In this paper, the fixed-time formation tracking control problem is addressed for second-order multi-agent systems with external disturbances and a non-autonomous leader. The non-zero control input of the leader, bringed into the closed-loop system of followers, is considered as a bounded disturbance and is dealt with by the sliding mode control method, instead of the traditional observer approach. Based on this methodology, the novel fixed-time formation tracking control protocols are designed for both the constant and variable exponent coefficient cases, which employ fewer regulatory parameters compared with existing results. Meanwhile, the theoretical analysis is derived to obtain the stability result. Comprehensive simulation results validate the effectiveness of the proposed methodologies.
CaiYZhangHZhangJ, et al. (2021) Fixed-time leader-following/containment consensus for a class of nonlinear multi-agent systems. Information Sciences555: 58–84.
2.
HuaYDongXHuG, et al. (2019) Distributed time-varying output formation tracking for heterogeneous linear multiagent systems with a nonautonomous leader of unknown input. IEEE Transactions on Automatic Control64(10): 4292–4299.
3.
LiQWeiJGouQ, et al. (2021) Distributed adaptive fixed-time formation control for second-order multi-agent systems with collision avoidance. Information Sciences564: 27–44.
4.
LinJWangYMiaoZ, et al. (2023) Robust linear-velocity-free formation tracking of multiple quadrotors with unknown disturbances. IEEE Transactions on Control of Network Systems10(4): 1757–1769.
5.
LiuZQGeXXieH, et al. (2024) Secure leader–follower formation control of networked mobile robots under replay attacks. IEEE Transactions on Industrial Informatics20(3): 4149–4159.
6.
MaJWangJFeiS, et al. (2022) Global fixed-time control for nonlinear systems with unknown control coefficients and dead-zone input. IEEE Transactions on Circuits and Systems II: Express Briefs69(2): 594–598.
7.
MengQMaQShiY (2023) Adaptive fixed-time stabilization for a class of uncertain nonlinear systems. IEEE Transactions on Automatic Control68(11): 6929–6936.
8.
MoulayELéchappéVBernuauE, et al. (2022) Robust fixed-time stability: application to sliding-mode control. IEEE Transactions on Automatic Control67(2): 1061–1066.
9.
PanZSunZDengH, et al. (2022) A multilayer graph for multiagent formation and trajectory tracking control based on mpc algorithm. IEEE Transactions on Cybernetics52(12): 13586–13597.
10.
PolyakovA (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control57(8): 2106–2110.
11.
SongWFengJZhangH, et al. (2023a) Formation tracking control for heterogeneous multiagent systems with multiple nonautonomous leaders via dynamic event-triggered mechanisms. IEEE Transactions on Cybernetics53(11): 7224–7237.
12.
SongWFengJZhangH, et al. (2023b) Dynamic event-triggered formation control for heterogeneous multiagent systems with nonautonomous leader agent. IEEE Transactions on Neural Networks and Learning Systems34(12): 9685–9699.
13.
SunHMadonskiRLiS, et al. (2022) Composite control design for systems with uncertainties and noise using combined extended state observer and kalman filter. IEEE Transactions on Industrial Electronics69(4): 4119–4128.
14.
TatariFModaresH (2023) Deterministic and stochastic fixed-time stability of discrete-time autonomous systems. IEEE/CAA Journal of Automatica Sinica10(4): 945–956.
15.
TianBLuHZuoZ, et al. (2019) Fixed-time leader–follower output feedback consensus for second-order multiagent systems. IEEE Transactions on Cybernetics49(4): 1545–1550.
16.
TrujilloMAAldana-LopezRGomez-GutierrezD, et al. (2020) Autonomous and non-autonomous fixed-time leader-follower consensus for second-order multi-agent systems. Nonlinear Dynamics102(4): 2669–2686.
17.
VoATruongTKangHJ (2021) A novel fixed-time control algorithm for trajectory tracking control of uncertain magnetic levitation systems. IEEE Access9: 47698–47712.
18.
WangPWenGYuW, et al. (2023a) An adaptive continuous approach to consensus tracking of nonlinear multiagent systems with a nonautonomous leader. IEEE Transactions on Systems, Man, and Cybernetics: Systems53(8): 4684–4695.
19.
WangPWenGYuW, et al. (2023b) Asymptotical consensus of MIMO linear multiagent systems with a nonautonomous leader and directed switching topology: a continuous approach. IEEE Transactions on Control of Network Systems10(3): 1326–1337.
20.
XuKWangHLiuPX (2024) Adaptive fixed-time control for high-order stochastic nonlinear time-delay systems: an improved Lyapunov-Krasovskii function. IEEE Transactions on Cybernetics54(2): 776–786.
21.
YangJCaoGChenW, et al. (2022) Finite-time formation control of second-order linear multi-agent systems with relative state constraints: a barrier function sliding mode control approach. IEEE Transactions on Circuits and Systems II: Express Briefs69(3): 1253–1256.
22.
YiYZhengWXLiuB (2022) Adaptive anti-disturbance control for systems with saturating input via dynamic neural network disturbance modeling. IEEE Transactions on Cybernetics52(6): 5290–5300.
23.
YuLHeGWangX, et al. (2022) A novel fixed-time sliding mode control of quadrotor with experiments and comparisons. IEEE Control Systems Letters6: 770–775.
24.
ZhangHLiWZhangJ, et al. (2023) Fully distributed dynamic event-triggered bipartite formation tracking for multiagent systems with multiple nonautonomous leaders. IEEE Transactions on Neural Networks and Learning Systems34(10): 7453–7466.
25.
ZhangJFuYFuJ (2024) Adaptive fixed-time output-feedback optimal time-varying formation control for multiple omnidirectional robot systems. IEEE Transactions on Fuzzy Systems32(3): 792–803.
26.
ZhengCBPangZHWangJX, et al. (2023a) Time-varying formation prescribed performance control with collision avoidance for multi-agent systems subject to mismatched disturbances. Information Sciences633: 517–530.
27.
ZhengCBPangZHWangJX, et al. (2023b) Null-space-based time-varying formation control of uncertain nonlinear second-order multi-agent systems with collision avoidance. IEEE Transactions on Industrial Electronics70(10): 10476–10485.
28.
ZhouPChenBM (2022) Formation-containment control of Eruler-Lagrange systems of leaders with bounded unknown inputs. IEEE Transactions on Cybernetics52(7): 6342–6353.
29.
ZhuSLvKYangZ, et al. (2024) Bearing-based formation tracking control of nonholonomic mobile agents with a persistently exciting leader. IEEE Transactions on Control of Network Systems11(1): 307–318.
