Restricted accessResearch articleFirst published online 2019-1
Smooth control design for adaptive leader-following consensus control of a class of high-order nonlinear systems with time-varying reference and unknown control directions
In this paper, we investigate the distributed adaptive leader-following consensus control for high-order nonlinear multi-agent systems with a time-varying reference trajectory under directed topology, subjected to mismatched unknown parameters and unknown control directions. By introducing local estimators for the bounds of the reference trajectory and a filter for each agent, a new backstepping-based smooth distributed adaptive control protocol is proposed. Meanwhile, a Nussbaum-type function is applied to address the consensus control with unknown control directions. It is shown that global uniform boundedness of all the closed-loop signals and asymptotic output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme.
ArcakM (2007) Passivity as a design tool for group coordination. IEEE Transactions on Automatic Control52(8): 1380–1390.
2.
BaiHArcakMWenT (2009) Adaptive motion coordination: Using relative velocity feedback to track a reference velocity. Automatica45(4):1020–1025.
3.
ChenWLiXRenWet al. (2014) Adaptive consensus of multi-agent systems with unknown identical control directions based on a novel Nussbaum-type function. IEEE Transactions on Automatic Control59(7): 1887–1892.
4.
ChenYQuXAleksandrovA (2017a) Consensus of heterogeneous linear multi-agent systems: Linear-transformation-based partial stability approach. Transactions of the Institute of Measurement and Control, 39(11):1623-1630.
5.
ChenCWenCLiuZ (2017b) Adaptive consensus of nonlinear multi-agent systems with non-identical partially unknown control directions and bounded modelling errors. IEEE Transactions on Automatic Control62(9): 4654–4659.
6.
ChuHZhangW (2017) Adaptive consensus tracking for linear multi-agent systems with input saturation. Transactions of the Institute of Measurement and Control38(12): 1434–1441.
7.
DasALewisF (2010) Distributed adaptive control for synchronization of unknown nonlinear networked systems. Automatica46(12): 2014–2021.
8.
DongW (2012) Adaptive consensus seeking of multiple nonlinear systems. International Journal of Adaptive Control and Signal Processing26(5): 419–434.
9.
El–FerikSQureshiALewisL (2014) Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems. Automatica50(3): 798–808.
10.
HongYHuJGaoL (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica42(7): 1177–1182.
11.
HuJCaoJ (2017) Consensus seeking for multi-agent systems by hybrid output feedback protocol. Transactions of the Institute of Measurement and Control39(7): 1104–1113.
12.
HuJZhengW (2014) Adaptive tracking control of leader follower systems with unknown dynamics and partial measurements. Automatica50(5): 1416–1423.
13.
HuangJWenCWeiWet al. (2015) Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems. Automatica51: 292–301.
14.
KrsticMKanellakopoulosIKokotovicP (1992) Adaptive nonlinear control without overparametrization. Systems Control Letters19: 177–185.
15.
KrsticMKanellakopoulosIKokotovicP (1995) Nonlinear and Adaptive Control Design. Hoboken, NJ: John Wiley and Sons.
16.
LiZLiuXRenWet al. (2013) Distributed tracking control for linear multiagent systems with a leader of bounded unknown input. IEEE Transactions on Automatic Control58(2): 518–523.
17.
LianJLiuJZhuangY (2017) Mean stability of positive Markov jump linear systems with homogeneous and switching transition probabilities. IEEE Transactions on Circuits and Systems II -Express Briefs62(8): 801–805.
18.
LiuWZhouSWuQ (2017) H-infinity consensus of multi-agent systems in directed networks with Lipschitz non-linear dynamics. Transactions of the Institute of Measurement and Control39(12): 1877–1884.
19.
LuJChenFChenG (2016) Nonsmooth leader-following formation control of nonidentical multi-agent systems with directed communication topologies. Automatica64: 112–120.
20.
MeiJRenWMaG (2011) Distributed coordinated tracking with a dynamic leader for multiple Euler–Lagrange systems. IEEE Transactions on Automatic Control56(6): 1415–1421.
21.
PengJYeX (2014) Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs. System & Control Letters68: 51–56.
22.
RenW (2007) Multi-vehicle consensus with a time-varying reference state. Systems & Control Letters56(7): 474–483.
23.
RenWBeardRW (2005) Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control50(5): 655–661.
24.
RezaeeHAbdollahiF (2017) Adaptive consensus control of nonlinear multiagent systems with unknown control directions under stochastic topologies. IEEE Transactions on Neural Networks and Learning Systems.
25.
SuY (2015) Cooperative global output regulation of second-order nonlinear multi-agent systems with unknown control direction. IEEE Transactions on Automatic Control60(12): 3275–3282.
26.
WangDZhangNWangJ (2017a) A PD-like protocol with a time delay to average consensus control for multi-agent systems under an arbitrarily fast switching topology. IEEE Transactions on Cybernetics47(4): 898–907.
27.
WangGWangCLiL (2017b) Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs. Journal of the Franklin Institute-Engineering and Applied Mathematics354(1): 571–592.
28.
WangGWangCCaiX (2016a) Distributed adaptive output consensus tracking of higher-order systems with unknown control directions. Neurocomputing203: 129–138.
29.
WangWHuangJWenCet al. (2014) Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots. Automatica50(4): 1254–1263.
30.
WangWWenCHuangJ (2016b) Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances. Automatica77(3): 133–142.
31.
WangWWangDPengZ (2016c) Prescribed performance consensus of uncertain nonlinear strict-feedback systems with unknown control directions, IEEE Transactions on Systems Man Cybernetics-Systems46(9): 1279–1286.
32.
WangWWenCHuangJet al. (2016d) Hierarchical decomposition based consensus tracking for uncertain interconnected systems via distributed adaptive output feedback control. IEEE Transactions on Automatic Control61(7): 1938–1945.
33.
XuXGaoL (2017) Distributed adaptive consensus control for multi-agent systems with Lipschitz nonlinear dynamics. Transactions of the Institute of Measurement and Control39(12): 1864–1876.
34.
YeXJiangJ (1998) Adaptive nonlinear design without a priori knowledge of control directions. IEEE Transactions on Automatic Control43(11): 1617–1621.
35.
YooSJ (2013) Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph. IEEE Transactions on Neural Networks and Learning Systems24(4): 666–672.
36.
YuHXiaX (2012) Adaptive consensus of multiagents in networks with jointly connected topologies. Automatica48(8): 1783–1790.
37.
ZhangHLewisF (2012) Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica48(7): 1432–1439.
38.
ZhangGXuJZengJ (2017) Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays. Transactions of the Institute of Measurement and Control39(8): 1182–1194.
