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Distributed finite-time attitude containment control for multiple rigid bodies. (English) Zbl 1205.93010
Summary: Distributed finite-time attitude containment control for multiple rigid bodies is addressed in this paper. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the attitudes of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors’ information. We also discuss the special case of a single stationary leader and propose a control law using only the one-hop neighbors’ information to guarantee cooperative attitude regulation in finite time. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time. We also explicitly show the finite settling time.

93A14 Decentralized systems
93D20 Asymptotic stability in control theory
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[1] Bai, H.; Arcak, M.; Wen, J.T.-Y., Rigid body attitude coordination without inertial frame information, Automatica, 44, 12, 3170-3175, (2008) · Zbl 1153.93422
[2] Bhat, S.P.; Bernstein, D.S., Finite-time stability of homogeneous systems, (), 2513-2514
[3] 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
[4] Cao, Y., & Ren, W. (2009). Containment control with multiple stationary or dynamic leaders under a directed interaction graph. In Proceedings of the IEEE Conference on Decision and Control, Shanghai, PR China (pp. 3014-3019).
[5] Chung, S.-J.; Ahsun, U.; Slotine, J.-J.E., Application of synchronization to formation flying spacecraft: Lagrangian approach, Journal of guidance, control and dynamics, 32, 2, 512-526, (2009)
[6] Dimarogonas, D.V.; Tsiotras, P.; Kyriakopoulos, K.J., Leader – follower cooperative attitude control of multiple rigid bodies, Systems and control letters, 58, 6, 429-435, (2009) · Zbl 1161.93002
[7] Feng, Y.; Yu, X.; Man, Z., Non-singular terminal sliding mode control of rigid manipulators, Automatica, 38, 12, 2159-2167, (2002) · Zbl 1015.93006
[8] Graham, A., Kronecker products and matrix calculus with applications, (1981), Halsted Press New York · Zbl 0497.26005
[9] Hardy, G.H.; Littlewood, J.E.; Plya, G., Inequalities, (1952), Cambridge University Press Cambridge
[10] Hong, Y.; Wang, J.; Cheng, D., Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE transactions on automatic control, 51, 5, 858-862, (2006) · Zbl 1366.93290
[11] Hong, Y.; Xu, Y.; Huang, J., Finite-time control for robot manipulators, Systems and control letters, 46, 4, 243-253, (2002) · Zbl 0994.93041
[12] Horn, R.A.; Johnson, C.R., Matrix analysis, (1985), Cambridge University Press · Zbl 0576.15001
[13] Hu, J.; Hong, Y., Leader-following coordination of multi-agent systems with coupling time delays, Physica A, 374, 2, 853-863, (2007)
[14] 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
[15] Ji, M.; Ferrari-Trecate, G.; Egerstedt, M.; Buffa, A., Containment control in mobile networks, IEEE transactions on automatic control, 53, 8, 1972-1975, (2008) · Zbl 1367.93398
[16] Jin, E.; Jiang, X.; Sun, Z., Robust decentralized attitude coordination control of spacecraft formation, Systems and control letters, 57, 7, 567-577, (2008) · Zbl 1140.93008
[17] Kristiansen, R.; Loria, A.; Chaillet, A.; Nicklasson, P.J., Spacecraft relative rotation tracking without angular velocity measurements, Automatica, 45, 3, 750-756, (2009) · Zbl 1168.93333
[18] Li, S.; Ding, S.; Li, Q., Global set stabilisation of the spacecraft attitude using finite-time control technique, International journal of control, 82, 5, 822-836, (2009) · Zbl 1165.93328
[19] Man, Z.; Paplinski, A.; Wu, H., A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators, IEEE transactions on automatic control, 39, 12, 2464-2469, (1994) · Zbl 0825.93551
[20] Meng, Z.; Ren, W.; You, Z., Distributed finite-time containment control for multiple Lagrangian systems, (), 2885-2890
[21] Miroslav, F., Special matrices and their applications in numerical mathematics, (2009), Dover publications
[22] Nair, S.; Leonard, N.E., Stable synchronization of rigid body networks, American institute of mathematical sciences, 2, 4, 595-624, (2007)
[23] Ren, W., Distributed attitude alignment in spacecraft formation flying, International journal of adaptive control and signal processing, 21, 2-3, 95-113, (2007) · Zbl 1115.93338
[24] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[25] Sarlettea, A.; Sepulchrea, R.; Leonard, N.E., Autonomous rigid body attitude synchronization, Automatica, 45, 2, 572-577, (2009) · Zbl 1158.93372
[26] Schaub, H.; Junkins, J.L., Analytical mechanics of space systems, (2003), American Institute of Aeronautics and Astronautics, Inc
[27] Slotine, J.-J.E.; Benedetto, M.D.D., Hamiltonian adaptive control of spacecraft, IEEE transactions on automatic control, 35, 7, 848-852, (1990) · Zbl 0709.93588
[28] Tang, Y., Terminal sliding mode control for rigid robots, Automatica, 34, 1, 51-56, (1998) · Zbl 0908.93042
[29] Tsiotras, P., Stabilization and optimality results for the attitude control problem, Journal of guidance, control and dynamics, 19, 4, 772-779, (1996) · Zbl 0854.93104
[30] VanDyake, M.; Hall, C., Decentralized coordinated attitude control of a formation of spacecraft, Journal of guidance, control and dynamics, 29, 5, 1101-1109, (2006)
[31] Wong, H.; de Queiroz, M.S.; Kapila, V., Adaptive tracking control using synthesized velocity from attitude measurements, Automatica, 37, 6, 947-953, (2001) · Zbl 0997.93076
[32] Xiao, F.; Wang, long; Jia, Y., Fast information sharing in networks of autonomous agents, (), 4388-4393
[33] Yu, S.; Yu, X.; Shirinzadeh, B.; Man, Z., Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica, 41, 11, 1957-1964, (2005) · Zbl 1125.93423
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