Skip to main content
Log in

Consensus in multi-agent systems: a review

  • Published:
Artificial Intelligence Review Aims and scope Submit manuscript

Abstract

This paper provides a review of the consensus problem as one of the most challenging issues in the distributed control of the multi-agent systems (MASs). In this survey, firstly, the consensus algorithms for the agents with the single-integrator, double-integrator and high-order dynamic models were collected from various research works, and the convergence condition for each of these algorithms was explained. Secondly, all the consensus-related problems such as those in the sampled-data consensus, quantized consensus, random-network consensus, leader–follower consensus, finite-time consensus, bipartite consensus, group consensus/cluster consensus, and the scaled consensus were analyzed and compared with each other. Thirdly, we focused on the common control techniques used for the consensus problems in the presence of disturbance and divided all these control methods into two categories: robust control and adaptive control. Finally, we reviewed the most prevalent consensus applications in the MASs, including the subjects of rendezvous, formation control, axial alignment and the wireless sensor networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Source: scientific papers with mentioned keywords on MASs field indexed by Google Scholar until August 2020

Fig. 2

Source: scientific papers with mentioned keywords on MASs field indexed by Scopus

Fig. 3
Fig. 4
Fig. 5

Source scientific papers with mentioned keywords on MASs field indexed by Google Scholar until August 2020

Fig. 6

Source scientific papers with mentioned keywords on MASs field indexed by Scopus

Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Abaid N, Porfiri M (2010) Consensus over numerosity-constrained random networks. IEEE Trans Automat Contr 56(3):649–654

    Article  MathSciNet  MATH  Google Scholar 

  • Adibzadeh A, Suratgar AA, Menhaj MB, Zamani M (2020) Constrained optimal consensus in multi-agent systems with single-and double-integrator dynamics. Int J Control 93(3):575–587

    Article  MathSciNet  MATH  Google Scholar 

  • Altafini C (2012) Consensus problems on networks with antagonistic interactions. IEEE Trans Automat Contr 58(4):935–946

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson WN Jr, Morley TD (1985) Eigenvalues of the Laplacian of a graph. Linear Multilinear Algebr 18(2):141–145

    Article  MATH  Google Scholar 

  • Ando H, Oasa Y, Suzuki I, Yamashita M (1999) Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans Robot Autom 15(5):818–828

    Article  Google Scholar 

  • Anggraeni P, Candra WA, Defoort M, Djemai M (2019) “Experimental implementation of fixed-time leader-follower axial alignment tracking,” in 2019 International Conference on Mechatronics, Robotics and Systems Engineering (MoRSE), pp. 86–91

  • Ao Y, Jia Y (2018) Distributed H 2/H infinity consensus control and iterative approach for multi-agent systems with directed graph. IEEE Int Conf Big Data Smart Comput (BigComp) 2018:141–146

    Google Scholar 

  • Åström KJ, Hägglund T (1995) PID controllers: theory, design, and tuning, vol 2. Instrument society of America Research Triangle Park, NC

    Google Scholar 

  • Barkai G, Mirkin L, Zelazo D (2021) On sampled-data consensus: divide and concur. IEEE Control Syst Lett. https://doi.org/10.1109/LCSYS.2021.3074589

    Article  Google Scholar 

  • Bernstein DS, Haddad WM (1989) LQG control with an H_infinity performance bound: a Riccati equation approach. IEEE Trans Autom Control 34(3):293–305

    Article  MATH  Google Scholar 

  • Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38(3):751–766

    Article  MathSciNet  MATH  Google Scholar 

  • Bollobás B (2013) Modern graph theory, vol 184. Springer, New York

    MATH  Google Scholar 

  • Bondy JA, Murty USR (1976) Graph theory with applications, vol 290. Macmillan, London

    Book  MATH  Google Scholar 

  • Boyd S, Ghosh A, Prabhakar B, Shah D (2006) Randomized gossip algorithms. IEEE Trans Inf Theory 52(6):2508–2530

    Article  MathSciNet  MATH  Google Scholar 

  • Campion G, Bastin G, Dandrea-Novel B (1996) Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE Trans Robot Autom 12(1):47–62

    Article  Google Scholar 

  • Cardei M, Wu J (2004) Coverage in wireless sensor networks. Handb Sens Netw 21:201–202

    Google Scholar 

  • Cartwright D, Harary F (1956) Structural balance: a generalization of Heider’s theory. Psychol Rev 63(5):277

    Article  Google Scholar 

  • Censi A, Murray RM (2009) Real-valued average consensus over noisy quantized channels. Am Control Conf 2009:4361–4366

    Google Scholar 

  • Chang Y-H, Chang C-W, Chen C-L, Tao C-W (2011) Fuzzy sliding-mode formation control for multirobot systems: design and implementation. IEEE Trans Syst Man Cybern Part B 42(2):444–457

    Article  Google Scholar 

  • Chen Y, Lü J, Han F, Yu X (2011) On the cluster consensus of discrete-time multi-agent systems. Syst Control Lett 60(7):517–523

    Article  MathSciNet  MATH  Google Scholar 

  • Chen W, Li X, Jiao LC (2013) Quantized consensus of second-order continuous-time multi-agent systems with a directed topology via sampled data. Automatica 49(7):2236–2242

    Article  MathSciNet  MATH  Google Scholar 

  • Chen CLP, Wen G-X, Liu Y-J, Wang F-Y (2014) Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Trans Neural Networks Learn Syst 25(6):1217–1226

    Article  Google Scholar 

  • Chen F, Dimarogonas DV (2019) Consensus control for leader-follower multi-agent systems under prescribed performance guarantees in 2019 IEEE 58th Conference on Decision and Control (CDC), pp 4785–4790

  • Cheng L, Wang Y, Ren W, Hou Z-G, Tan M (2015) Containment control of multiagent systems with dynamic leaders based on a $ PI^{n} $-type approach. IEEE Trans Cybern 46(12):3004–3017

    Article  Google Scholar 

  • Cheng L, Hou Z-G, Tan M (2008) Decentralized adaptive consensus control for multi-manipulator system with uncertain dynamics in 2008 IEEE International Conference on Systems, Man and Cybernetics pp 2712–2717

  • Chowdhury M, Zaharia M, Ma J, Jordan MI, Stoica I (2011) Managing data transfers in computer clusters with orchestra. ACM SIGCOMM Comput Commun Rev 41(4):98–109

    Article  Google Scholar 

  • Chu S-Y, Teng C-C (1999) Tuning of PID controllers based on gain and phase margin specifications using fuzzy neural network. Fuzzy Sets Syst 101(1):21–30

    Article  Google Scholar 

  • Colunga JA, Vázquez CR, Becerra HM, Gómez-Gutiérrez D (2018) Predefined-time consensus of nonlinear first-order systems using a time base generator. Math Probl Eng 2018:1–11

    Article  MathSciNet  MATH  Google Scholar 

  • Consolini L, Morbidi F, Prattichizzo D, Tosques M (2008) Leader–follower formation control of nonholonomic mobile robots with input constraints. Automatica 44(5):1343–1349

    Article  MathSciNet  MATH  Google Scholar 

  • CortéS J (2006) Finite-time convergent gradient flows with applications to network consensus. Automatica 42(11):1993–2000

    Article  MathSciNet  MATH  Google Scholar 

  • Davis JA (1967) Clustering and structural balance in graphs. Hum Relations 20(2):181–187

    Article  Google Scholar 

  • De Queiroz M, Cai X, Feemster M (2019) Formation control of multi-agent systems: a graph rigidity approach. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Deshpande PB (1989) Multivariable process control. Instrument Society of America. Research Triangle Park, NC, U.S.A

  • Diego S, Krstic´ M, Kanellakopoulos I, Kokotovic´ PV (1995) Nonlinear and adaptive control design. Wiley, New York

    Google Scholar 

  • Ding T-F, Ge M-F, Xiong C-H, Park JH, Li M (2021) Second-order bipartite consensus for networked robotic systems with quantized-data interactions and time-varying transmission delays. ISA Trans 108:178–187

    Article  Google Scholar 

  • Dong X, Zhou Y, Ren Z, Zhong Y (2016) Time-varying formation control for unmanned aerial vehicles with switching interaction topologies. Control Eng Pract 46:26–36

    Article  Google Scholar 

  • Dong G, Li H, Ma H, Lu R (2020) Finite-time consensus tracking neural network FTC of multi-agent systems. IEEE Trans Neural Netw Learn Syst 32(2):653–662

    Article  MathSciNet  Google Scholar 

  • Edwards C, Spurgeon SK (2002) Dynamic sliding mode control and output feedback. In: Sliding mode control in engineering, 1st edn. CRC Press, New York

  • Erdős P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5(1):17–60

    MathSciNet  MATH  Google Scholar 

  • Euston M, Coote P, Mahony R, Kim J, Hamel T (2008) A complementary filter for attitude estimation of a fixed-wing UAV. IEEE/RSJ Int Conf Intell Robots Syst 2008:340–345

    Google Scholar 

  • Ezal K, Pan Z, Kokotovic PV (2000) Locally optimal and robust backstepping design. IEEE Trans Automat Contr 45(2):260–271

    Article  MathSciNet  MATH  Google Scholar 

  • Ferrari-Trecate G, Galbusera L, Marciandi MPE, Scattolini R (2009) Model predictive control schemes for consensus in multi-agent systems with single-and double-integrator dynamics. IEEE Trans Automat Contr 54(11):2560–2572

    Article  MathSciNet  MATH  Google Scholar 

  • Fu J, Wen G, Yu W, Ding Z (2017) Finite-time consensus for second-order multi-agent systems with input saturation. IEEE Circuits Syst II Express Briefs 65(11):1758–1762

    Google Scholar 

  • Fu W, Qin J, Wu J, Zheng WX, Kang Y (2020) Interval consensus over random networks. Automatica 111:108603

    Article  MathSciNet  MATH  Google Scholar 

  • Glorennec PY (1996) Fuzzy logic-based navigation for an autonomous robot. IFAC Proc 29(4):45–49

    Article  Google Scholar 

  • Goldin D, Raisch J (2010) Controllability of second order leader-follower systems. IFAC Proc 43(19):233–238

    Article  Google Scholar 

  • Gong P (2016) Distributed consensus of non-linear fractional-order multi-agent systems with directed topologies. IET Control Theory Appl 10(18):2515–2525

    Article  MathSciNet  Google Scholar 

  • Gravelle E, Martínez S (2014) Quantized distributed load balancing with capacity constraints in 53rd IEEE Conference on Decision and Control, pp 3866–3871

  • Guo J, Li L, Li K, Wang R (2013) An adaptive fuzzy-sliding lateral control strategy of automated vehicles based on vision navigation. Veh Syst Dyn 51(10):1502–1517

    Article  Google Scholar 

  • Han T, Guan Z-H, Liao R-Q, Chen J, Chi M, He D-X (2017a) Distributed finite-time formation tracking control of multi-agent systems via FTSMC approach. IET Control Theory Appl 11(15):2585–2590

    Article  MathSciNet  Google Scholar 

  • Han T, Guan Z-H, Chi M, Hu B, Li T, Zhang X-H (2017b) Multi-formation control of nonlinear leader-following multi-agent systems. ISA Trans 69:140–147

    Article  Google Scholar 

  • Hatano Y, Mesbahi M (2005) Agreement over random networks. IEEE Trans Automat Contr 50(11):1867–1872

    Article  MathSciNet  MATH  Google Scholar 

  • He W, Cao J (2011) Consensus control for high-order multi-agent systems. IET Control Theory Appl 5(1):231–238

    Article  MathSciNet  Google Scholar 

  • He W, Zhang B, Han Q-L, Qian F, Kurths J, Cao J (2016) Leader-following consensus of nonlinear multiagent systems with stochastic sampling. IEEE Trans Cybern 47(2):327–338

    Google Scholar 

  • He W, Xu C, Han Q-L, Qian F, Lang Z (2017) Finite-time $\mathcal L _ 2 $ leader-follower consensus of networked Euler-Lagrange systems with external disturbances. IEEE Trans Syst Man Cybern Syst 48(11):1920–1928

    Article  Google Scholar 

  • Hill J, Szewczyk R, Woo A, Hollar S, Culler D, Pister K (2000) System architecture directions for networked sensors. ACM Sigplan Not 35(11):93–104

    Article  Google Scholar 

  • Hou Z-G, Cheng L, Tan M (2009) Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans. Syst. Man Cybern. Part B 39(3):636–647

    Article  Google Scholar 

  • Hu G (2012) Robust consensus tracking of a class of second-order multi-agent dynamic systems. Syst Control Lett 61(1):134–142

    Article  MathSciNet  MATH  Google Scholar 

  • Hu J (2014) Bipartite consensus control of multiagent systems on coopetition networks. Abstract Appl Anal 2014:1–9

    MathSciNet  MATH  Google Scholar 

  • Hu J, Li S, Zhao C et al (2017) Finite-time consensus for multi UAV system with collision avoidance. IEEE Int Conf Unmanned Syst (ICUS) 2017:517–522

    Google Scholar 

  • Huang Z (2017) Consensus control of multiple-quadcopter systems under communication delays

  • Huang M, Manton JH (2009) Stochastic consensus seeking with noisy and directed inter-agent communication: fixed and randomly varying topologies. IEEE Trans Automat Contr 55(1):235–241

    Article  MathSciNet  MATH  Google Scholar 

  • Ioannou P, Kokotovic P (1985) Decentralized adaptive control of interconnected systems with reduced-order models. Automatica 21(4):401–412

    Article  MathSciNet  MATH  Google Scholar 

  • Ismail ZH and Sariff N (2018) A survey and analysis of cooperative multi-agent robot systems: challenges and directions in Applications of Mobile Robots IntechOpen

  • Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr 48(6):988–1001

    Article  MathSciNet  MATH  Google Scholar 

  • Kashyap A, Başar T, Srikant R (2007) Quantized consensus. Automatica 43(7):1192–1203

    Article  MathSciNet  MATH  Google Scholar 

  • Kingston DB, Ren W, and Beard RW (2005) Consensus algorithms are input-to-state stable,” in Proceedings of the 2005, American Control Conference, 2005, pp 1686–1690

  • Klotz JR, Kan Z, Shea JM, Pasiliao EL, Dixon WE (2014) Asymptotic synchronization of a leader-follower network of uncertain Euler-Lagrange systems. IEEE Trans Control Netw Syst 2(2):174–182

    Article  MathSciNet  MATH  Google Scholar 

  • Lafferriere G, Williams A, Caughman J, Veerman JJP (2005) Decentralized control of vehicle formations. Syst Control Lett 54(9):899–910

    Article  MathSciNet  MATH  Google Scholar 

  • Lavaei J, Murray RM (2011) Quantized consensus by means of gossip algorithm. IEEE Trans Automat Contr 57(1):19–32

    Article  MathSciNet  MATH  Google Scholar 

  • Li M, Deng F (2021) Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises. ISA Trans 116:113–120

    Article  Google Scholar 

  • Li Y, Tan C (2019) A survey of the consensus for multi-agent systems. Syst Sci Control Eng 7(1):468–482

    Article  Google Scholar 

  • Li S, Wang X (2013) Finite-time consensus and collision avoidance control algorithms for multiple AUVs. Automatica 49(11):3359–3367

    Article  MathSciNet  MATH  Google Scholar 

  • Li D, Liu Q, Wang X, Yin Z (2014) Quantized consensus over directed networks with switching topologies. Syst Control Lett 65:13–22

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Chen MZQ, Su H (2018) Quantized consensus of multi-agent networks with sampled data and Markovian interaction links. IEEE Trans Cybern 49(5):1816–1825

    Article  Google Scholar 

  • Li D, Ge SS, He W, Ma G, Xie L (2019) Multilayer formation control of multi-agent systems. Automatica 109:108558

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Yu Z, Li Z, Wu N (2021) Group consensus via pinning control for a class of heterogeneous multi-agent systems with input constraints. Inf Sci (ny) 542:247–262

    Article  MathSciNet  MATH  Google Scholar 

  • Liang S, Wang F, Liu Z, Chen Z (2021) Necessary and sufficient conditions for leader-follower consensus of discrete-time multiagent systems with smart leader. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2021.3055578

    Article  Google Scholar 

  • Lin P, Jia Y, Li L (2008) Distributed robust H∞ consensus control in directed networks of agents with time-delay. Syst Control Lett 57(8):643–653

    Article  MathSciNet  MATH  Google Scholar 

  • Lin J, Morse AS, Anderson BDO (2003) The multi-agent rendezvous problem,” in 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475), vol 2, pp 1508–1513

  • Liu X, He S, Lu P, Liu H, Du C (2021) Finite-time consensus for multi-agent systems with nonlinear dynamics under Euler digraph via pinning control. Int J Syst Sci 52(8):1664–1674

    Article  MathSciNet  MATH  Google Scholar 

  • Lu X, Chen S, Lü J (2013) Finite-time tracking for double-integrator multi-agent systems with bounded control input. IET Control Theory Appl 7(11):1562–1573

    Article  MathSciNet  Google Scholar 

  • Lu K, Liu Z, Lai G, Chen CLP, Zhang Y (2019) Adaptive consensus tracking control of uncertain nonlinear multiagent systems with predefined accuracy. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2019.2933436.

  • Ma Z, Wang Y, Li X (2016) Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics. Nonlinear Dyn 83(3):1303–1310

    Article  MathSciNet  MATH  Google Scholar 

  • Ma J, Ji H, Sun D, Feng G (2018) An approach to quantized consensus of continuous-time linear multi-agent systems. Automatica 91:98–104

    Article  MathSciNet  MATH  Google Scholar 

  • Mesbahi M, Egerstedt M (2010) Graph theoretic methods in multiagent networks, vol 33. Princeton University Press, Princeton

    Book  MATH  Google Scholar 

  • Moreau L (2005) Stability of multiagent systems with time-dependent communication links. IEEE Trans Automat Contr 50(2):169–182

    Article  MathSciNet  MATH  Google Scholar 

  • Morse AS, Kanellakopoulos I, Kokotovi PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Automat Contr 36(11):1241–1253

    MathSciNet  MATH  Google Scholar 

  • Nguyen DH (2016) Reduced-order distributed consensus controller design via edge dynamics. IEEE Trans Automat Contr 62(1):475–480

    Article  MathSciNet  MATH  Google Scholar 

  • Oh K-K, Park M-C, Ahn H-S (2015) A survey of multi-agent formation control. Automatica 53:424–440

    Article  MathSciNet  MATH  Google Scholar 

  • Olfati-Saber R (2006) Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Automat Contr 51(3):401–420

    Article  MathSciNet  MATH  Google Scholar 

  • Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Automat Contr 49(9):1520–1533

  • Olfati-Saber R, Shamma JS (2005) Consensus filters for sensor networks and distributed sensor fusion in Proceedings of the 44th IEEE Conference on Decision and Control pp 6698–6703

  • Olfati-Saber R, Franco E, Frazzoli E, Shamma JS (2006) Belief consensus and distributed hypothesis testing in sensor networks. In: Antsaklis PJ, Tabuada P (eds) Networked embedded sensing and control. Lecture notes in control and information science, vol 331. Springer, Berlin, Heidelberg

    MATH  Google Scholar 

  • Parks P (1966) Liapunov redesign of model reference adaptive control systems. IEEE Trans Automat Contr 11(3):362–367

    Article  Google Scholar 

  • Partridge BL (1984) The chorus-line hypothesis of maneuver in avian flocks. Nature 309(6):344–345

    Google Scholar 

  • Patterson S, McGlohon N, Dyagilev K (2016) Optimal k-leader selection for coherence and convergence rate in one-dimensional networks. IEEE Trans Control Netw Syst 4(3):523–532

    Article  MathSciNet  MATH  Google Scholar 

  • Polycarpou MM, Ioannou PA (1991) Identification and control of nonlinear systems using neural network models: design and stability analysis University of Southern Calif

  • Prasanna S, Rao S (2012) An overview of wireless sensor networks applications and security. Int. J. Soft Comput. Eng. (IJSCE) 2231:2307

    Google Scholar 

  • Puccinelli D, Haenggi M (2005) Wireless sensor networks: applications and challenges of ubiquitous sensing. IEEE Circuits Syst Mag 5(3):19–31

    Article  Google Scholar 

  • Qin J, Yu C (2013) Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica 49(9):2898–2905

    Article  MathSciNet  MATH  Google Scholar 

  • Qin J, Fu W, Zheng WX, Gao H (2016) On the bipartite consensus for generic linear multiagent systems with input saturation. IEEE Trans Cybern 47(8):1948–1958

    Article  Google Scholar 

  • Qin J, Zheng WX, Gao H (2010) Sampled-data consensus for multiple agents with discrete second-order dynamics,” in 49th IEEE Conference on Decision and Control (CDC), pp 1391–1396

  • Ren W, Atkins E (2007) Distributed multi-vehicle coordinated control via local information exchange. Int J Robust Nonlinear Control IFAC-Affiliated J 17(10–11):1002–1033

    Article  MathSciNet  MATH  Google Scholar 

  • Ren W, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Automat Contr 50(5):655–661

    Article  MathSciNet  MATH  Google Scholar 

  • Ren W, Beard RW (2008) Distributed consensus in multi-vehicle cooperative control, vol 27. Springer, London

    Book  MATH  Google Scholar 

  • Ren W, Beard RW, Atkins EM (2007a) Information consensus in multivehicle cooperative control. IEEE Control Syst Mag 27(2):71–82

    Article  Google Scholar 

  • Ren W, Moore KL, Chen Y (2007b) High-order and model reference consensus algorithms in cooperative control of multivehicle systems. ASME J Dyn Syst Measure Control 129(5):678–688

    Article  Google Scholar 

  • Ren W, Chao H, Bourgeous W, Sorensen N, Chen Y (2008) Experimental validation of consensus algorithms for multivehicle cooperative control. IEEE Trans Control Syst Technol 16(4):745–752

    Article  Google Scholar 

  • Ren W, Beard RW (2008) Consensus algorithms for double-integrator dynamics. In: Distributed consensus in multi-vehicle cooperative control. Communications and control engineering. Springer, London

  • Ren W, Moore K, Chen Y (2006) High-order consensus algorithms in cooperative vehicle systems in 2006 IEEE International Conference on Networking, Sensing and Control pp 457–462

  • Reynolds CW (1987) “Flocks, herds and schools: a distributed behavioral model,” in Proceedings of the 14th annual conference on Computer graphics and interactive techniques pp 25–34

  • Rong L, Su P, Gao H, Xu S (2021a) Distributed quantized consensus with recursive channel filters over directed networks. IEEE Trans Circuits Syst II Express Briefs. https://doi.org/10.1109/TCSII.2021.3099875

    Article  Google Scholar 

  • Rong L, Liu X, Jiang G-P, Xu S (2021b) Observer-based multiagent bipartite consensus with deterministic disturbances and antagonistic interactions. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3087645

    Article  Google Scholar 

  • Roy S (2015) Scaled consensus. Automatica 51:259–262

    Article  MathSciNet  MATH  Google Scholar 

  • Runolfsson T (1990) “Stationary risk-sensitive LQG control and its relation to LQG and H-infinity control,” in 29th IEEE Conference on Decision and Control pp 1018–1023

  • Schenato L, Gamba G (2007) A distributed consensus protocol for clock synchronization in wireless sensor network in 2007 46th IEEE Conference on Decision and Control, pp 2289–2294

  • Shang Y (2010) Multi-agent coordination in directed moving neighbourhood random networks. Chin Phys B 19(7):70201

    Article  Google Scholar 

  • Shang Y (2018) Finite-time scaled consensus in discrete-time networks of agents. Asian J Control 20(6):2351–2356

    Article  MathSciNet  MATH  Google Scholar 

  • Shang Y (2019) Scaled consensus of switched multi-agent systems. IMA J Math Control Inf 36(2):639–657

    Article  MathSciNet  MATH  Google Scholar 

  • Shang Y (2020a) On the structural balance dynamics under perceived sentiment. Bull Iran Math Soc 46(3):717–724

    Article  MathSciNet  MATH  Google Scholar 

  • Shang Y (2020) Resilient consensus in multi-agent systems with state constraints. Automatica 122:109288

    Article  MathSciNet  MATH  Google Scholar 

  • Shang L, Cai M (2021) Adaptive practical fast finite-time consensus protocols for high-order nonlinear multi-agent systems with full state constraints. IEEE Access. https://doi.org/10.1109/ACCESS.2021.3085843

    Article  Google Scholar 

  • Shang Y, Ye Y (2017) Fixed-time group tracking control with unknown inherent nonlinear dynamics. IEEE Access 5:12833–12842

    Article  Google Scholar 

  • Shang Y (2020) Resilient cluster consensus of multiagent systems IEEE Trans Syst Man Cybern Syst

  • Shang Y, Chen B, Lin C (2018) Consensus tracking control for distributed nonlinear multiagent systems via adaptive neural backstepping approach. IEEE Trans Syst Man Cybern Syst 50(7):2436–2444

  • Shi C-X, Yang G-H (2018) Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics. Appl Math Comput 316:73–88

    MathSciNet  MATH  Google Scholar 

  • Sun Y, Ji Z, Qi Q, Ma H (2019) Bipartite consensus of multi-agent systems with intermittent interaction. IEEE Access 7:130300–130311

    Article  Google Scholar 

  • Sun J, Wang Z, Rong N (2020) Sampled-data consensus of multiagent systems with switching jointly connected topologies via time-varying Lyapunov function approach. Int J Robust Nonlinear Control 30(14):5369–5385

    Article  MathSciNet  MATH  Google Scholar 

  • Sundaram S, Hadjicostis CN (2007) Finite-time distributed consensus in graphs with time-invariant topologies. Am Control Conf 2007:711–716

    Google Scholar 

  • Tahbaz-Salehi A, Jadbabaie A (2008) A necessary and sufficient condition for consensus over random networks. IEEE Trans Automat Contr 53(3):791–795

    Article  MathSciNet  MATH  Google Scholar 

  • Tanner HG, Jadbabaie A and Pappas GJ (2003) Flocking in fixed and switching networks. IEEE Transactions on Automatic Control 52(5):863–868,

  • Tian L, Ji Z, Hou T, Liu K (2018) Bipartite consensus on coopetition networks with time-varying delays. IEEE Access 6:10169–10178

    Article  Google Scholar 

  • Valcher ME, Misra P (2014) On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Syst Control Lett 66:94–103

    Article  MathSciNet  MATH  Google Scholar 

  • Vermunt JK, Magidson J (2002) Latent class cluster analysis. Appl Latent Cl Anal 11(89–106):60

    Google Scholar 

  • Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel type of phase transition in a system of self-driven particles. Phys Rev Lett 75(6):1226

    Article  MathSciNet  Google Scholar 

  • Wang Q (2017) Scaled consensus of multi-agent systems with output saturation. J Franklin Inst 354(14):6190–6199

    Article  MathSciNet  MATH  Google Scholar 

  • Wang X, Hong Y (2008) Finite-time consensus for multi-agent networks with second-order agent dynamics. IFAC Proc 41(2):15185–15190

    Article  Google Scholar 

  • Wang L, Xiao F (2010) Finite-time consensus problems for networks of dynamic agents. IEEE Trans Automat Contr 55(4):950–955

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Rad AB, Chan PT (2001) Indirect adaptive fuzzy sliding mode control: Part I: fuzzy switching. Fuzzy Sets Syst 122(1):21–30

    Article  MATH  Google Scholar 

  • Wang J, Duan Z, Li Z, Wen G (2013) Distributed H∞ and H 2 consensus control in directed networks. IET Control Theory Appl 8(3):193–201

    Article  MathSciNet  Google Scholar 

  • Wang X, Li S, Yu X, Yang J (2016) Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances. IEEE Trans Automat Contr 62(11):5795–5801

    Article  MathSciNet  MATH  Google Scholar 

  • Wang X, Li S, Chen MZQ (2017) Composite backstepping consensus algorithms of leader–follower higher-order nonlinear multiagent systems subject to mismatched disturbances. IEEE Trans Cybern 48(6):1935–1946

    Article  Google Scholar 

  • West DB (1996) Introduction to graph theory, vol 2. Prentice hall Upper Saddle River, NJ

    MATH  Google Scholar 

  • Wood AD, Stankovic JA (2002) Denial of service in sensor networks. Computer 35(10):54–62

    Article  Google Scholar 

  • Wu Y, Wang Z, Ding S, Zhang H (2018) Leader–follower consensus of multi-agent systems in directed networks with actuator faults. Neurocomputing 275:1177–1185

    Article  Google Scholar 

  • Xiao F, Wang L (2007) Consensus problems for high-dimensional multi-agent systems. IET Control Theory Appl 1(3):830–837

    Article  Google Scholar 

  • Xie G, Wang L (2007) Consensus control for a class of networks of dynamic agents. Int J Robust Nonlinear Control IFAC-Affil J 17(10–11):941–959

    Article  MathSciNet  MATH  Google Scholar 

  • Yi J, Wang W, Zhao D, Liu X (2005) Cascade sliding-mode controller for large-scale underactuated systems. IEEE/RSJ Int Conf Intell Robots Syst 2005:301–306

    Google Scholar 

  • Yi J-W, Wang Y-W, Xiao J-W (2014) Consensus in Markovian jump second-order multi-agent systems with random communication delay. IET Control Theory Appl 8(16):1666–1675

    Article  MathSciNet  Google Scholar 

  • Yick J, Mukherjee B, Ghosal D (2008) Wireless sensor network survey. Comput Netw 52(12):2292–2330

    Article  Google Scholar 

  • Yu W, Wang H, Hong H, Wen G (2017) Distributed cooperative anti-disturbance control of multi-agent systems: an overview. Sci China Inf Sci 60(11):110202

    Article  MathSciNet  Google Scholar 

  • Zhan J, Li X (2017) Cluster consensus in networks of agents with weighted cooperative–competitive interactions. IEEE Trans Circuits Syst II Express Briefs 65(2):241–245

    Google Scholar 

  • Zhang H, Chen J (2014) Bipartite consensus of linear multi-agent systems over signed digraphs: an output feedback control approach. IFAC Proc 47(3):4681–4686

    Article  Google Scholar 

  • Zhang H, Sundaram S (2012) Robustness of information diffusion algorithms to locally bounded adversaries. Am Control Conf (ACC) 2012:5855–5861

    Google Scholar 

  • Zhang X, Liu L, Feng G (2015) Leader–follower consensus of time-varying nonlinear multi-agent systems. Automatica 52:8–14

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang Z, Zhang L, Hao F, Wang L (2016) Leader-following consensus for linear and Lipschitz nonlinear multiagent systems with quantized communication. IEEE Trans Cybern 47(8):1970–1982

    Article  Google Scholar 

  • Zhang Z, Shi Y, Zhang Z, Yan W (2018) New results on sliding-mode control for Takagi-Sugeno fuzzy multiagent systems. IEEE Trans Cybern 49(5):1592–1604

    Article  Google Scholar 

  • Zhang Z, Chen S, Su H (2019) Scaled consensus of second-order nonlinear multiagent systems with time-varying delays via aperiodically intermittent control. IEEE Trans Cybern 50:3503

    Article  Google Scholar 

  • 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 (ny) 555:314–338

    Article  MathSciNet  Google Scholar 

  • Zhang D, Feng G (2021) A new switched system approach to leader-follower consensus of heterogeneous linear multiagent systems with dos attack. IEEE Trans Syst Man Cybern Syst 51(2):1258–1266

    Article  Google Scholar 

  • Zhang W, Tang Y, Han Q-L, Liu Y (2020) Sampled-data consensus of linear time-varying multiagent networks with time-varying topologies. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.2977720

  • Zhao Y, Duan Z, Wen G, Chen G (2012) Distributed H∞ consensus of multi-agent systems: a performance region-based approach. Int J Control 85(3):332–341

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao L, Jia Y, Yu J, Du J (2017) H∞ sliding mode based scaled consensus control for linear multi-agent systems with disturbances. Appl Math Comput 292:375–389

    MathSciNet  MATH  Google Scholar 

  • Zhao H, Peng L, Yu H (2022) Quantized model-free adaptive iterative learning bipartite consensus tracking for unknown nonlinear multi-agent systems. Appl Math Comput 412:126582

    MathSciNet  MATH  Google Scholar 

  • Zhiqiang Z, Zhicheng Z, Yijing W (2015) Finite-time consensus of double integrator multi-agent systems subject to input saturation in 2015 34th Chinese Control Conference (CCC), 2015, pp 7280–7284

  • Zhu J, Tian Y-P, Kuang J (2009) On the general consensus protocol of multi-agent systems with double-integrator dynamics. Linear Algebra Appl 431(5–7):701–715

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu J, Lu J, Yu X (2012) Flocking of multi-agent non-holonomic systems with proximity graphs. C IEEE Trans Circuits Syst I Regul Pap 60(1):199–210

    Article  MathSciNet  MATH  Google Scholar 

  • Zuo Z, Tian B, Defoort M, Ding Z (2017) Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Trans Automat Contr 63(2):563–570

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abdollah Amirkhani.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amirkhani, A., Barshooi, A.H. Consensus in multi-agent systems: a review. Artif Intell Rev 55, 3897–3935 (2022). https://doi.org/10.1007/s10462-021-10097-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10462-021-10097-x

Keywords

Navigation