The fixed-time flocking of multi-agent systems with a virtual leader is investigated in this paper. The motion dynamics of the agents are assumed to be unknown and only satisfy the boundedness, which does not need to be modelled by the Lipschitz condition. To achieve the flocking and collision avoidance for all agents in the fixed time, a control protocol in the high-dimensional space is developed by using the graph theory and the theoretical properties of differential equations. Moreover, the upper bound of the settling time only depending on the control protocol and the topology of network is estimated. Numerical examples are used to verify the theoretical results, and show that the proposed method provides an applicable method for the control of the nonlinear dynamic systems.
CuckerFSmaleS (2007) Emergent behavior in flocks. IEEE Transactions on Automatic Control52(5): 852–862.
2.
DengQWuJHanT, et al. (2019) Fixed-time bipartite consensus of multi-agent systems with disturbances. Physica A: Statistical Mechanics and its Applications516: 37–49.
3.
DongXYuBShiZ, et al. (2014) Time-varying formation control for unmanned aerial vehicles: Theories and applications. IEEE Transactions on Control Systems Technology23(1): 340–348.
4.
GaoFShangYWuY, et al. (2019) Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity. Transactions of the Institute of Measurement and Control41(7): 1888–1895.
5.
GaoJXu.XDingN, et al. (2017) Flocking motion of multi-agent system by dynamic pinning control. IET Control Theory & Applications11(5): 714–722.
6.
HongYHuJGaoL (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica42(7): 1177–1182.
7.
HuXChenLTangB, et al. (2018) Dynamic path planning for autonomous driving on various roads with avoidance of static and moving obstacles. Mechanical Systems and Signal Processing100: 482–500.
8.
LiuTJiangZ (2020) Distributed control of multi-agent systems with pulse-width-modulated controllers. Automatica119: 109020.
9.
LiuHWangXHuangY, et al. (2020) A new class of fixed-time bipartite flocking protocols for multi-agent systems. Applied Mathematical Modelling84: 501–521.
10.
MuXHeY (2019) Leader-follower multi-agent flocking with bounded missing data and random communication radius. Transactions of the Institute of Measurement and Control41(9): 2441–2450.
11.
NieFLiuY (2020) Fixed-time flocking problem of a Cucker–Smale model. Mathematical Problems in Engineering2020: 7319608.
12.
NingBJinJZhengJ, et al. (2017a) Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics. International Journal of Control19(6): 1259–1270.
13.
NingBJinJZhengJ (2017b) Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology. International journal of Systems Science48(10): 2023–2032.
14.
Olfati-SaberR (2006) Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control51(3): 401–420.
15.
ReynoldsCW (1987) Flocks, herds, and schools: a distributed behavioral model. Computer Graphics21(4): 25–34.
16.
SuHChenXChenMZQ, et al. (2016) Distributed estimation and control for mobile sensor networks with coupling delays. ISA Transactions64: 141–150.
17.
SuHLiZChenMZQ (2017) Distributed estimation and control for two-target tracking mobile sensor networks. Journal of the Franklin Institute354(7): 2994–3007.
18.
SuHWangXLinZ (2009a) Flocking of multi-agents with a virtual leader. IEEE Transactions on Automatic Control54(2): 293–307.
19.
SuHWangXChenG (2009b) A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements. International Journal of Control82(7): 1334–1343.
20.
SuHZhangNChenMZQ, et al. (2013) Adaptive flocking with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity. Nonlinear Analysis: Real World Applications14(1): 798–806.
21.
SunFWangRZhuW, et al. (2019) Flocking in nonlinear multi-agent systems with time-varying delay via event-triggered control. Applied Mathematics and Computation350: 66–77.
22.
TanFZhouLChuY, et al. (2020) Fixed-time stochastic outer synchronization in double-layered multi-weighted coupling networks with adaptive chattering-free control. Neurocomputing399: 8–17.
23.
ValcherMEMisraP (2014) On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Systems & Control Letters66: 94–103.
24.
WangZCaoJCaiZ, et al. (2020) Anti-synchronization in fixed time for discontinuous reaction–diffusion neural networks with time-varying coefficients and time delay. IEEE Transactions on Cybernetics50(6): 2758–2769.
25.
WenGZhengWX (2019) On constructing multiple Lyapunov functions for tracking control of multiple agents with switching topologies. IEEE Transactions on Automatic Control64(9): 3796–3803.
26.
WenGDuanZLiZ, et al. (2012) Flocking of multi-agent dynamical systems with intermittent nonlinear velocity measurements. International Journal of Robust and Nonlinear Control22(16): 1790–1805.
27.
XiaoQLiuHWangX, et al. (2020) A note on the fixed-time bipartite flocking for nonlinear multi-agent systems. Applied Mathematics Letters99: 105973.
YangZZhangQChenZ (2010) Flocking of multi-agents with nonlinear inner-coupling functions. Nonlinear Dynamics60(3): 255–264.
30.
ZhangHNiePSunY, et al. (2020) Fixed-time flocking problem of a Cucker–Smale type self-propelled particle model. Journal of the Franklin Institute357(11): 7054–7068.
31.
ZhangQWangJYangZ, et al. (2019) High gain feedback robust control for flocking of multi-agents system. Transactions of the Institute of Measurement and Control41(13): 3769–3776.
32.
ZhangWYangXXuC, et al. (2018a) Finite-time synchronization of discontinuous neural networks with delays and mismatched parameters. IEEE Transactions on Neural Networks & Learning Systems29(8): 3761–3771.
33.
ZhangZLiHYanW (2020) Fully distributed control of linear systems with optimal cost on directed topologies. IEEE Transactions on Circuits and Systems II: Express Briefs68(1): 336–340.
34.
ZhangZShiYZhangZ, et al. (2018b) New results on sliding-mode control for Takagi–Sugeno fuzzy multiagent systems. IEEE Transactions on Cybernetics49(5): 1592–1604.
35.
ZhengHPaneratiJBeltrameG, et al. (2020) An adversarial approach to private flocking in mobile robot teams. IEEE Robotics and Automation Letters5(2): 1009–1016.
36.
ZuoZTieL (2014) A new class of finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Control87(2): 363–370.
