ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2019. Vol. 30

Stabilization of Coupled Linear Systems Via Bounded Distributed Feedbacks

N. M. Dmitruk

This article deals with a stabilization problem for a team of linear interconnected systems via bounded feedbacks. Effective approaches to stabilization of constrained systems from model predictive control theory are developed for the decentralized case when each system of the group is controlled by its local controller. We propose formulations of local optimal control problems and an algorithm based on them that constructs a distributed feedback guaranteeing asymptotic stability of the group.

About the Authors

Natalia Dmitruk, Cand. Sci. (Phys.–Math.), Assoc. Prof., Belarusian State University, 4, Nezavisimosti av., Minsk, 220030, Republic of Belarus, tel.: +375 (17) 2095074, e-mail: dmitrukn@bsu.by

For citation

Dmitruk N.M. Stabilization of Coupled Linear Systems Via Bounded Distributed Feedbacks. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 30, pp. 31-44. https://doi.org/10.26516/1997-7670.2019.30.31

stabilization, feedback, distributed control
93D15, 93C05, 49J15
  1. Balashevich N.V. Stabilization of Linear Systems by Bounded Controlling Actions. Journal of Automation and Information Sciences, 2009, vol. 41, no. 5, pp. 16–28.
  2. Barbashin E.A. Introduction to the Theory of Stability. Wolters-Noordhoff, 1970.
  3. Gabasov R., Dmitruk N.M., Kirillova F.M. Decentralized optimal control of a group of dynamical objects. Comput. Math. and Math. Phys., 2008, vol. 48, pp. 561-576.
  4. Gabasov R., Dmitruk N.M., Kirillova F.M. Decentralized optimal control of dynamical systems under uncertainty. Comput. Math. and Math. Phys., 2011, vol. 51, pp. 1128-1145.
  5. Gabasov R., Kirillova F.M., Kostyukova O.I. Methods of stabilizing dynamic systems. Izv. Ross. Akad. Nauk, Tekh. Kibern., 1994, no. 3.
  6. Kaljaev I.A., Gajduk A.R., Kapustjan S.G. Modeli i algoritmy kollektivnogo upravlenija v gruppah robotov [Models and algorithms of collective control in groups of robots] Moscow, Fizmatlit Publ., 2009. (In Russian)
  7. Kurzhanskii A. B. On a team control problem under obstacles. Proc. of the Steklov Institute of Mathematics, 2015, vol. 291, no. 1, pp. 128-142.
  8. Bemporad A., Borelli F., Morari M. Model predictive control based on linear programming – the explicit solution. IEEE Transactions on Automatic Control, 2002, vol. 47, no. 12, pp. 1974-1985.
  9. Camponogara E. et. al. Distributed model predictive control. IEEE Control Systems Magazine, 2002, vol. 22, no. 1, pp. 44-52.
  10. Christofides P. D. et al. Distributed model predictive control: A tutorial review and future research directions. Computers & Chemical Eng., 2013, vol. 51, pp. 21-41.
  11. Distributed Model Predictive Control Made Easy. Eds. J. M. Maestre, R. R. Negenborn. Springer, 2014.
  12. Dmitruk N. Robust Optimal Control of Dynamically Decoupled Systems via Distributed Feedbacks. Optimization in the Natural Sciences. Communications in Computer and Information Science, 2015, vol. 499, pp. 95-106.
  13. Keviczky T., Borrelli F., Balas G.J. Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica, 2006, vol. 42, pp. 2105-2115.
  14. Muller M. A., Reble M., Allgower F. Cooperative control of dynamically decoupled systems via distributed model predictive control. Internat. Journal of Robust and Nonlinear Control, 2012, vol. 22, no. 12, pp. 1376-1397.
  15. Rawlings J.B., Mayne D.Q. Model Predictive Control: Theory and Design. Madison, Nob Hill Publishing, 2009.
  16. Stewart B. T. et. al. Cooperative distributed model predictive control. Systems & Control Letters, 2010, vol. 59, pp. 460-469.

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