×

zbMATH — the first resource for mathematics

Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. (English) Zbl 1207.93103
Summary: A simple but efficient framework is proposed to achieve finite-time decentralized formation tracking of multiple autonomous vehicles with the introduction of decentralized sliding mode estimators. First, we propose and study both first-order and second-order decentralized sliding mode estimators. In particular, we show that the proposed first-order decentralized sliding mode estimator can guarantee accurate position estimation in finite time and the proposed second-order decentralized sliding mode estimator can guarantee accurate position and velocity estimation in finite time. Then the decentralized sliding mode estimators are employed to achieve decentralized formation tracking of multiple autonomous vehicles. In particular, it is shown that formation tracking can be achieved for systems with both single-integrator kinematics and double-integrator dynamics in finite time. By using the decentralized sliding mode estimators, many formation tracking/flying scenarios can be easily decoupled into two subtasks, that is, decentralized sliding mode estimation and vehicle desired state tracking, without imposing a stringent condition on the information flow. Finally, several simulation results are presented as a proof of concept.

MSC:
93E10 Estimation and detection in stochastic control theory
93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 988-1001, (2003) · Zbl 1364.93514
[2] Olfati-Saber, R.; Murray, R.M., Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301
[3] Ren, W.; Beard, R.W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control, 50, 5, 655-661, (2005) · Zbl 1365.93302
[4] Moreau, L., Stability of multi-agent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[5] Fang, L.; Antsaklis, P.J., Asynchronous consensus protocols using nonlinear paracontractions theory, IEEE transactions on automatic control, 53, 10, 2351-2355, (2008) · Zbl 1367.90020
[6] Xiao, F.; Wang, L., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE transactions on automatic control, 53, 8, 1804-1816, (2008) · Zbl 1367.93255
[7] Cao, M.; Morse, A.S.; Anderson, B.D.O., Agreeing asynchronously, IEEE transactions on automatic control, 53, 8, 1826-1838, (2008) · Zbl 1367.93359
[8] Fax, J.A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056
[9] Lafferriere, G.; Williams, A.; Caughman, J.; Veerman, J.J.P., Decentralized control of vehicle formations, Systems and control letters, 54, 9, 899-910, (2005) · Zbl 1129.93303
[10] Smith, R.S.; Hadaegh, F.Y., Closed-loop dynamics of cooperative vehicle formations with parallel estimators and communication, IEEE transactions on automatic control, 52, 8, 1404-1414, (2007) · Zbl 1366.93020
[11] Sepulchre, R.; Paley, D.A.; Leonard, N.E., Stabilization of planar collective motion with limited communication, IEEE transactions on automatic control, 53, 3, 706-719, (2008) · Zbl 1367.93145
[12] Qu, Z.; Wang, J.; Hull, R.A., Cooperative control of dynamical systems with application to autonomous vehicles, IEEE transactions on automatic control, 53, 4, 894-911, (2008) · Zbl 1367.93076
[13] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[14] Tanner, H.G.; Jadbabaie, A.; Pappas, G.J., Flocking in fixed and switching networks, IEEE transactions on automatic control, 52, 5, 863-868, (2007) · Zbl 1366.93414
[15] Cucker, F.; Smale, S., Emergent behavior in flocks, IEEE transactions on automatic control, 52, 5, 852-862, (2007) · Zbl 1366.91116
[16] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE transactions on automatic control, 54, 2, 293-307, (2009) · Zbl 1367.37059
[17] Hatano, Y.; Mesbahi, M., Agreement over random networks, IEEE transactions on automatic control, 50, 11, 1867-1872, (2005) · Zbl 1365.94482
[18] Porfiri, M.; Stilwell, D.J., Consensus seeking over random weighted directed graphs, IEEE transactions on automatic control, 52, 9, 1767-1773, (2007) · Zbl 1366.93330
[19] Wu, C.W., Synchronization and convergence of linear dynamics in random directed networks, IEEE transactions on automatic control, 51, 7, 1207-1210, (2006) · Zbl 1366.93537
[20] Tahbaz-Salehi, A.; Jadbabaie, A., A necessary and sufficient condition for consensus over random networks, IEEE transactions on automatic control, 53, 3, 791-795, (2008) · Zbl 1367.90015
[21] Ren, W.; Atkins, E.M., Distributed multi-vehicle coordinated control via local information exchange, International journal of robust and nonlinear control, 17, 10-11, 1002-1033, (2007) · Zbl 1266.93010
[22] Xie, G.; Wang, L., Consensus control for a class of networks of dynamic agents, International journal of robust and nonlinear control, 17, 10-11, 941-959, (2007) · Zbl 1266.93013
[23] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[24] Cao, Y.; Ren, W., Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction, in a sampled-data setting, International journal of robust and nonlinear control, 20, 9, 987-1000, (2010) · Zbl 1298.93225
[25] Tuna, S., Conditions for synchronizability in arrays of coupled linear systems, IEEE transactions on automatic control, 54, 10, 2416-2420, (2009) · Zbl 1367.93542
[26] Li, Z.-K.; Duan, Z.-S.; Chen, G.-R.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, IEEE transactions on circuits and systems I: regular papers, 57, 1, 213-224, (2010)
[27] Ren, W., Multi-vehicle consensus with a time-varying reference state, Systems & control letters, 56, 7-8, 474-483, (2007) · Zbl 1157.90459
[28] Cao, Y.; Ren, W.; Li, Y., Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication, Automatica, 45, 5, 1299-1305, (2009) · Zbl 1162.93004
[29] Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182, (2006) · Zbl 1117.93300
[30] Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850, (2008) · Zbl 1283.93019
[31] Peng, K.; Yang, Y., Leader-following consensus problem with a varying-velocity leader and time-varying delays, Physica A, 388, 2-3, 193-208, (2009)
[32] Y. Cao, W. Ren, Z. Meng, Decentralized finite-time sliding mode estimators with applications to formation tracking, in: Proceedings of the American Control Conference, Baltimore, MD, 2010, pp. 4160-4165.
[33] Jiang, F.; Wang, L., Finite-time information consensus for multi-agent systems with fixed and switching topologies, Physica D, 238, 1550-1560, (2009) · Zbl 1170.93304
[34] F. Xiao, L. Wang, Y. Jia, Fast information sharing in networks of autonomous agents, in: Proceedings of the American Control Conference, Seattle, WA, 2008, pp. 4388-4393.
[35] Hui, Q.; Haddad, W.M.; Bhat, S.P., Finite-time semistability and consensus for nonlinear dynamical networks, IEEE transactions on automatic control, 53, 8, 1887-1890, (2008) · Zbl 1367.93434
[36] Cortes, J., Finite-time convergent gradient flows with applications to network consensus, Automatica, 42, 11, 1993-2000, (2006) · Zbl 1261.93058
[37] Y. Cao, W. Ren, Containment control with multiple stationary or dynamic leaders under a directed interaction graph, in: Proceedings of the IEEE Conference on Decision and Control, Shanghai, China, 2009, pp. 3014-3019.
[38] Bhat, S.P.; Bernstein, D.S., Continuous finite-time stabilization of the translational and rotational double integrators, IEEE transactions on automatic control, 43, 5, 678-682, (1998) · Zbl 0925.93821
[39] Ren, W., Decentralization of virtual structures in formation control of multiple vehicle systems via consensus strategies, European journal of control, 14, 2, 1-11, (2008)
[40] Yang, P.; Freeman, R.A.; Lynch, K.M., Multi-agent coordination by decentralized estimation and control, IEEE transactions on automatic control, 53, 11, 2480-2496, (2008) · Zbl 1367.93040
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.