A problem of the equidistant deployment for discrete-time multiagent systems

Authors

  • Alexander Yu. Aleksandrov St. Petersburg State University, 199034, St. Petersburg, Russian Federation
  • Al’bert I. Arakelov St. Petersburg State University, 199034, St. Petersburg, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2022.114

Abstract

This article explores a discrete-time multiagent system on a line. This requires the design of a control protocol providing equidistant agent deployment on a given segment of the line under the constraint that each agent receives information about distances to its neighbors via an auxiliary agent. An approach to the solution of the stated problem is developed. This proves that, under the proposed control protocol, neither communication delay nor switching of communication graph destroy convergence of agents to the equidistant distribution. The results of a numerical simulation confirming the obtained theoretical conclusions are presented.

Keywords:

multiagent system, formation control, discrete-time system, delay, switching, asymptotic stability

Downloads

Download data is not yet available.
 

References

Martinez S., Bullo F. Optimal sensor placement and motion coordinationfor target tracking. Automatica, 2006, vol. 42, pp. 661–668.

Olfati-Saber R., Murray R. M. Consensus problems in networks ofagents with switching topology and time-delays. IEEE Trans. Automat. Control, 2004, vol. 49, no. 9, pp. 1520–1533.

Garcia-Planas M. I. Analyzing control properties of multiagent linear systems. Cybernetics and Physics, 2020, vol. 9, no. 2, pp. 81–85.

Provotorov V. V., Sergeev S. M., Hoang V. N. Point control of a differential-difference system with distributed parameters on the graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 3, pp. 277–286. https://doi.org/10.21638/11701/spbu10.2021.305

Zhabko A. P., Provotorov V. V., Ryazhskikh V. I., Shindyapin A. I. Optimal control of a differential-difference parabolic systems with distributed parameters on the graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 4, pp. 433–448. https://doi.org/10.21638/11701/spbu10.2021.411

Wagner I., Bruckstein A. M. Row straightening by local interactions. Circuits, Systems and Signal Processing, 1997, vol. 16, no. 3, pp. 287–305.

Shcherbakov P. S. Formation control. The Van Loan scheme and other algorithms. Automation and Remote Control, 2011, vol. 72, no. 10, pp. 681–696.

Kvinto Ya. I., Parsegov S. E. Equidistant arrangement of agents on line: Analysis of the algorithm and its generalization. Automation and Remote Control, 2012, vol. 73, no. 11, pp. 1784–1793.

Parsegov S. E., Polyakov A. E., Shcherbakov P. S. Nonlinear control protocol for uniform allocation of agents on a segment. Dokl. Math., 2013, vol. 87, no. 1, pp. 133–136.

Aleksandrov A., Fradkov A., Semenov A. Delayed and switched control of formations on a line segment: Delays and switches do not matter. IEEE Trans. Automat. Control, 2020, vol. 65, no. 2, pp. 794–800.

Aleksandrov A., Semenov A., Fradkov A. Discrete-time deployment of agents on a line segment: Delays and switches do not matter. Automation and Remote Control, 2020, vol. 81, no. 4, pp. 637–648.

Aleksandrov A. Yu., Andriyanova N. R. Fixed-time stability of switched systems with application to a problem of formation control. Nonlinear Analysis. Hybrid Systems, 2021, vol. 40, no. 101008.

Kaszkurewicz E., Bhaya A. Matrix diagonal stability in systems and computation. Boston, Basel, Berlin, Birkhauser Press, 1999, 267 p.

Aleksandrov A., Mason O. Diagonal Lyapunov — Krasovskii functionals for discrete-time positive systems with delay. Syst. Control Lett., 2014, vol. 63, pp. 63–67.

Aleksandrov A., Mason O. Diagonal stability of a class of discrete-time positive switched systemswith delay. IET Control Theory & Applications, 2018, vol. 12, no. 6, pp. 812–818.

Lin H., Antsaklis P. J. Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Trans. Automat. Control, 2009, vol. 54, no. 2, pp. 308–322.

Downloads

Published

2022-06-02

How to Cite

Aleksandrov, A. Y., & Arakelov, A. I. (2022). A problem of the equidistant deployment for discrete-time multiagent systems: . Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 18(1), 171–178. https://doi.org/10.21638/11701/spbu10.2022.114

Issue

Section

Control Processes