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Problem of Consensus for Linear Dynamic Systems with Stochastic Disturbances

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Abstract

A multi-agent system with identical linear agents is considered. The consensus problem is to synchronize the agents’ state vector. The distributed control algorithm that solves the problem is known for a system without disturbances. The applicability of this algorithm is also shown for when stochastic disturbances act on the agents’ dynamics and output.

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REFERENCES

  1. Y. Shang, D. Li, Z. Peng, A. Heydari, K. Turkoglu, and J. Thunberg, ‘‘IEEE access special section editorial: Recent developments in consensus problems for complex networked systems,’’ IEEE Access 6, 60993–60995 (2018).

    Article  Google Scholar 

  2. I. Navarro and F. Matía, ‘‘An introduction to swarm robotics,’’ ISRN Robotics 2013, Article ID 608164 (2013).

  3. F. Chen, Y. Cao, and W. Ren, ‘‘Distributed average tracking of multiple time-varying reference signals with bounded derivatives,’’ IEEE Trans. Autom. Control 57 (12), 3169–3174 (2012).

    Article  MathSciNet  Google Scholar 

  4. W. Ren and U. M. Al-Saggaf, ‘‘Distributed Kalman–Bucy filter with embedded dynamic averaging algorithm,’’ IEEE Syst. J. 12 (2), 1722–1730 (2018).

    Article  Google Scholar 

  5. S. S. Kia, ‘‘Distributed optimal in-network resource allocation algorithm design via a control theoretic approach,’’ Syst. Control Lett. 107, 49–57 (2017).

    Article  MathSciNet  Google Scholar 

  6. J. Khazaei and Z. Miao, ‘‘Consensus control for energy storage systems,’’ IEEE Trans. Smart Grid 9 (4), 3009–3017 (2018).

    Article  Google Scholar 

  7. X. Zhang, Y. Huang, L. Li, and W.-C. Yeh, ‘‘Power and capacity consensus tracking of distributed battery storage systems in modular microgrids,’’ Energies 11 (6), 1439 (2018).

    Article  Google Scholar 

  8. S. S. Kia, B. Van Scoy, J. Cortes, R. A. Freeman, K. M. Lynch, and S. Martinez, ‘‘Tutorial on dynamic average consensus: The problem, its applications, and the algorithms,’’ IEEE Control Syst. Mag. 39 (3), 40–72 (2019).

    Article  MathSciNet  Google Scholar 

  9. Z. Li, Z. Duan, G. Chen, and L. Huang, ‘‘Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint,’’ IEEE Trans. Circuits Syst. I: Regular Pap. 57 (1), 213–224 (2010).

    Article  MathSciNet  Google Scholar 

  10. J. Jiao, H. L. Trentelman, and M. K. Camlibel, ‘‘Distributed linear quadratic optimal control: Compute locally and act globally,’’ IEEE Control Syst. Lett. 4 (1), 67–72 (2020).

    Article  MathSciNet  Google Scholar 

  11. K. Brammer and G. Siffling, Kalman-Bucy-Filter: Deterministische Beobachtung und Stochastische Filterung (Oldenbourg, München, 1975) [in German]; Kalman-Bucy Filter: Deterministic Observation and Stochastic Filtering (Nauka, Moscow, 1982) [in Russian].

  12. Description of the Nelder-Mead algorithm implementation. https://julianlsolvers.github.io/Optim.jl/stable/#algo/nelder_mead/.

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Funding

This work was performed as part of the research by the Moscow Center of Fundamental and Applied Mathematics. It was supported by the Russian Foundation for Basic Research, project no. 20-57-00001.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    A. I. Samarin

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  1. A. I. Samarin
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Correspondence to A. I. Samarin.

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Translated by E. Smirnova

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Samarin, A.I. Problem of Consensus for Linear Dynamic Systems with Stochastic Disturbances. MoscowUniv.Comput.Math.Cybern. 45, 21–33 (2021). https://doi.org/10.3103/S0278641921010052

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  • DOI: https://doi.org/10.3103/S0278641921010052

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