# zbMATH — the first resource for mathematics

##### Examples
 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.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 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)
Collective rotating motions of second-order multi-agent systems in three-dimensional space. (English) Zbl 1225.93018
Summary: This paper addresses collective rotating motions of second-order multi-agent systems in three-dimensional space (3D). Two distributed control protocols are proposed and sufficient conditions are derived under which all agents rotate around a common point with a specified formation structure. Simulation results are provided to illustrate the effectiveness of the theoretical results.
##### MSC:
 93A14 Decentralized systems 93C95 Applications of control theory 05C90 Applications of graph theory
##### Keywords:
rotating motion; formation control; multi-agent system
##### 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, No. 6, 988-1001 (2003) [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, No. 9, 1520-1533 (2004) [3] Ren, W.; Beard, R. W.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE transactions on automatic control 50, No. 5, 655-661 (2005) [4] Ren, W.: On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control 53, No. 6, 1503-1509 (2008) [5] Hong, Y.; Gao, L.; Cheng, D.; Hu, J.: Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 42, No. 7, 1177-1182 (2006) · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013 [6] Li, Z.; Duan, Z.; Chen, G.; Huang, L.: Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint, IEEE transactions on circuits and systems. I. regular papers 57, No. 1, 213-224 (2010) [7] Xie, G.; Wang, L.: Consensus control for a class of networks of dynamic agents, International journal of robust and nonlinear control 17, No. 10–11, 941-959 (2007) [8] Porfiri, M.; Stilwell, D. J.: Consensus seeking over random weighted directed graphs, IEEE transactions on automatic control 52, No. 9, 1767-1773 (2007) [9] Olfati-Saber, R.; Fax, J. A.; Murray, R. M.: Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95, No. 1, 215-233 (2007) [10] 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, No. 8, 1804-1816 (2008) [11] Cao, M.; Morse, A. S.; Anderson, B. D. O.: Agreeing asynchronously, IEEE transactions on automatic control 53, No. 8, 1826-1838 (2008) [12] Lin, P.; Jia, Y.: Average-consensus in networks of multi-agents with both switching topology and coupling time-delay, Physica A 387, No. 1, 303-313 (2008) [13] Lin, P.; Jia, Y.; Li, L.: Distributed robust H$\infty$ consensus control in directed networks of agents with time-delay, Systems and control letters 57, No. 8, 643-653 (2008) · Zbl 1140.93355 · doi:10.1016/j.sysconle.2008.01.002 [14] Lafferriere, G.; Williams, A.; Caughman, J.; Veerman, J. J. P.: Decentralized control of vehicle formations, Systems and control letters 54, No. 9, 899-910 (2005) · Zbl 1129.93303 · doi:10.1016/j.sysconle.2005.02.004 [15] Smith, R. S.; Hadaegh, F. Y.: Closed-loop dynamics of cooperative vehicle formations with parallel estimators and communication, IEEE transactions on automatic control 52, No. 8, 1404-1414 (2007) [16] Tanner, H.; Jadbabaie, A.; Pappas, G.: Flocking in fixed and switching networks, IEEE transactions on automatic control 52, No. 5, 863-868 (2007) [17] Su, H.; Wang, X.; Lin, Z.: Flocking of multi-agents with a virtual leader, IEEE transactions on automatic control 54, No. 2, 293-307 (2009) [18] Sepulchre, R.; Paley, D.; Leonard, N. E.: Stabilization of planar collective motion with limited communication, IEEE transactions on automatic control 53, No. 3, 706-719 (2007) [19] S. Hernandez, D. Paley, Three-dimensional motion coordination in a time-invariant flowfield, in: Proceedings of the 48th Decision and Control Conference, 2009, pp. 7042–7048. [20] Pavone, M.; Frazzoli, E.: Decentralized policies for geometric pattern formation and path coverage, ASME journal of dynamic systems, measurement, and control 129, No. 5, 633-643 (2007) [21] Ren, W.: Collective motion from consensus with Cartesian coordinate coupling, IEEE transactions on automatic control 54, No. 6, 1330-1335 (2009) [22] Lin, P.; Jia, Y.: Distributed rotating formation control of multi-agent systems, Systems and control letters 59, No. 10, 587-595 (2010) · Zbl 1201.93010 · doi:10.1016/j.sysconle.2010.06.015 [23] Godsil, C.; Royle, G.: Algebraic graph theory, (2001) [24] Battin, Richard H.: An introduction to the mathematics and methods of astrodynamics, (1987) · Zbl 0892.00015