10.1002/rnc.1278
[38] Mahmoud, Networked feedback control for nonlinear systems with random varying delays, Journal of the Franklin Institute 351 pp 3145– (2014) · Zbl 1290.93072 · doi:10.1016/j.jfranklin.2014.02.011
[39] Jiang, H static output feedback control for nonlinear networked control systems with time delays and packet dropouts, ISA Transactions 52 pp 215– (2013) · doi:10.1016/j.isatra.2012.10.006
[40] Seuret, Wirtinger-based integral inequality: Application to time-delay systems, Automatica 49 pp 2860– (2013) · Zbl 1364.93740 · doi:10.1016/j.automatica.2013.05.030
[41] Zhang, Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach, Neural Networks 54 pp 57– (2014) · Zbl 1322.93079 · doi:10.1016/j.neunet.2014.02.012
[42] Šiljak, Robust stabilization of nonlinear systems: the LMI approach, Mathematical Problems in Engineering 6 pp 461– (2000) · Zbl 0968.93075 · doi:10.1155/S1024123X00001435
[43] Liu, Discrete-time network-based control under scheduling and actuator constraints, International Journal of Robust and Nonlinear Ccontrol 25 pp 1816– (2015) · Zbl 1326.93078 · doi:10.1002/rnc.3179
[44] Liu, Networked control with stochastic scheduling, IEEE Transactions on Automatic Control 60 pp 3071– (2015) · Zbl 1360.93745 · doi:10.1109/TAC.2015.2414812
[45] Liu, Networked control systems in the presence of scheduling protocols and communication delays, SIAM Journal on Control and Optimization 53 pp 1768– (2015) · Zbl 1317.93212 · doi:10.1137/140980570
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.