zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Finite-time stability of multi-agent system in disturbed environment. (English) Zbl 1243.93105
Summary: Finite-time stability problem of multi-agent system in disturbed environment is a question with practical significance. In this paper, a multi-agent system moving with obstacle avoidance is studied. The multi-agent system is expected to form a desired formation in finite time. Finite-time control law for continuous multi-agent system is proposed, which ensures that all the agents can pass the obstacles on their way, and the relative position between two agents reaches a constant value in finite time. Based on some notations and proposition given in the paper, the stability analysis is presented. Finally some simulations are presented to show the effectiveness of the method.

93D99Stability of control systems
03C15Countable models
93A14Decentralized systems
93C85Automated control systems (robots, etc.)
Full Text: DOI
[1] Hong, Y.: Finite-time stabilization and stabilizability of a class of controllable systems. Syst. Control Lett. 46, 231--236 (2002) · Zbl 0994.93049 · doi:10.1016/S0167-6911(02)00119-6
[2] Hong, Y., Huang, J., Xu, Y.: On an output feedback finite-time stabilization problem. IEEE Trans. Autom. Control 46, 305--309 (2001) · Zbl 0992.93075 · doi:10.1109/9.905699
[3] Wolfe, J.D., Chichka, D.F., Speyer, J.L.: Decentralized controllers for unmanned aerial vehicle formation flight. In: Proc. AIAA Conf. Guidance, Navigation, and Control 96-3833, San Diego, CA (1996)
[4] Smith, T.R., Hanssmann, H., Leonard, N.E.: Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In: Proc. IEEE Conf. Decision and Control, Orlando, FL, pp. 4598--4603 (2001)
[5] Cortés, J., Bullo, F.: Coordination and geometric optimization via distributed dynamical systems. SIAM J. Control Optim. 44, 1543--1574 (2005) · Zbl 1108.37058 · doi:10.1137/S0363012903428652
[6] Swaroop, D., Hedrick, J.K.: Constant spacing strategies for platooning in automated highway systems. ASME J. Dyn. Syst. Meas. Control 121, 462--470 (1999) · doi:10.1115/1.2802497
[7] Vidal, R., Shakernia, O., Sastry, S.: Formation control of nonholonomic mobile robots with omnidirectional visual servoing and motion segmentation. Proc. - IEEE Int. Conf. Robot. Autom. 1, 584--589 (2003)
[8] Fax, J.A., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49, 1465--1476 (2004) · doi:10.1109/TAC.2004.834433
[9] Paganini, F., Doyle, J.C., Low, S.H.: Scalable laws for stable network congestion control. In: Proc. IEEE Conf. Decision and Control, Orlando, FL, pp. 185--190 (2001)
[10] Han, J., Li, M., Guo, L.: Soft control on collective behavior of group of autonomous agents by a shill agent. J. Syst. Sci. Complex. 19(1), 54--62 (2006) · doi:10.1007/s11424-006-0054-z
[11] Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48, 988--1001 (2003) · doi:10.1109/TAC.2003.812781
[12] Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520--1533 (2004) · doi:10.1109/TAC.2004.834113
[13] Marshall, J.A., Broucke, M.E., Francis, B.A.: Formations of vehicles in cyclic pursuit. IEEE Trans. Autom. Control 49, 1963--1974 (2004) · doi:10.1109/TAC.2004.837589
[14] Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51, 401--420 (2006) · doi:10.1109/TAC.2005.864190
[15] Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robot. Autom. 15, 818--828 (1999) · doi:10.1109/70.795787
[16] Yang, Z., Zhang, Q., Chen, Z.: Flocking of multi-agents with nonlinear inner-coupling functions. Nonlinear Dyn. 60(3), 225--264 (2010) · Zbl 1189.92003
[17] Wang, L., Chen, Z., Liu, Z., Yuan, Z.: Finite time agreement protocol design of multi-agent systems with communication delays. Asian J. Control 11(3), 281--286 (2009) · doi:10.1002/asjc.104
[18] Cortés, J.: Finite-time convergent gradient flows with applications to network consensus. Automatica 42, 1993--2000 (2006) · Zbl 1261.93058 · doi:10.1016/j.automatica.2006.06.015
[19] Saber, R.O., Murray, R.M.: Flocking with obstacle avoidance: cooperations with limited communication in mobile networks. In: IEEE Conf. on Decision and Control, Maui, Hawaii, USA, pp. 2022--2028 (2003)
[20] Tanner, H.: Flocking with obstacle avoidance in switching networks of interconnected vehicles. In: IEEE International Conference Robotics and Automation, New Orleans, LA, pp. 3006--3011 (2004)
[21] Ogren, P., Leonard, N.E.: Obstacle avoidance in formation. In: IEEE International Conf. Robotics and Automation, Taipei, Taiwan, pp. 2492--2497 (2003)
[22] Godsil, C., Royal, G.: Algebraic Graph Theory. Springer, New York (2001)
[23] Bhat, S.P., Bernstein, D.S.: Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibra. SIAM J. Control Optim. 42, 1745--1775 (2003) · Zbl 1078.34031 · doi:10.1137/S0363012902407119