×

Observer-based leader-following consensus of uncertain nonlinear multi-agent systems. (English) Zbl 1386.93018

Summary: In this paper, the leader-following consensus problem of uncertain high-order nonlinear multi-agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer-based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi-globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed-loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C10 Nonlinear systems in control theory
93C41 Control/observation systems with incomplete information
Full Text: DOI

References:

[1] DefoortM, FloquetT, KokosyA, PerruquettiW. Sliding‐mode formation control for cooperative autonomous mobile robots. IEEE Transactions on Industrial Electronics2008; 55: 3944-3953.
[2] CruzD, McClintockJ, PerteetB, OrquedaO, CaoY, FierroR. Decentralized cooperative control‐a multivehicle platform for research in networked embedded systems. IEEE Control Systems Magazine2007; 27: 58-78.
[3] WangX, YadavV, BalakrishnanS. Cooperative UAV formation flying with obstacle/collision avoidance. IEEE Transactions on Control Systems Technology2007; 15: 672-679.
[4] ChenJ, CaoX, ChengP, XiaoY, SunY. Distributed collaborative control for industrial automation with wireless sensor and actuator networks. IEEE Transactions on Industrial Electronics2010; 57: 4219-4230.
[5] MurrayR. Recent research in cooperative control of multivehicle systems. ASME Journal of Dynamic Systems, Measurement, and Control2007; 129: 571-583.
[6] RenW, CaoC. Distributed Coordination of Multi‐agent Networks: Emergent Problems, Models, and Issues. Springer‐Verlag: London, 2011. · Zbl 1225.93003
[7] ZhangH, LewisFL. Adaptive cooperative tracking control of higher‐order nonlinear systems with unknown dynamics. Automatica2012; 48: 1432-1439. · Zbl 1348.93144
[8] RenW, BeardR, AtkinsE. Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine2007; 27: 71-82.
[9] ChengL, HouZG, TanM, LinY, ZhangWJ. Solving a modified consensus problem of linear multi‐agent systems. Automatica2011; 47: 2218-2223. · Zbl 1228.93008
[10] ZhuW, ChengD. Leader‐following consensus of second‐order agents with multiple time‐varying delays. Automatica2010; 46: 1994-1999. · Zbl 1205.93056
[11] WangW, SlotineJ. A theoretical study of different leader roles in networks. IEEE Transactions on Automatic Control2006; 51: 1156-1161. · Zbl 1366.93416
[12] RenW, MooreK, ChenY. High‐order and model reference consensus algorithms in cooperative control of multivehicle systems. ASME Journal of Dynamic Systems, Measurement, and Control2007; 129: 678-688.
[13] HongY, ChenG, BushnellL. Distributed observers design for leader‐following control of multi‐agent networks. Automatica2008; 44: 846-850. · Zbl 1283.93019
[14] LiZ, DuanZ, LewisFL. Distributed robust consensus control of multi‐agent systems with heterogeneous matching uncertainties. Automatica2014; 50: 883-889. · Zbl 1298.93026
[15] ChengL, HouZG, TanM, LinY, ZhangWJ. Neural‐network‐based adaptive leader‐following control for multi‐agent systems with uncertainties. IEEE Transactions on Neural Networks2010; 21: 1351-1358.
[16] ZhangH, LewisFL, DasA. Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Transactions on Automatic Control2011; 56: 1948-1952. · Zbl 1368.93265
[17] ZhangH, LewisFL, QuZ. Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs. IEEE Transactions on Industrial Electronics2012; 59: 3026-3041.
[18] YuH, XiaX. Adaptive consensus of multi‐agents in networks with jointly connected topologies. Automatica2012; 48: 1783-1790. · Zbl 1267.93007
[19] Semsar‐KazerooniE, KhorasaniK. Optimal consensus algorithms for cooperative team of agents subject to partial information. Automatica2008; 44: 2766-2777. · Zbl 1194.49056
[20] DuH, LiS, ShiP. Robust consensus algorithm for second‐order multi‐agent systems with external disturbances. International Journal of Control, Correctly2012; 85: 1913-1928. · Zbl 1401.93080
[21] MengZ, LinZ, RenW. Robust cooperative tracking for multi non‐identical second‐order nonlinear systems. Automatica2013; 49: 2363-2372. · Zbl 1364.93027
[22] ShenQK, JiangB, ShiP, ZhaoJ. Cooperative adaptive fuzzy tracking control for networked unknown nonlinear multi‐agent systems with time‐varying actuator faults. IEEE Transactions on Fuzzy Systems2014; 22: 494-504.
[23] ShiG, JohanssonKH. Robust consensus for continuous‐time multiagent dynamics. SIAM Journal on Control and Optimization2013; 51: 3673-3691. · Zbl 1279.93013
[24] QiaoW, SipahiR. A linear time‐invariant consensus dynamics with homogeneous delays: analytical study and synthesis of rightmost eigenvalues. SIAM Journal on Control and Optimization2013; 51: 3971-3992. · Zbl 1279.93011
[25] PengZ, WangD, ZhangH, SunG. Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems. IEEE Transactions on Neural Networks and Learning Systems2014; 25: 1508-1519.
[26] ZhangH, LiZ, QuZ, LewisFL. On constructing Lyapunov functions for multi‐agent systems. Automatica2015; 58: 39-42. · Zbl 1330.93182
[27] ZhouQ, ShiP, LuJ, XuS. Adaptive output feedback fuzzy tracking control for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems2011; 19: 972-982.
[28] ZhangJ, ShiP, XiaY. Robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties. IEEE Transactions on Fuzzy Systems2010; 18: 700-711.
[29] TongSC, LiY. Observer‐based fuzzy adaptive control for strict‐feedback nonlinear systems. Fuzzy Sets and Systems2009; 160: 1749-1764. · Zbl 1175.93135
[30] GeSS, HongF, LeeTH. Robust adaptive control of nonlinear systems with unknown time delays. Automatica2005; 41: 1181-1190. · Zbl 1078.93046
[31] SlotineJE, LiW. Applied Nonlinear Control. Prentine‐Hall: Englewood Cliffs, NJ, 1991. · Zbl 0753.93036
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.