This paper is concerned with the consensus tracking problem in nonlinear multi-agent systems against external disturbances and multiple actuator faults. The nonlinear dynamics are unknown and the leader’s input is unavailable to any follower. By using finite-time Lyapunov stability theory, a distributed discontinuous protocol is developed. On this basis, a fixed-time control protocol is further designed to obtain a settling time regardless of initial conditions. In addition, the practical finite-time consensus and practical fixed-time consensus are investigated by the adaptive technique, under which the bounds of the faults can be estimated online adaptively. The innovation of this work lies in the fact that the finite/fixed-time consensus problem is solved when multiple faults and mismatched nonlinearity are simultaneously considered. The relationship between the settling time and design parameters is well established. Finally, some numerical simulations are given to verify the effectiveness of the theoretical results.
AdamsRBuffingtonJSparksA, et al. (2012) Robust Multivariable Flight Control. Springer Science & Business Media.
2.
BacciottiACeragioliF (1999) Stability and stabilization of discontinuous systems and nonsmooth lyapunov functions. ESAIM: Control, Optimisation and Calculus of Variations4: 361–376.
3.
BhatSBernsteinD (2000) Finite-time stability of continuous autonomous systems. Automatica38(3): 751–766.
4.
ChenYQuXAleksandrovAY (2016) Consensus of heterogeneous linear multi-agent systems: Linear-transformation-based partial stability approach. Transactions of the Institute of Measurement and Control39(11): 1623–1630.
5.
ClarkeF (1983) Optimization and Nonsmooth Analysis. Siam.
6.
DefoortMPolyakovADemesureG, et al. (2015) Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics. IET Control Theory & Applications9(14): 2165–2170.
7.
FilippovA (2013) Differential Equations with Discontinuous Righthand Sides: Control Systems. Springer Science & Business Media.
8.
HanJWangCYiG (2013) Cooperative control of UAV based on multi-agent system. In: 2013 IEEE 8th Conference on Industrial Electronics and Applications (ICIEA), Melbourne, VIC, Australia, pp. 96–101.
9.
HardyGLittlewoodJPólyaG, et al. (1952) Inequalities. Cambridge, UK: Cambridge University Press.
10.
HongYHuJGaoL (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica42(7): 1177–1182.
11.
HwangIKimSKimY, et al. (2010) A survey of fault detection, isolation, and reconfiguration methods. IEEE Transactions on Control Systems Technology18(3): 636–653.
12.
JiangBHuQFriswellMI (2016) Fixed-time attitude control for rigid spacecraft with actuator saturation and faults. IEEE Transactions on Control Systems Technology24(5): 1892–1898.
13.
Kwang-KyoOParkMCAhnHS (2015) A survey of multi-agent formation control. Automatica53: 424–440.
14.
LesserVOrtizCLJr, et al. (2012) Distributed Sensor Networks: A Multiagent Perspective. Springer Science & Business Media.
15.
LiSDuHLinX (2012a) Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica47(8): 1706–1712.
16.
LiZRenWLiuX, et al. (2012b) Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Transactions on Automatic Control58(7): 1786–1791.
17.
LiuHXieGWangL (2012) Necessary and sufficient conditions for containment control of networked multi-agent systems. Automatica48(7): 1415–1422.
18.
LiuYJiaY (2012) An iterative learning approach to formation control of multi-agent systems. Systems & Control Letters61(1): 148–154.
19.
MirabdollahiSEHaeriM (2019) Multi-agent system finite-time consensus control in the presence of disturbance and input saturation by using of adaptive terminal sliding mode method. Cogent Engineering6: 1–16.
20.
Olfati-SaberRMurrayRM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control49(9): 1520–1533.
21.
ParsegovSEPolyakovAEShcherbakovPS (2013) Fixed-time consensus algorithm for multi-agent systems with integrator dynamics. IFAC Proceedings Volumes46(27): 110–115.
22.
Pérez-VilledaHMArechavaletaGMorales-DíazA (2020) Multi-vehicle coordination based on hierarchical quadratic programming. Control Engineering Practice94: 1–9.
23.
RoydenHFitzpatrickP (2007) Real Analysis. Prentice Hall.
24.
SabooriIKhorasaniK (2015) Actuator fault accommodation strategy for a team of multi-agent systems subject to switching topology. Automatica62: 200–207.
25.
Semsar-KazerooniEKhorasaniK (2010) Team consensus for a network of unmanned vehicles in presence of actuator faults. IEEE Transactions on Control Systems Technology18(5): 1155–1161.
26.
ShevitzDPadenB (1994) Lyapunov stability theory of nonsmooth systems. IEEE Transactions on Automatic Control39(9): 1910–1914.
27.
StevensBLewisFJohnsonE (2015) Aircraft Control and Simulation: Dynamics, Controls Design, and Autonomous Systems. Hoboken, NJ: John Wiley & Sons.
28.
TaheriMTaheriMNajafiM, et al. (2019) Consensus in first-order nonlinear multi-agent systems with state time delays using adaptive fuzzy wavelet networks. Transactions of the Institute of Measurement and Control41(11): 3021–3032.
29.
WangFLiuZChenZ (2019) Leader-following consensus of second-order nonlinear multi-agent systems with intermittent position measurements. Science China-Information Sciences62(10): 202–204.
30.
WangFYangHLiuZ, et al. (2017a) Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays. Neurocomputing260: 341–348.
31.
WangHChenBLinC, et al. (2017b) Adaptive finite-time control for a class of uncertain high-order non-linear systems based on fuzzy approximation. IET Control Theory & Applications11(5): 677–684.
32.
WangZYuanJPanY, et al. (2017c) Neural network-based adaptive fault tolerant consensus control for a class of high order multiagent systems with input quantization and time-varying parameters. Neurocomputing266: 315–324.
33.
WuBPohEKWangD, et al. (2009) Satellite formation keeping via real-time optimal control and iterative learning control. In: Proceedings of the IEEE Aerospace Conference. Big Sky, MT, USA, pp. 1–8.
34.
YangHJiangYYinS (2020) Adaptive fuzzy fault tolerant control for Markov jump systems with additive and multiplicative actuator faults. IEEE Transactions on Fuzzy Systems 10.1109/TFUZZ.2020.2965884.
35.
YangHYinS (2019a) Descriptor observers design for Markov jump systems with simultaneous sensor and actuator faults. IEEE Transactions on Automatic Control64(8): 3370–3377.
36.
YangHYinS (2019b) Reduced-order sliding-mode-observer-based fault estimation for Markov jump systems. IEEE Transactions on Automatic Control64(11): 4733–4740.
37.
YuSLongX (2015) Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode. Automatica54: 158–165.
38.
ZhaoYDuanZWenG, et al. (2013) Distributed finite-time tracking control for multi-agent systems: An observer-based approach. Systems & Control Letters62(1): 22–28.
39.
ZhengYWangL (2014) Containment control of heterogeneous multi-agent systems. International Journal of Control87(1): 1–8.
40.
ZhengYZhuYWangL (2011) Consensus of heterogeneous multi-agent systems. IET Control Theory & Applications5(16): 1881–1888.
41.
ZuoZTianBDefoortM, et al. (2017) Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Transactions on Automatic Control63(2): 563–570.
42.
ZuoZZhangJWangY (2014) Adaptive fault-tolerant tracking control for linear and Lipschitz nonlinear multi-agent systems. IEEE Transactions on Control Systems Technology62(6): 3923–3931.
