×

Fully distributed tracking control for non-identical multi-agent systems with matching uncertainty. (English) Zbl 1330.93019

Summary: This article addresses the fully distributed consensus tracking control problem of linear multi-agent systems with parameter uncertainties. First, a new class of distributed protocol, based on the relative states of neighbors, is proposed. Theoretical analysis indicates that the considered problem can be solved if the control gain constant of the protocol is larger than the norm bound of the leader’s nonlinear inputs. Furthermore, a distributed adaptive control protocol is proposed for the case without available global information. The distributed consensus tracking control problem of uncertain linear multi-agent systems is solved based only on local information under the proposed adaptive protocol. Finally, an application in low-Earth-orbit satellite formation flying is provided to illustrate the theoretical results.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C41 Control/observation systems with incomplete information
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI

References:

[1] JadbabaieA, LinJ, MorseAS. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control2003; 48(6):988-1001. · Zbl 1364.93514
[2] VicsekT, CzirókA, Ben‐JacobE, CohenI, ShochetO. Novel type of phase transition in a system of self‐driven particles. Physical Review Letters1995; 75(6):1226-1229.
[3] Olfati‐SaberR, MurrayRM. Consensus problems in networks of agents with switching topology and time‐delays. IEEE Transactions on Automatic Control2004; 49(9):1520-1533. · Zbl 1365.93301
[4] RenW, BeardRW. Consensus seeking in multi‐agent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control2005; 50(5):655-661. · Zbl 1365.93302
[5] RenW, BeardRW, AtkinsEM. Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine2007; 27(2):71-82.
[6] QinJ, GaoH, ZhengW. Second‐order consensus for multi‐agent systems with switching topology and communication delay. System & Control Letters2011; 60(6):390-397. · Zbl 1225.93020
[7] QinJ, ZhengW, GaoH. Consensus of multiple second‐order vehicles with a time‐varying reference signal under directed topology. Automatica2011; 47(9):1983-1991. · Zbl 1227.93011
[8] YuWW, ChenGR, CaoM. Consensus in directed networks of agents with nonlinear dynamics. IEEE Transactions on Automatic Control2010; 56(6):1436-1441. · Zbl 1368.93015
[9] ZhaoJ, DavidJH, LiuT. Synchronization of dynamical networks with nonidentical nodes: criteria and control. IEEE Transactions on Circuits and Systems I2011; 58(3):584-594. · Zbl 1468.34082
[10] TunaSE. Synchronizing linear systems via partial‐state coupling. Automatica2008; 44(8):2179-2184. · Zbl 1283.93028
[11] YuWW, ChenGR, RenW, KürthsJ, ZhengW. Distributed higher‐order consensus protocols in multi‐agent dynamical systems. IEEE Transactions on Circuits and Systems I2011; 58(8):1924-1932. · Zbl 1468.93044
[12] DuanZS, ChenGR, HuangL. Disconnected synchronized regions of complex dynamical networks. IEEE Transactions on Automatic Control2009; 54(4):845-849. · Zbl 1367.93461
[13] LiZK, DuanZS, ChenGR, HuangL. Consensus of multi‐agent systems and synchronization of complex networks: a unified viewpoint. IEEE Transactions on Circuits and Systems I201057(1):213-224. · Zbl 1468.93137
[14] LiZK, DuanZS, ChenGR. On H_∞ and H_2 performance regions of multi‐agent systems. Automatica2011; 47(4):797-803. · Zbl 1215.93042
[15] LinP, JiaY, LiL. Distributed robust H_∞ consensus control in directed networks of agents with time‐delay. System & Control Letters2008; 57(8):643-653. · Zbl 1140.93355
[16] ZhaoY, DuanZS, WenGH, ChenGR. Distributed H_∞ consensus of multi‐agent systems: a performance region based approach. International Journal of Control2012; 85(3):332-341. · Zbl 1282.93030
[17] HongY, ChenGR, BushnellL. Distributed observers design for leader‐follower control of multi‐agent networks. Automatica2008; 44(3):846-850. · Zbl 1283.93019
[18] MeiJ, RenW, MaG. Distributed coordinated tracking with a dynamic leader for multiple Euler-Lagrange systems. IEEE Transactions on Automatic Control562011; (6):1415-1421. · Zbl 1368.93432
[19] ZhaoY, DuanZS, WenGH, ZhangYJ. Distributed finite‐time tracking control for multi‐agent systems: an observer‐based approach. Systems & Control Letters2013; 62(1):22-28. · Zbl 1257.93011
[20] ZhangHW, LewisFL, DasA. Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Transactions on Automatic Control2011; 56(8):1948-1952. · Zbl 1368.93265
[21] CaoY, RenW. Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Transactions on Automatic Control2012; 57(1):33-48. · Zbl 1369.93012
[22] RenW. Synchronization of coupled harmonic oscillators with local interaction. Automatica2008; 44(12):3195-3200. · Zbl 1153.93421
[23] DuanZS, ChenGR. Global robust stability and synchronization of networks with Lorenz‐type nodes. IEEE Transactions on Circuits and Systems II2009; 56(8):679-683.
[24] LiZK, LiuX, RenW, XieL. Disributed tracking control for linear multi‐agent systems with a leader of bounded unknown input. IEEE Transactions on Automatic Control2013; 58(2):518-523. · Zbl 1369.93306
[25] ShevitzD, PadenB. Lyapunov stability theory of nonsmooth systems. IEEE Transactions on Automatic Control1994; 39(9):1910-1914. · Zbl 0814.93049
[26] LiZK, DuanZS, LewisFL. Distributed robust consensus control of multi‐agent systems with heterogeneous matching uncertainties. Automatica2014; 50(3):883-889. · Zbl 1298.93026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.