×

zbMATH — the first resource for mathematics

Event-triggered containment control for multi-agent systems with constant time delays. (English) Zbl 1373.93027
Summary: The paper investigates containment control for the first-order and second-order multi-agent systems with constant time delays under event-triggered conditions, respectively. By applying existing sum of square methods to stability analysis of containment control for multi-agent systems, sufficient containment conditions for multi-agent systems are obtained. First, we discussed the case of containment control for multi-agent system with single time delay, and event-triggered conditions are proposed. Then, we extend the results of containment control for multi-agent systems with single time delay to the case with multiple time delays. Finally, simulation examples are given to illustrate the effectiveness of our theoretical results.

MSC:
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93D99 Stability of control systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Li, Z.; Ren, W.; Liu, X.; Fu, M., Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders, Int. J. Robust Nonlinear Control, 23, 534-547, (2013) · Zbl 1284.93019
[2] Liu, K.; Xie, G.; Wang, L., Containment control for second-order multi-agent systems with time-varying delays, Syst. Control Lett., 67, 24-31, (2014) · Zbl 1288.93004
[3] Meng, Z.; Ren, W.; You, Z., Distributed finite-time attitude containment control for mutiple rigid bodies, Automatica, 46, 2092-2099, (2010) · Zbl 1205.93010
[4] Liu, K.; Ji, Z.; Xie, G.; Xu, R., Event-based broadcasting containment control for multi-agent systems under directed topology, Int. J. Control, 89, 2360-2370, (2016) · Zbl 1360.93040
[5] Li, B.; Chen, Z.; Liu, Z.; Zhang, C.; Zhang, Q., Containment control of multi-agent systems with fixed time-delays in fixed directed networks, Neurocomputing, 173, 2069-2075, (2016)
[6] Hu, J.; Yu, J.; Cao, J., Distributed containment control for nonlinear multi-agent systems with time-delayed protocol, Asian J. Control, 18, 747-756, (2016) · Zbl 1346.93021
[7] Gu, K., A further refinement of discretized Lyapunov functional method for the stability of time-delay systems, Int. J. Control, 74, 967-976, (2001) · Zbl 1015.93053
[8] Gu, K.; Liu, Y., Lyapunov-krasovskii functional for uniform stability of coupled differential-functional equations, Automatica, 45, 798-804, (2009) · Zbl 1168.93384
[9] Zhang, X.; Han, Q., Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems, Automatica, 57, 199-202, (2015) · Zbl 1330.93213
[10] Zhang, X.; Han, Q., Novel delay derivative-dependent stability criteria using new bounding technique, Int. J. Robust Nonlinear Control, 23, 1419-1432, (2013) · Zbl 1278.93230
[11] Peet, M. M.; Papachristodoulou, A.; Lall, S., Positive forms and stability of linear time-delay systems, SIAM J. Control Optim., 47, 3237-3258, (2009) · Zbl 1187.34101
[12] Zhang, Y.; Peet, M. M.; Gu, K., Reducing the complexity of the sum-of-squares test for stability of delayed linear systems, IEEE Trans. Autom. Control, 56, 229-234, (2011) · Zbl 1368.93618
[13] Peet, M. M., LMI parametrization of Lyapunov functions for infinite-dimensional systems: a framework, Proceedings of American Control Conference, 359-366, (2014)
[14] G. Miao, M.M. Peet, K. Gu, Inversion of separable kernel operators in coupled differential-functional equations and applications to controller synthesis, Available at: https://arxiv.org/abs/1703.10253.
[15] M.M. Peet, SOS methods for multi-delay systems: a dual form of Lyapunov-Krasovskii functional, Available at: https://www.researchgate.net/publication/303221914.
[16] Zhang, X.; Han, Q.; Zhang, B., An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked system, IEEE Trans. Ind. Inf., 13, 4-16, (2017)
[17] Zhang, X.; Han, Q.; Yu, X., Survey on recent advances in networked control systems, IEEE Trans. Ind. Inf., 12, 1740-1752, (2016)
[18] Yan, H.; Shen, Y.; Zhang, H.; Shi, H., Decentralized event-triggered consensus control for second-order multi-agent systems, Neurocomputing, 133, 18-24, (2014)
[19] Yin, X.; Yue, D.; Hu, S., Adaptive periodic event-triggered consensus for multi-agent systems subject to input saturation, Int. J. Control, 89, 653-667, (2015) · Zbl 1338.93241
[20] Wang, A.; Zhao, Y., Event-triggered consensus control for leader-following multi-agent systems with time-varying delays, J. Franklin Inst., 353, 4754-4771, (2016) · Zbl 1349.93019
[21] Zhu, W.; Jiang, Z., Event-based leader-following consensus of multi-agent systems with input time delay, IEEE Trans. Autom. Control, 60, 1362-1367, (2015) · Zbl 1360.93268
[22] Xie, T.; Liao, X.; Li, H., Leader-following consensus in second-order multi-agent systems with input time delay: an event-triggered sampling approach, Neurocomputing, 177, 130-135, (2016)
[23] Fan, Y.; Yang, Y.; Zhang, Y., Sampling-based event-triggered consensus for multi-agent systems, Neurocomputing, 191, 141-147, (2016)
[24] Wu, Y.; Su, H.; Shi, P.; Shu, Z.; Wu, Z., Consensus of multi-agent systems using aperiodic sampled-data control, IEEE Trans. Cybern., 46, 2132-2143, (2016)
[25] Garcia, E.; Cao, Y.; Casbeer, D. W., Decentralised event-triggered consensus of double integrator multi-agent systems with packet losses and communication delays, IET Control Theory Appl., 10, 1835-1843, (2016)
[26] Garcia, E.; Cao, Y.; Yu, H.; Antsakiis, P.; Casbeer, D., Decentralised event-triggered cooperative control with limited communication, Int. J. Control, 86, 1479-1488, (2013) · Zbl 1278.93005
[27] Hu, A.; Cao, J.; Hu, M.; Guo, L., Event-triggered consensus of multi-agent systems with noises, J. Franklin Inst., 352, 3489-3505, (2015) · Zbl 1395.93040
[28] Shen, J.; Cao, J., Consensus of multi-agent systems on time scales, IMA J. Math. Control Inf., 29, 507-517, (2012) · Zbl 1256.93068
[29] Cao, Y.; Zhang, L.; Li, C.; Chen, M. Z.Q., Observer-based consensus tracking of nonlinear agents in hybrid varying directed topology, IEEE Trans. Cybern., 47, 2212-2222, (2017)
[30] Wan, Y.; Wen, G.; Cao, J.; Yu, W., Distributed node-to-node consensus of multi-agent systems with stochastic sampling, Int. J. Robust Nonlinear Control, 26, 110-124, (2016) · Zbl 1333.93016
[31] Liu, Y.; Wang, Z.; He, X.; Zhou, D. H., Filtering and fault detection for nonlinear systems with polynomial approximation, Automation, 54, 348-359, (2015) · Zbl 1318.93090
[32] Sun, Y.; Zhao, D.; Ruan, J., Consensus in noisy environments with switching topology and time-varying delays, Physica A, 389, 4149-4161, (2010)
[33] Horn, R.; Johnson, C., Matrix Analysis, (1985), Cambridge University Press New York · Zbl 0576.15001
[34] Gu, K., An integral inequality in the stability problem of time-delay systems, Proceedings of IEEE Conference on Decision and Control, 2805-2810, (2000)
[35] Peet, M. M., Full state feedback of delayed systems using SOS: a new theory of duality, IFAC Proceedings Volumes, 24-29, (2013)
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.