×

Finite-time consensus of nonlinear multi-agent system with prescribed performance. (English) Zbl 1392.34023

Summary: In this paper, the finite-time consensus tracking problem of uncertain nonlinear multi-agent systems with consensus error constraints is addressed. The multiple agents are assumed to interact on directed graph with a directed spanning tree. In order to obtain some satisfactory consensus performances, the error constrained control is employed by applying the barrier Lyapunov function. With the consensus error constraints, some high performances such as high convergence speed, small overshoot, and an arbitrarily predefined small residual constrained synchronization error can be achieved simultaneously. By using a nonsingular fast sliding mode control technique, a new distributed finite-time consensus controller is proposed to guarantee that the multi-agent system synchronizes with prescribed performances. Finally, two examples are provided to demonstrate the effectiveness of the proposed method.

MSC:

34B45 Boundary value problems on graphs and networks for ordinary differential equations
93C10 Nonlinear systems in control theory
34D06 Synchronization of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Li, S; Wang, X, Finite-time consensus and collision avoidance control algorithms for multiple auvs, Automatica, 49, 3359-3367, (2013) · Zbl 1315.93004 · doi:10.1016/j.automatica.2013.08.003
[2] Luo, X; Li, X; Li, S; Jiang, Z; Guan, X, Flocking for multi-agent systems with optimally rigid topology based on information weighted Kalman consensus filter, Int. J. Control Autom Syst, 15, 138-148, (2017) · doi:10.1007/s12555-015-0134-8
[3] Oh, K-K; Ahn, H-S, Formation control of mobile agents based on inter-agent distance dynamics, Automatica, 47, 2306-2312, (2011) · Zbl 1228.93014 · doi:10.1016/j.automatica.2011.08.019
[4] Zhao, S; Zelazo, D, Bearing rigidity and almost global bearing-only formation stabilization, IEEE Trans. Autom. Control, 61, 1255-1268, (2016) · Zbl 1359.93383 · doi:10.1109/TAC.2015.2459191
[5] La, H, Cooperative and active sensing in mobile sensor networks for scalar field mapping, IEEE Trans. Syst. Man Cybern. Syst., 45, 831-836, (2015) · doi:10.1109/TSMC.2014.2318282
[6] Yang, Y; Hua, C; Guan, X, Finite time control design for bilateral teleoperation system with position synchronization error constrained, IEEE Trans. Cybern., 46, 609-619, (2016) · doi:10.1109/TCYB.2015.2410785
[7] Mei, J; Ren, W; Ma, G, Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph, Automatica, 48, 653-659, (2012) · Zbl 1238.93009 · doi:10.1016/j.automatica.2012.01.020
[8] Hua, C; Ge, C; Guan, X, Synchronization of chaotic lur’e systems with time delays using sampled-data control, IEEE Trans. Neural Netw. Learn. Syst., 26, 1214-1221, (2014)
[9] Hua, C; Zhang, L; Guan, X, Distributed adaptive neural network output tracking of leader-following high-order stochastic nonlinear multiagent systems with unknown dead-zone input, IEEE Trans. Cybern., 47, 177-185, (2017) · doi:10.1109/TCYB.2015.2509482
[10] Saber, RO; Murray, RM, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49, 1520-1533, (2004) · Zbl 1365.93301 · doi:10.1109/TAC.2004.834113
[11] Kim, Y; Mesbahi, M, On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian, IEEE Trans. Autom. Control, 51, 116-120, (2006) · Zbl 1366.05069 · doi:10.1109/TAC.2005.861710
[12] Xiao, L; Boyd, S, Fast linear iterations for distributed averaging, Syst. Control Lett., 53, 65-78, (2004) · Zbl 1157.90347 · doi:10.1016/j.sysconle.2004.02.022
[13] Li, X; Soh, YC; Xie, L, Output-feedback protocols without controller interaction for consensus of homogeneous multi-agent systems: a unified robust control view, Automatica, 81, 37-45, (2017) · Zbl 1372.93022 · doi:10.1016/j.automatica.2017.03.001
[14] Li, X., Soh, Y.C., Xie, L.: Output-feedback \(H-∞ \) consensus of linear multi-agent systems over general directed graphs. In: Proceedings of the 13th IEEE International Conference on Control & Automation (ICCA), pp. 689-694. Ohrid, Macedonia, July (2017) · Zbl 1281.93006
[15] Li, X., Soh, Y.C., Xie, L.: Design of output-feedback protocols for robust consensus of uncertain linear multi-agent systems. In: Proceedings of the 2017 American Control Conference (ACC), pp. 936-941. Seattle, May (2017)
[16] Cheng, J; Park, JH; Liu, Y; Liu, Z; Tang, L, Finite-time \({H}-∞ \) fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions, Fuzzy Sets Syst., 314, 99-115, (2017) · Zbl 1368.93147 · doi:10.1016/j.fss.2016.06.007
[17] Shen, H; Park, JH; Wu, ZG, Finite-time synchronization control for uncertain Markov jump neural networks with input constraints, Nonlinear Dyn., 77, 1709-1720, (2014) · Zbl 1331.92019 · doi:10.1007/s11071-014-1412-3
[18] Shen, H; Park, JH; Wu, ZG; Zhang, Z, Finite-time \(H-∞ \) synchronization for complex networks with semi-Markov jump topology, Commun. Nonlinear Sci. Numer. Simul., 24, 40-51, (2015) · Zbl 1440.93074 · doi:10.1016/j.cnsns.2014.12.004
[19] Shen, H; Li, F; Wu, ZG; Park, JH, Finite-time \(l_{2}-l_{∞ }\) tracking control for Markov jump repeated scalar nonlinear systems with partly usable model information, Inf. Sci., 332, 153-166, (2016) · Zbl 1386.93272 · doi:10.1016/j.ins.2015.10.043
[20] Xiao, F; Wang, L; Chen, J; Gao, Y, Finite-time formation control for multi-agent systems, Automatica, 45, 2605-2611, (2009) · Zbl 1180.93006 · doi:10.1016/j.automatica.2009.07.012
[21] Zhang, Y., Yang, Y., Zhao, Y.: Finite-time consensus tracking for harmonic oscillators using both state feedback control and output feedback control. Int. J. Robust Nonlinear Control 23(8), 878-893 (2013) · Zbl 1270.93007
[22] Zhao, L; Hua, C, Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM, Nonlinear Dyn., 75, 311-318, (2014) · Zbl 1281.93006 · doi:10.1007/s11071-013-1067-5
[23] Lu, K; Xia, Y; Yu, C; Liu, H, Finite-time tracking control of rigid spacecraft under actuator saturations and faults, IEEE Trans. Autom. Sci. Eng., 13, 368-381, (2016) · doi:10.1109/TASE.2014.2379615
[24] Lu, K; Xia, Y, Adaptive attitude tracking control for rigid spacecraft with finite-time convergence, Automatica, 49, 3591-3599, (2013) · Zbl 1315.93045 · doi:10.1016/j.automatica.2013.09.001
[25] Karayiannidis, Y., Dimarogonas, D.V., Kragic, D.: Multi-agent average consensus control with prescribed performance guarantees. In: Proceedings of the 51th IEEE Conference on Decision and Control, pp. 2219-2225. Maui, December (2012)
[26] Bechlioulis, C.P., Kyriakopoulos, K.J.: Robust model-free formation control with prescribed performance and connectivity maintenance for nonlinear multi-agent systems. In: Proceedings of the 53th IEEE Conference on Decision and Control, pp. 4509-4514. Los Angeles, December (2014) · Zbl 1366.05069
[27] Wang, W; Wang, D; Peng, Z; Li, T, Prescribed performance consensus of uncertain nonlinear strict-feedback systems with unknown control directions, IEEE Trans. Syst. Man Cybern. Syst., 46, 1-8, (2015)
[28] Abdessameud, A; Polushin, IG; Tayebi, A, Synchronization of Lagrangian systems with irregular communication delays, IEEE Trans. Autom. Control, 59, 187-193, (2014) · Zbl 1360.93341 · doi:10.1109/TAC.2013.2270053
[29] Ghasemi, M; Nersesov, SG, Finite-time coordination in multiagent systems using sliding mode control approach, Automatica, 50, 1209-1216, (2014) · Zbl 1298.93023 · doi:10.1016/j.automatica.2014.02.019
[30] Wang, L; Mendel, JM, Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Netw., 3, 807-814, (1992) · doi:10.1109/72.159070
[31] Godsil, C., Royle, G.: Algebraic Graph Theory. Cambridge University, Cambridge (1975) · Zbl 0968.05002
[32] Bechlioulis, CP; Rovithakis, GA, Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems, Automatica, 45, 532-538, (2009) · Zbl 1158.93325 · doi:10.1016/j.automatica.2008.08.012
[33] Yu, S; Yu, X; Shirinzadeh, B; Man, Z, Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica, 41, 1957-1964, (2005) · Zbl 1125.93423 · doi:10.1016/j.automatica.2005.07.001
[34] Dads, EHA; Ezzinbi, K, Boundedness and almost periodicity for some state-dependent delay differential equations, Electron. J. Differ. Equ., 2002, 225-228, (2002) · Zbl 1010.34068
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.