Abstract
This paper investigates the time-varying formation control (TVFC) problem of multi-agent systems (MASs) with general linear dynamics under fixed topology by utilizing event-triggered mechanisms. In order to achieve the TVFC problem, two kinds of distributed event-triggered formation control schemes are proposed. Moreover, the Zeno behavior is excluded under these event-triggered mechanisms. Since these control protocols are constructed on the basis of the sampling information of the event time instants instead of the real-time information of each agent, each agent does not require to communicate continuously with its neighbors, thus effectively reducing the bandwidth requirement of communication and greatly reducing the use of energy in MASs. It deserves to be mentioned that the second control protocol introduces time-varying coupling weights, does not require to utilize any global information of the system networks, and is more suitable for systems with large-scale network. Moreover, the proposed event-triggered formation control protocols are suitable for arbitrarily switching topologies, and its related results are extended to the case of switching topologies. Finally, several examples are introduced to achieve the TVFC problem by utilizing the adaptive event-triggered control protocol, and Zeno behavior is not observed during the process of simulation.
Similar content being viewed by others
References
Li Y, Zhang H, Liang X, Huang B (2019) Event-triggered-based distributed cooperative energy management for multienergy systems. IEEE Trans Ind Inf 15(4):2008–2022
Lu Y, Wang H, Hu F, Zhou B, Xi H (2021) Effective recognition of human lower limb jump locomotion phases based on multi-sensor information fusion and machine learning. Med Biol Eng Comput 59(4):883–899
Lu Y, Wang H, Qi Y, Xi H (2021) Evaluation of classification performance in human lower limb jump phases of signal correlation information and LSTM models. Biomed Signal Proces 64:102279
Dong X, Yu B, Shi Z, Zhong Y (2015) Time-varying formation control for unmanned aerial vehicles: theories and applications. IEEE Trans Control Syst Technol 23(1):340–348
Song R, Li J, Lewis F (2019) Robust optimal control for disturbed nonlinear zero-sum differential games based on single NN and least-squares. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2897379
Su H, Zhang H, Jiang H, Wen Y (2020) Decentralized event-triggered adaptive control of discrete-time non-zero games over wireless sensor-actuator networks with input constraints. IEEE Trans Neural Netw Learn Syst 31(10):4254–4266
Song R, Wei Q, Zhang H, Lewis F (2019) Discrete-time non-zero-sum games with completely unknown dynamics. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2019.2957406
Song R, Zhu L (2019) Optimal tracking control for discrete time nonlinear system via ADP. IEEE/CAA J Autom Sinica 6(3):657–666
Zhang J, Zhang H, Li W, Li K (2021) Distributed edge-event triggered consensus control for multi-agent systems by edge-based asynchronous communications. Appl Math Comput 397(15):125920
Zhang H, Duan J, Wang Y, Gao Z (2021) Bipartite fixed-time output consensus of heterogeneous linear multiagent systems. IEEE Trans Cybern 51(2):548–557
Zhang J, Zhang H, Sun S, Gao Z (2021) Leader-follower consensus control for linear multi-agent systems by fully distributed edge-event-triggered adaptive strategies. Inf Sci 555:314–338
Zhang H, Cai Y, Wang Y, Su H (2020) Adaptive bipartite event-triggered output consensus of heterogeneous linear multiagent systems under fixed and switching topologies. IEEE Trans Neural Netw Learn Syst 31(11):4816–4830
Zhang J, Zhang H, Cai Y, Lu Y (2020) Distributed cooperative output regulation of heterogeneous linear multi-agent systems based on event- and self-triggered control with undirected topology. ISA Trans 100:221–234
Li Z, Duan Z, Ren W, Feng G (2015) Containment control of linear multi-agent systems with multiple leaders of bpunded inputs using distributed continuous controllers. Int J Robust Nonlinear Control 25:2102–2121
Gong Y, Wen G, Peng Z, Huang T, Chen Y (2020) Observer-based time-varying formation control of fractional-order multi-agent systems with general linear dynamics. IEEE Trans Circuits Syst II 67(1):82–86
Dong X, Xi J, Lu G, Zhong Y (2014) Formation control for high-order linear time-invariant multiagent systems with time delays. IEEE Trans Control Netw Syst 1(3):232–240
Li X, Xie L (2018) Dynamic formation control over directed networks using graphical Laplacian approach. IEEE Trans Autom Control 63(11):3761–3774
Dong X, Hu G (2016) Time-varying formation control for generally linear multi-agent systems with switching directed topologies. Automatica 73:47–55
Deng C, Che W (2019) Fault-tolerant fuzzy formation control for a class of nonlinear multiagent systems under directed and switching topology. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2954870
Ren W, Sorensen N (2008) Distributed coordination architecture for multi-robot formation control. Robust Auton Syst 56(4):324–333
Deng C, Wen C, Huang J, Zhang X, Zou Y (2021) Distributed observer-based cooperative control approach for uncertain nonlinear MASs under event-triggered communication. IEEE Trans Autom Control. https://doi.org/10.1109/TAC.2021.3090739
Zhang J, Zhang H, Lu Y, Sun S (2020) Cooperative output regulation of heterogeneous linear multi-agent systems with edge-event triggered adaptive control under time-varying topologies. Neural Comput Appl 32:15573–15584
Zhang H, Liang Y, Su H, Liu C (2019) Event-driven guaranteed cost control design for nonlinear systems with actuator faults via reinforcement learning algorithm. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2946857
Li T, Yang D, Xie X, Zhang H (2021) Event-triggered control of nonlinear discrete-time system with unknown dynamics based on HDP\((\lambda )\). IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3044595
Zhang H, Zhang K, Xiao G, Jiang H (2019) Robust optimal control scheme for unknown constrained-input nonlinear systems via a plug-n-play event-sampled critic-only algorithm. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2018.2889377
Ge X, Han Q (2017) Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Trans Ind Electron 64(10):8118–8127
Zhang H, Han J, Wang Y, Jiang H (2019) \(H_{\infty }\) consensus for linear heterogeneous multiagent systems based on event-triggered output feedback control scheme. IEEE Trans Cybern 49(6):2268–2279
Liu X, Ge S, Goh C, Li Y (2019) Event-triggered coordination for formation tracking control in constrained space with limited communication. IEEE Trans Cybern 49(3):1000–1011
Zhou J, Guo Y, Li G, Zhang J (2019) Event-triggered control for nonlinear uncertain second-order multi-agent formation with collision avoidance. IEEE Access 7:104489–104499
Li X, Chen M, Su H, Li C (2017) Distributed bounds on the algebraic connectivity of graphs with application to agent networks. IEEE Trans Cybern 47(8):2121–2131
Cheng B, Wu Z, Li Z (2021) Distributed edge-based event-triggered formation control. IEEE Trans Cybern 51(3):1241–1252
Cheng B, Li Z (2019) Fully distributed event-triggered protocols for linear multiagent networks. IEEE Trans Autom Control 64(4):1655–1662
Qian Y, Liu L, Feng G (2019) Output consensus of heterogeneous linear multi-agent systems with adaptive event-triggered control. IEEE Trans Autom Control 64(6):2606–2613
Zhang J, Zhang H, Liang Y, Song W (2021) Adaptive bipartite output tracking consensus in switching networks of heterogeneous linear multi-agent systems based on edge events. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3089596
Zhang H, Zhang J, Cai Y, Sun S, Sun J (2020) Leader-following consensus for a class of nonlinear multiagent systems under event-triggered and edge-event triggered mechanisms. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3035907
Zhang H, Liu Y, Dai J, Wang Y (2020) Command filter based adaptive fuzzy finite-time control for a class of uncertain nonlinear systems with hysteresis. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.3003499
Zhang J, Zhang H, Zhang K, Cai Y (2021) Observer-based output feedback event-triggered adaptive control for linear multiagent systems under switching topologies. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3084317
Liu T, Jiang Z (2013) Distributed formation control of nonholonomic mobile robots without global position measurements. Automatica 49(2):592–600
Wang R, Dong X, Li Q, Ren Z (2019) Distributed time-varying output formation control for general linear multiagent systems with directed topology. IEEE Trans Control Netw Syst 6(2):609–620
Wang R, Dong X, Li Q, Ren Z (2016) Distributed adaptive formation control for linear swarm systems with time-varying formation and switching topologies. IEEE Access 4:8995–9004
Cheng T, Kan Z, Rosenfeld J, Dixon W (2014) Decentralized formation control with connectivity maintenance and collision avoidance under limited and intermittent sensing, In Proc Am Control Conf, 3201-3206
Li H, Liao X, Huang T, Zhu W (2015) Second-order global consensus in multiagent networks with random directional link failure. IEEE Trans Neural Netw Learn Syst 26(3):565–575
Sun S, Zhang H, Han J, Zhang J (2021) Dissipativity-based finite-time filtering for uncertain semi-Markovian jump random systems with multiple time delays and state constraints. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3047991
Sun J, Zhang H, Wang Y, Shi Z (2021) Dissipativity-based fault-tolerant control for stochastic switched systems with time-varying delay and uncertainties’’. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3068631
Su Y, Huang J (2012) Cooperative output regulation of linear multi-agent systems. IEEE Trans Autom Control 57(4):1062–1066
Tan G, Wang Z (2021) Generalized dissipativity state estimation of delayed static neural networks based on a proportional-integral estimator with exponential gain term, IEEE Trans. Circuits Syst II Express Briefs 68(1):356–360
Tan G, Wang Z, Li C (2020) \(H_{\infty }\) performance state estimation of delayed static neural networks based on an improved proportional-integral estimator. Appl Math Comput 370:124908
Li Z, Duan Z, Chen G, Huang L (2010) Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans Circuits Syst I Reg Papers 57(1):213–224
Khalil HK (2002) Nonlinear Systems, 3rded., Englewood Cliffs, NJ, USA: Prentice-Hall
Wu Z, Xu Y, Lu R, Wu Y, Huang T (2018) Event-triggered control for consensus of multiagent systems with fixed/switching topologies. IEEE Trans Syst Man Cybern Syst 48(10):1736–1746
Ioannou P, Sun J (1996) Robust Adaptive Control. Prentice-Hall, New York, NY, USA
Du H, Li S, Lin X (2013) Finite-time formation control of multiagents via dynamic output feedback. Int J Robust Nonlinear Control 23(14):1609–1628
Xiao F, Wang L, Chen J, Gao Y (2009) Finite-time formation control for multi-agent systems. Automatica 45(11):2605–2611
Hawwary M (2015) Three-dimensional circular formations via set stabilization. Automatica 54:374–381
Wang C, Xie G, Gao M (2014) Controlling anonymous mobile agents with unidirectional locomotion to form formations on a circle. Automatica 50(4):1100–1108
Yu P, Ding L, Liu Z, Duan Z (2015) A distributed event-triggered transmission strategy for exponential consensus of general linear multi-agent systems with directed topology. J Franklin Inst 352:5866–5881
Zhao Y, Duan Q, Wen G, Zhang D, Wang B (2018) Time-varying formation for general linear multiagent systems over directed topologies: a fully distributed adaptive technique. IEEE Trans Syst Man Cybern Syst 51(1):532–541
Acknowledgements
This work was supported by National Key R&D Program of China under grant 2018YFA0702200, and National Natural Science Foundation of China (61627809, 621030666), and Liaoning Revitalization Talents Program (XLYC1801005).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no financial and personal relationships with other people or organizations that can inappropriately influence our work. And there are no potential conflicts of interest with respect to this work.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhang, J., Zhang, H., Gao, Z. et al. Time-varying formation control with general linear multi-agent systems by distributed event-triggered mechanisms under fixed and switching topologies. Neural Comput & Applic 34, 4277–4294 (2022). https://doi.org/10.1007/s00521-021-06539-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-021-06539-w