This article examines the bipartite consensus problem in multi-agent systems affected by actuator saturation and external disturbances. Based on the enlargement of the contractively invariant set, sufficient conditions are derived to ensure bipartite consensus and to evaluate the domain of consensus attraction under input saturation and magnitude-bounded disturbances. For systems subject to energy-bounded disturbances, a criterion is further developed to ensure that the system trajectories starting from an inner ellipsoid remain within an outer ellipsoid while achieving bipartite consensus. Moreover, the analytical problems are reformulated as convex optimization problems constrained by linear matrix inequalities. This formulation improves both the feasibility and computational efficiency of the proposed control method. Finally, numerical simulations are conducted to validate the effectiveness and superiority of the developed bipartite consensus control strategy.
HouTBiWHuangZ, et al. Time-varying formation tracking for multi-agent systems based on prescribed-time control. Proc Inst Mech Eng Part I: J Syst Control Eng2025; 239(6): 1093–1106.
2.
WangJJiYDingF.Iterative parameter estimation for a class of fractional-order hammerstein nonlinear systems disturbed by colored noise. Proc Inst Mech Eng Part I: J Syst Control Eng2025; 239(7): 1222–1238.
3.
SongZLiuJSunK.Performance-guaranteed fault tolerant control for Euler–Lagrange systems with actuator faults and uncertain disturbance. Proc Inst Mech Eng Part I: J Syst Control Eng2025; 239(7): 1279–1291.
4.
WangFGaoZHeS, et al. Dynamic event-triggered control of nonlinear system with state constraints. Proc Inst Mech Eng Part I: J Syst Control Eng2025; 239(7): 1268–1278.
5.
WenGDuanZChenG, et al. Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies. IEEE Trans Circuits Syst I Regul Pap2013; 61(2): 499–511.
6.
BhowmickSPanjaS.Leader–follower bipartite consensus of uncertain linear multi-agent systems with external bounded disturbances over signed directed graph. IEEE Control Syst Lett2019; 3(3): 595–600.
7.
WenGWangHYuX, et al. Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Trans Circuits Syst II Express Briefs2017; 65(9): 1204–1208.
8.
LiKHuaCYouX, et al. Output feedback predefined-time bipartite consensus control for high-order nonlinear multi-agent systems. IEEE Trans Circuits Syst I Regul Pap2021; 68(7): 3069–3078.
9.
LuiDGPetrilloASantiniS.Bipartite tracking consensus for high-order heterogeneous uncertain nonlinear multi-agent systems with unknown leader dynamics via adaptive fully-distributed PID control. IEEE Trans Netw Sci Eng2022; 10(2): 1131–1142.
10.
GuoXGZhangDYWangJL, et al. Observer-based event-triggered composite anti-disturbance control for multi-agent systems under multiple disturbances and stochastic FDIAs. IEEE Trans Autom Sci Eng2022; 20(1): 528–540.
11.
HuaCZhangLGuanX.Distributed adaptive neural network output tracking of leader-following high-order stochastic nonlinear multi-agent systems with unknown dead-zone input. IEEE Trans Cybern2015; 47(1): 177–185.
12.
YouXHuaCGuanX.Event-triggered leader-following consensus for nonlinear multi-agent systems subject to actuator saturation using dynamic output feedback method. IEEE Trans Autom Control2018; 63(12): 4391–4396.
13.
WangBChenWWangJ, et al. Semi-global tracking cooperative control for multi-agent systems with input saturation: a multiple saturation levels framework. IEEE Trans Autom Control2020; 66(3): 1215–1222.
14.
LiuFHuaYDongX, et al. Adaptive fault-tolerant time-varying formation tracking for multi-agent systems under actuator failure and input saturation. ISA Trans2020; 104: 145–153.
15.
GaoCWangZHeX, et al. Consensus control of linear multi-agent systems under actuator imperfection: when saturation meets fault. IEEE Trans Syst Man Cybern Syst2022; 52(4): 2651–2663.
16.
ZhongJFengYZengC.LMI-based boundary practical consensus control for nonlinear multi-agent systems with actuator saturation. ISA Trans2023; 135: 261–271.
17.
SaderMLiWJiangH, et al. Semi-global bipartite fault-tolerant containment control for heterogeneous multi-agent systems with antagonistic communication networks and input saturation. IEEE Trans Neural Netw Learn Syst2024; 35(5): 6265–6272.
18.
YaoXLiSLiX.Composite adaptive anti-disturbance fault tolerant control of high-speed trains with multiple disturbances. IEEE Trans Intell Transp Syst2022; 23(11): 21799–21809.
19.
WangXLiSYuX, et al. Distributed active anti-disturbance consensus for leader–follower higher-order multi-agent systems with mismatched disturbances. IEEE Trans Autom Control2016; 62(11): 5795–5801.
20.
WangFGaoHWangK, et al. Disturbance observer-based finite-time control design for a quadrotor UAV with external disturbance. IEEE Trans Aerosp Electron Syst2020; 57(2): 834–847.
21.
ZhaoGHuaC.A hybrid dynamic event-triggered approach to consensus of multi-agent systems with external disturbances. IEEE Trans Autom Control2020; 66(7): 3213–3220.
22.
PangDGuoYCaoJ, et al. Hybrid dynamic event-triggered leader-following consensus for multi-agent systems with external disturbances. J Franklin Inst2024; 361(7): 106778.
23.
ZhongJFengYWuHN.Adaptive RBF neural network-based boundary consensus control for nonlinear reaction–diffusion agents with non-collocated measurements. Neurocomputing2025; 660: 131854.
24.
SelvarajPKaviarasanBSakthivelR, et al. Fault-tolerant SMC for Takagi–Sugeno fuzzy systems with time-varying delay and actuator saturation. IET Control Theory Appl2017; 11(8): 1112–1123.
25.
ZhangXLiuXLewisFL, et al. Bipartite tracking consensus of nonlinear multi-agent systems. Phys A Stat Mech Appl2020; 545: 123504.
26.
FangHLinZHuT.Analysis of linear systems in the presence of actuator saturation and -disturbances. Automatica2004; 40(7): 1229–1238.
27.
DengCYangGH.Consensus of linear multi-agent systems with actuator saturation and external disturbances. IEEE Trans Circuits Syst II Express Briefs2016; 64(3): 284–288.
28.
ZhangWHuangQAlhudhaifA.Event-triggered fixed-time bipartite consensus for nonlinear disturbed multi-agent systems with leader–follower and leaderless controller. Inf Sci2024; 662: 120243.
29.
WuSLiX.Finite-time stabilization of nonlinear systems with actuator saturation. IEEE Trans Autom Sci Eng2024; 22: 7582–7589.
30.
WuJDengQHanT, et al. Bipartite tracking consensus for multi-agent systems with Lipschitz-type nonlinear dynamics. Phys A Stat Mech Appl2019; 525: 1360–1369.
