Bipartite consensus tracking for antagonistic topologies with leader’s unknown input. (English) Zbl 07886994
Summary: In this paper, the bipartite consensus tracking problem of linear multiagent systems on leader-follower signed directed graph is studied, where the leader’s unknown input is taken into consideration. Based on only local relative information of neighboring agents, discontinuous distributed adaptive protocols are proposed, where nonlinear function is introduced for each agent to tackle leader’s unknown input. To avoid tremors phenomenon, continuous distributed protocols are further presented to achieve practical bipartite consensus. Both the state feedback and output feedback cases are investigated. Different from existing literature showing bipartite consensus achievement with gauge transformation, this paper reveals a novel property of the signed Laplacian matrix, which plays a key role in simplifying the bipartite consensus demonstration. Two practical examples on synchronization of Chua’s circuits are presented to illustrate the effectiveness of the designed protocols.
© 2021 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
© 2021 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
MSC:
| 93-XX | Systems theory; control |
References:
| [1] | W.Ren, On consensus algorithms for double‐integrator dynamics, IEEE Trans. Autom. Control6 (2008), 1503-1509. · Zbl 1367.93567 |
| [2] | P.Wieland et al., On consensus in multi‐agent systems with linear high‐order agents, IFAC Proc.41 (2008), 1541-1546. |
| [3] | A.Wang, T.Dong, and X.Liao, On the general consensus protocol in multi‐agent networks with second‐order dynamics and sampled data, Asian J. Control18 (2016), no. 5, 1914-1922. · Zbl 1347.93027 |
| [4] | F.Wang et al., Finite‐time consensus problem for second‐order multi‐agent systems under switching topologies, Asian J. Control19 (2017), no. 5, 1756-1766. · Zbl 1386.93021 |
| [5] | R.Hendel, F.Khaber, and N.Essounbouli, Adaptive high‐order sliding mode controller‐observer for MIMO uncertain nonlinear systems, Asian J. Control18 (2020), 2309-2329. · Zbl 07879341 |
| [6] | Q.Wang et al., Distributed model predictive control for linear‐quadratic performance and consensus state optimization of multiagent systems, IEEE Trans. Cybern. (2020), 1-11. |
| [7] | Z.Ye, Y.Chen, and H.Zhang, Distributed consensus of delayed multi‐agent systems with nonlinear dynamics via intermittent control, Asian J. Control18 (2016), no. 3, 964-975. · Zbl 1348.93023 |
| [8] | Y.Lv et al., Distributed adaptive output feedback consensus protocols for linear systems on directed graphs with a leader of bounded input, Automatica74 (2016), 308-314. · Zbl 1348.93013 |
| [9] | Y.Lv, Z.Li, and Z.Duan, Distributed adaptive consensus protocols for linear multi‐agent systems over directed graphs with relative output information, IET Control Theory Appl.12 (2018), 613-620. |
| [10] | H.Wang et al., Fixed‐time consensus of nonlinear multi‐agent systems with general directed topologies, IEEE Trans. Circuits Syst. II: Express Briefs66 (2019), 1587-1591. |
| [11] | Q.Wang et al., Lq synchronization of discrete‐time multiagent systems: a distributed optimization approach, IEEE Trans. Autom. Control64 (2019), 5183-5190. · Zbl 1482.93056 |
| [12] | J.Liu et al., Robust distributed consensus tracking control for high‐order uncertain nonlinear MASs with directed topologies, Asian J. Control64 (2020), 2558-2568. · Zbl 07879363 |
| [13] | Y.Zhao et al., Designing distributed specified‐time consensus protocols for linear multiagent systems over directed graphs, IEEE Trans. Autom. Control64 (2019), no. 7, 2945-2952. · Zbl 1482.93065 |
| [14] | Y.Zhao et al., Distributed average tracking for Lipschitz‐type of nonlinear dynamical systems, IEEE Trans. Cybern.49 (2019), no. 12, 4140-4152. |
| [15] | D.Zhang et al., Pinning consensus analysis for nonlinear second‐order multi‐agent systems with time‐varying delays, Asian J. Control20 (2018), no. 6, 2343-2350. · Zbl 1407.93010 |
| [16] | C.Li and G.Liu, Predictive consensus for networked multi‐agent systems with switching topology and variable delay, Asian J. Control21 (2019), no. 2, 924-933. · Zbl 1422.93169 |
| [17] | Y.Yang and D.Yue, NNs‐based event‐triggered consensus control of a class of uncertain nonlinear multi‐agent systems, Asian J. Control21 (2019), no. 2, 660-673. · Zbl 1422.93170 |
| [18] | J.Wang et al., Rendezvous of heterogeneous multiagent systems with nonuniform time‐varying information delays: an adaptive approach, IEEE Trans. Syst. Man Cybern.: Syst. (2019). https://doi.org/10.1109/TSMC.2019.2945592 · doi:10.1109/TSMC.2019.2945592 |
| [19] | Y.Lv et al., Fully distributed anti‐windup consensus protocols for linear MASs with input saturation: the case with directed topology, IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2977554 · doi:10.1109/TCYB.2020.2977554 |
| [20] | J.Wang et al., Stochastic consensus control integrated with performance improvement: a consensus region‐based approach, IEEE Trans. Indust. Electron.67 (2020), no. 4, 3000-3012. |
| [21] | C.Altafini, Consensus problems on networks with antagonistic interactions, IEEE Trans. Autom. Control58 (2013),935-946. · Zbl 1369.93433 |
| [22] | D.Meng, Y.Jia, and J.Du, Finite‐time consensus for multiagent systems with cooperative and antagonistic interactions, IEEE Trans. Neural Netw. Learn. Syst.27 (2015), 762-770. |
| [23] | D.Meng, M.Du, and Y.Jia, Interval bipartite consensus of networked agents associated with signed digraphs, IEEE Trans. Autom. Control61 (2016), 3755-3770. · Zbl 1359.93195 |
| [24] | H.Wang et al., Finite‐time bipartite consensus for multi‐agent systems on directed signed networks, IEEE Trans. Circuits Syst. I: Reg. Papers65 (2018), 4336-4348. |
| [25] | C.Ma, W.Zhao, and Y.Zhao, Bipartite linear χ‐consensus of double‐integrator multi‐agent systems with measurement noise, Asian J. Control20 (2018), no. 1, 577-584. · Zbl 1391.93015 |
| [26] | D.Wang, H.Ma, and D.Liu, Distributed control algorithm for bipartite consensus of the nonlinear time‐delayed multi‐agent systems with neural networks, Neurocomputing174 (2016), 928-936. |
| [27] | Y.Jiang, H.Zhang, and J.Chen, Sign‐consensus of linear multi‐agent systems over signed directed graphs, IEEE Trans. Indust. Electron.64 (2016), 5075-5083. |
| [28] | H.Zhang and J.Chen, Bipartite consensus of multi‐agent systems over signed graph: state feedback and output feedback control approaches, Int. J. Robust Nonlin. Control27 (2017),3-14. · Zbl 1353.93011 |
| [29] | L.Shi, Multi‐agent bipartite tracking control over general cooperative‐hostile networks, IEEE Trans. Circuits Syst. II: Express Briefs67 (2019) (no. 10), 1964-1968. |
| [30] | G.Wen et al., Bipartite tracking consensus of linear multi‐agent systems with a dynamic leader, IEEE Trans. Circuits Syst. II: Express Briefs65 (2017), 1204-1208. |
| [31] | P.Gong and Q.Han, Fixed‐time bipartite consensus tracking of fractional‐order multi‐agent systems with a dynamic leader, IEEE Trans. Circuits Syst. II: Express Briefs67 (2020) no. 10,2054-2058. |
| [32] | Y.Wu, Y.Zhao, and J.Hu, Bipartite consensus control of high‐order multiagent systems with unknown disturbances, IEEE Trans. Syst. Man Cybern. Syst.49 (2017), 2189-2199. |
| [33] | S.Bhowmick and S.Panja, Leader‐follower bipartite consensus of linear multiagent systems over a signed directed graph, IEEE Trans. Circuits Syst. II: Express Briefs66 (2018), 1436-1440. |
| [34] | J.Qin et al., On the bipartite consensus for generic linear multiagent systems with input saturation, IEEE Trans. Cybern.47 (2016), 1948-1958. |
| [35] | J.Duan et al., Semi‐global bipartite output consensus of heterogeneous multi‐agent systems subject to input saturation by finite‐time observer, Asian J. Control22 (2020), 1639-1648. · Zbl 07872696 |
| [36] | H.Hu et al., Robust distributed stabilization of heterogeneous agents over cooperation‐competition networks, IEEE Trans. Circuits Syst. II: Express Briefs67 (2019), no. 8, 1419-1423. |
| [37] | H.Hu et al., Distributed stabilization of multiple heterogeneous agents in the strong‐weak competition network: a switched system approach, IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2995154 · doi:10.1109/TCYB.2020.2995154 |
| [38] | J.Hu and H.Zhu, Adaptive bipartite consensus on coopetition networks, Phys. D: Nonlin. Phenomena307 (2015), 14-21. · Zbl 1364.91130 |
| [39] | D.Meng, Y.Jia, and J.Du, Nonlinear finite‐time bipartite consensus protocol for multi‐agent systems associated with signed graphs, Int. J. Control88 (2015), 2074-2085. · Zbl 1334.93017 |
| [40] | T.Ding et al., Bipartite consensus for networked robotic systems with quantized‐data interactions, Info. Sci.511 (2020), 229-242. · Zbl 1461.93465 |
| [41] | Z.Qu, Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles, Springer Publishing Company, London, UK, 2009. · Zbl 1171.93005 |
| [42] | H.Zhang, F. L.Lewis, and Z.Qu, Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs, IEEE Trans. Indust. Electron.59 (2012), 3026-3041. |
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