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 distributed consensus via binary control protocols. (English) Zbl 1226.93008
Summary: This paper investigates the finite-time distributed consensus problem for multi-agent systems using a binary consensus protocol and the pinning control scheme. Compared with other consensus algorithms which need the complete state or output information of neighbors, the proposed algorithm only requires sign information of the relative state measurements, that is, the differences between a node’s state and that of its neighbors. This corresponds to only requiring a single-bit quantization error relative to each neighbor. This signum protocol is realistic in terms of observed behavior in animal groups, where relative motion is determined not by full time-signal measurements, but by coarse estimates of relative heading differences between neighbors. The signum protocol does not require explicit measurement of time signals from neighbors, and hence has the potential to significantly reduce the requirements for both computation and sensing. Analysis of discontinuous dynamical systems is used, including the Filippov solutions and set-valued Lie derivative. Based on the second-order information on the evolution of Lyapunov functions, the conditions that guarantee the finite-time consensus for the systems are identified. Numerical examples are given to illustrate the theoretical results.
93A14Decentralized systems
94C15Applications of graph theory to circuits and networks
93C15Control systems governed by ODE
93C10Nonlinear control systems
[1]Bacciotti, A.; Ceragioli, F.: Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions, ESAIM. control, optimization calculus of variations 4, 361-376 (1999) · Zbl 0927.34034 · doi:10.1051/cocv:1999113 · doi:http://www.edpsciences.org/articles/cocv/abs/1999/01/cocvVol4-13/cocvVol4-13.htm
[2]Bhat, S. P.; Bernstein, D. S.: Finite-time stability of continuous autonomous systems, SIAM journal on control and optimization 38, No. 3, 751-766 (2000) · Zbl 0945.34039 · doi:10.1137/S0363012997321358
[3]Chen, F.; Chen, Z.; Xiang, L.; Liu, Z.; Yuan, Z.: Reaching a consensus via pinning control, Automatica 45, 1215-1220 (2009) · Zbl 1162.93305 · doi:10.1016/j.automatica.2008.12.027
[4]Clarke, F. H.: Optimization and nonsmooth analysis, Canadian mathematical society series of monographs and advanced texts (1983) · Zbl 0582.49001
[5]Cortés, J.: Finite-time convergence gradient flows with applications to network consensus, Automatica 42, 1993-2000 (2006)
[6]Cortés, J.; Bullo, F.: Coordination and geometric optimization via distributed dynamical systems, SIAM journal on control and optimisation 44, 1543-1574 (2005) · Zbl 1108.37058 · doi:10.1137/S0363012903428652
[7]Filippov, A. F.: Differential equations with discontinuous righthand sides. Mathematics and its applications, Differential equations with discontinuous righthand sides. Mathematics and its applications 18 (1988)
[8]Hui, Q.; Haddad, W. M.; Bhat, S. P.: Finite-time semistability and consensus for nonlinear dynamical networks, IEEE transactions on automatic control 53, No. 8, 1887-1900 (2008)
[9]Hui, Q.; Haddad, W. M.; Bhat, S. P.: Semistability, finite-time stability, differential inclusions, and discontinuous dynamical systems having a continuum of equilibria, IEEE transactions on automatic control 54, No. 10, 2465-2470 (2009)
[10]Hui, Q.; Haddad, W. M.; Bhat, S. P.: Finite-time semistability, Filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies, Nonlinear analysis: hybrid systems 4, 557-573 (2010) · Zbl 1205.37102 · doi:10.1016/j.nahs.2010.03.002
[11]Jadbabaie, A.; Lin, J.; Morse, S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control 48, No. 6, 988-1001 (2003)
[12]Khoo, S.; Xie, L.; Man, Z.: Robust finite-time consensus tracking algorithm for multirobot systems, IEEE transactions on mechatronics 14, No. 2, 219-228 (2009)
[13]Li, X.; Wang, X. F.; Chen, G. R.: Pinning a complex dynamical network to its equilibrium, IEEE transactions on circuits and systems 51, No. 10, 2074-2087 (2004)
[14]Liu, S., Xie, L., & Lewis, F. L. (2010). Synchronization of multi-agent systems with delayed control input information from neighbors. In IEEE conference on decision and control, Atlanta, Georgia.
[15]Martínez, S.; Cortés, J.; Bullo, F.: Motion coordination with distributed information, IEEE control systems magazine 27, No. 4, 75-88 (2007)
[16]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)
[17]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)
[18]Paden, B.; Sastry, S. S.: A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators, IEEE transactions on circuits and systems 34, No. 1, 73-82 (1987) · Zbl 0632.34005 · doi:10.1109/TCS.1987.1086038
[19]Qu, Z.: Cooperative control of dynamical systems: applications to autonomous vehicles, (2009)
[20]Ren, W.: Multi-vehicle consensus with a time-varying reference state, Systems control letters 56, 474-483 (2007) · Zbl 1157.90459 · doi:10.1016/j.sysconle.2007.01.002
[21]Ren, W.; Beard, R. W.; Atkins, E. M.: Information consensus in multivehicle cooperative control, IEEE control systems magazine 27, No. 2, 71-82 (2007)
[22]Shevitz, D.; Paden, B.: Lyapunov stability theory of nonsmooth systems, IEEE transactions on automatic control 39, No. 9, 1910-1914 (1994) · Zbl 0814.93049 · doi:10.1109/9.317122
[23]Sundaram, S., & Hadjicostis, C. N. (2007). Finite-time distributed consensus in graphs with time-invariant topologies. In Proc. of the American control conference, NY (pp. 711–716).
[24]Tanner, H., Jadbabaie, A., & Pappas, G. J. (2003). Stable flocking of mobile agents, Part: dynamic topology. In IEEE conference on decision and control, Maui, HI (pp. 2016-2021).
[25]Wang, X., & Hong, Y. (2008). Finite-time consensus for multi-agent networks with second-order agent dynamics. In Proc. of the 17th world congress (pp. 15185–15190).
[26]Wang, L.; Xiao, F.: Finite-time consensus problems for networks of dynamic agents, IEEE transactions on automatic control 55, No. 4, 950-955 (2010)
[27]Xiao, F.; Wang, L.; Chen, J.; Gao, Y.: Finite-time formation control for multi-agent systems, Automatica 45, 2605-2611 (2009) · Zbl 1180.93006 · doi:10.1016/j.automatica.2009.07.012