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Finite-time consensus problem for multiple non-holonomic mobile agents. (English) Zbl 1255.93118
Summary: In this paper, the problem of finite time consensus is discussed for multiple non-holonomic mobile agents. The objective is to design a distributed finite time control law such that the controlled multiple non-holonomic mobile agents can reach consensus within any given finite settling time. We propose a novel switching control strategy with the help of time-rescalling technique and graph theory. The numerical simulations are presented to show the effectiveness of the method.

MSC:
93D15 Stabilization of systems by feedback
93D21 Adaptive or robust stabilization
94C15 Applications of graph theory to circuits and networks
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[1] Bhat, S. P., Bernstein, D. S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Control 43 (1998), 5, 678-682. · Zbl 0925.93821
[2] Bhat, S. P., Bernstein, D. S.: Geometric homogeneity with applications to finite-time stability. Math. Control, Signals, and Systems 17 (2005), 2, 101-127. · Zbl 1110.34033
[3] Dong, W. J., Farrell, J. A.: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Automat. Control 53 (2008), 6, 1434-1448. · Zbl 1367.93226
[4] Du, H., Li, S., Qian, C.: Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans. Automat. Control 56 (2011), 11, 2711-2717. · Zbl 1368.70036
[5] Du, H., Li, S., Lin, X.: Finite-time formation control of multi-agent systems via dynamic output feedback. Internat. J. Robust and Nonlinear Control (2012), published online.
[6] Feng, X., Long, W.: Reaching agreement in finite time via continuous local state feedback. Chinese Control Conference 2007, pp. 711-715.
[7] Hong, Y., Wang, J.: Stabilization of uncertain chained form systems within finite settling time. IEEE Trans. Automat. Control 50 (2005), 9, 1379-1384. · Zbl 1365.93444
[8] Hong, Y., Hu, J. P., Gao, L. X.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42 (2006), 7, 1177-1182. · Zbl 1117.93300
[9] Hong, Y., Jiang, Z., Feng, G.: Finite-time input-to-state stability and applications to finite-time control design. SIAM J. Control Optim. 48 (2010), 7, 4395-4418. · Zbl 1210.93066
[10] Justh, E. W., Krishnaprasad, P. S.: Equilibrium and steering laws for planar formations. Systems Control Lett. 52 (2004), 1, 25-38. · Zbl 1157.93406
[11] Beard, R. W., Lawton, J., Young, B. J.: A decentralized approach to formation maneuvers. IEEE Trans. Robotics Automat. 19 (2003), 6, 933-941.
[12] Li, S., Liu, H., Ding, S.: A speed control for a pmsm using finite-time feedback control and disturbance compensation. Trans. Inst. Measurement and Control 32 (2010), 2, 170-187.
[13] Li, S., Du, H., Lin, X.: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47 (2011), 8, 1706-1712. · Zbl 1226.93014
[14] Olfati-Saber, R., Murray, R. M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004), 9, 1520-1533. · Zbl 1365.93301
[15] Wang, J., Zhang, G., Li, H.: Adaptive control of uncertain nonholonomic systems in finite time. Kybernetika 45 (2009), 5, 809-824. · Zbl 1190.93086
[16] Wang, J., Zhao, Y., Song, X., Zhang, G.: Semi-global robust finite time stabilization of non-holonomic chained form systems with perturbed terms. 8th World Congress on Intelligent Control and Automation (WCICA) 2010, pp. 3662-3667.
[17] Wang, X. L., Hong, Y.: Finite-time consensus for multi-agent networks with second-order agent dynamics. Proc. 17th World Congress The International Federation of Automatic Control (2008), pp. 15185-15190.
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