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)
Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements. (English) Zbl 1252.93009
Summary: This paper studies the finite-time consensus problem of heterogeneous multi-agent systems composed of first-order and second-order integrator agents. By combining the homogeneous domination method with the adding a power integrator method, we propose two classes of consensus protocols with and without velocity measurements. First, we consider the protocol with velocity measurements and prove that it can solve the finite-time consensus under a strongly connected graph and leader-following network, respectively. Second, we consider the finite-time consensus problem of heterogeneous multi-agent systems, for which the second-order integrator agents cannot obtain the velocity measurements for feedback. Finally, some examples are provided to illustrate the effectiveness of the theoretical results.
MSC:
93A14Decentralized systems
93C15Control systems governed by ODE
References:
[1]Chu, T.; Wang, L.; Chen, T.; Mu, S.: Complex emergent dynamics of anisotropic swarms: convergence vs. Oscillation, Chaos, solitons and fractals 30, No. 4, 875-885 (2006) · Zbl 1142.34346 · doi:10.1016/j.chaos.2005.08.133
[2]Ji, Z.; Wang, Z.; Lin, H.; Wang, Z.: Interconnection topologies for multi-agent coordination under leader–follower framework, Automatica 45, No. 12, 2857-2863 (2009) · Zbl 1192.93013 · doi:10.1016/j.automatica.2009.09.002
[3]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)
[4]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)
[5]Ren, W.; Beard, R. W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control 50, No. 5, 655-661 (2005)
[6]Kim, Y.; Mesbahi, M.: On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian, IEEE transactions on automatic control 51, No. 1, 116-120 (2006)
[7]Xiao, L.; Boyd, S.: Fast linear iterations for distributed averaging, Systems and control letters 53, No. 1, 65-78 (2004) · Zbl 1157.90347 · doi:10.1016/j.sysconle.2004.02.022
[8]Cortés, J.: Finite-time convergent gradient flows with applications to network consensus, Automatica 42, No. 11, 1993-2000 (2006)
[9]Hui, Q.: Finite-time rendezvous algorithms for mobile autonomous agent, IEEE transactions on automatic control 56, No. 1, 207-211 (2011)
[10]Chen, G.; Lewis, F. L.; Xie, L.: Finite-time distributed consensus via binary control protocols, Automatica 47, No. 9, 1962-1968 (2011) · Zbl 1226.93008 · doi:10.1016/j.automatica.2011.05.013
[11]Bhat, S. P.; Bernstein, D. S.: Finite-time stability of continuos autonomous systems, SIAM journal on control and optimization 38, No. 3, 751-766 (2000) · Zbl 0945.34039 · doi:10.1137/S0363012997321358
[12]Wang, L.; Xiao, F.: Finite-time consensus problems for networks of dynamic agents, IEEE transactions on automatic control 55, No. 4, 950-955 (2010)
[13]F. Xiao, Consensus problems in networks of multiple autonomous agents, Ph.D. Thesis, Peking University, Beijing, China, 2008.
[14]Jiang, F.; Wang, L.: Finite-time information consensus for multi-agent systems with fixed and switching topologies, Physica D 238, No. 16, 1550-1560 (2009) · Zbl 1170.93304 · doi:10.1016/j.physd.2009.04.011
[15]Jiang, F.; Wang, L.: Finite-time weighted average consensus with respect to a monotinic function and its application, Systems and control letters 60, No. 9, 718-725 (2011) · Zbl 1226.93012 · doi:10.1016/j.sysconle.2011.05.009
[16]Zheng, Y.; Chen, W.; Wang, L.: Finite-time consensus for stochastic multi-agent systems, International journal of control 84, No. 10, 1644-1652 (2011)
[17]X. Wang, Y. Hong, Finite-time consensus for multi-agent networks with second-order agent dynamics, in: Proceedings of the 17th World Congress The International Federation of Automatic Control, Seoul, Korea, July 6–11, 2008, pp. 15185–15190.
[18]Li, S.; Du, H.; Lin, X.: Finite-time consensus for multi-agent systems with double-integrator dynamics, Automatica 47, No. 8, 1706-1712 (2011) · Zbl 1226.93014 · doi:10.1016/j.automatica.2011.02.045
[19]Qian, C.; Li, J.: Global finite-time stabilization by output feedback for plannar systems without observable linearization, IEEE transactions on automatic control 50, No. 6, 885-890 (2005)
[20]Liu, C.; Liu, F.: Stationary consensus of heterogeneous multi-agent systems with bounded communication delays, Automatica 47, No. 9, 2130-2133 (2011) · Zbl 1227.93010 · doi:10.1016/j.automatica.2011.06.005
[21]Zheng, Y.; Zhu, Y.; Wang, L.: Consensus of heterogeneous multi-agent systems, IET control theory and applications 5, No. 16, 1881-1888 (2011)
[22]Zheng, Y.; Wang, L.: Consensus of heterogeneous multi-agent systems without velocity measrements, International journal of control 85, No. 7, 906-914 (2012)
[23]Ren, W.: On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control 53, No. 6, 1503-1509 (2008)
[24]Y. Gao, L. Wang, Y. Jia, Consensus of multiple second-order agents without velocity measurements, in: Proceedings of the American Control Conference, St. Louis, USA, June 10–12, 2009, pp. 4464–4469.
[25]Abdessameud, A.; Tayebi, A.: On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints, Systems and control letters 59, No. 12, 812-821 (2010) · Zbl 1217.93009 · doi:10.1016/j.sysconle.2010.06.019
[26]Godsil, C.; Royal, G.: Algebraic graph theory, (2001)
[27]Hong, Y.: Finite-time stabilization and stabilizability of a class of controllable systems, Systems and control letters 46, No. 4, 231-236 (2002) · Zbl 0994.93049 · doi:10.1016/S0167-6911(02)00119-6