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Game Minimax Control of Automatic System Bandwidth under Information Counteraction

  • OPTIMIZATION, SYSTEM ANALYSIS, OPERATIONS RESEARCH
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Abstract

We consider the problem of finding algorithms for controlling the bandwidth of an automatic system in a game setting, when one of the players (the main control system) tries to improve the quality of transients and the other (the information countermeasure system), to worsen it. Approximately optimal minimax and maximin information-control algorithms of the players are obtained. An example illustrating the operation of the algorithm is given.

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REFERENCES

  1. Isaacs, R., Differential Games, New York–London–Sydney: John Wiley and Sons, 1965. Translated under the title: Differentsial’nye igry, Moscow: Mir, 1967.

    MATH  Google Scholar 

  2. Pugachev, V.S., Teoriya sluchainykh funktsii i ee primenenie k zadacham avtomaticheskogo upravleniya (Theory of Random Functions and Application to Automatic Control Problems), Moscow: Fizmatlit, 1960.

    Google Scholar 

  3. Fel’dbaum, A.A., Osnovy teorii optimal’nykh avtomaticheskikh sistem (Fundamentals of the Theory of Optimal Automatic Systems), Moscow: Nauka, 1966.

    Google Scholar 

  4. Aoki, M., Optimization of Stochastic Systems, New York–London: Academic Press, 1967. Translated under the title: Optimizatsiya stokhasticheskikh sistem, Moscow: Nauka, 1971.

    MATH  Google Scholar 

  5. Bryson, A.E. and Ho Yu-Chi, Applied Optimal Control, Waltham, MA–Toronto–London: Blaisdell, 1969. Translated under the title: Prikladnaya teoriya optimal’nogo upravleniya, Moscow: Mir, 1972.

    Google Scholar 

  6. Saridis, G.N., Self-Organizing Control of Stochastic Systems, New York–Basel: Marcel Dekker, 1977. Translated under the title: Samoorganizuyushchiesya stokhasticheskie sistemy upravleniya, Moscow: Nauka, 1980.

    MATH  Google Scholar 

  7. Kazakov, Y.E., Artemiev, V.M., and Bukhalev, V.A., Principles of the construction of complex algorithms for information processing and control in system with stochastic exchange structure, II IFAC Symp. Stochastic Control, 1986, Part 1.

  8. Piers, B.D. and Sworder, D.D., Bayes and minimax controllers for a linear systems for stochastic jump parameters, IEEE Trans. AC-16, 1971, no. 4, pp. 677–685.

  9. Bukhalev, V.A., Game control problem in a system with a random jump structure, Izv. Akad. Nauk CCCR. Tekh. Kibern., 1993, no. 2, pp. 122–132.

  10. Bukhalev, V.A., Raspoznavanie, otsenivanie i upravlenie v sistemakh so sluchainoi skachkoobraznoi strukturoi (Recognition, Estimation, and Control in Systems with Random Jump Structure), Moscow: Nauka, 1996.

    MATH  Google Scholar 

  11. Bukhalev, V.A., Skrynnikov, A.A., and Boldinov, V.A., Algoritmicheskaya pomekhozashchita bespilotnykh letatel’nykh apparatov (Algorithmic Anti-Jamming of Unmanned Aerial Vehicles), Moscow: Fizmatlit, 2018.

    Google Scholar 

  12. Bukhalev, V.A., Skrynnikov, A.A., and Boldinov, V.A., Igrovoe upravlenie sistemami so sluchainoi skachkoobraznoi strukturoi (Game Control of Systems with Random Jump Structure), Moscow: Fizmatlit, 2021.

    Google Scholar 

  13. Owen, G., Game Theory, Philadelphia–London–Toronto: W.B. Saunders, 1968. Translated under the title: Teoriya igr, Moscow: Vuzovskaya Kniga, 2007.

    MATH  Google Scholar 

  14. Zhang, C., Zhu, H., Zhou, H., and Bin, N., Deterministic and stochastic differential games, in Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems. Studies in Systems, Decision and Control. Vol. 67 , Cham: Springer, 2017, pp. 17–29.

  15. Moon, J., A sufficient condition for linear-quadratic stochastic zero-sum differential games for Markov jump systems, IEEE Trans. Autom. Control, 2019, vol. 64, no. 4, pp. 1619–1626.

    Article  MathSciNet  Google Scholar 

  16. Mariton, M., Jump Linear Systems in Automatic Control, New York: Taylor & Francis, 1990.

    Google Scholar 

  17. Kats, I.Ya. and Martynyuk, A.A., Stability and Stabilization of Nonlinear Systems with Random Structures, New York: CRC Press, 2003.

    MATH  Google Scholar 

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Funding

This work was financially supported by the Russian Foundation for Basic Research, projects nos. 19-08-00502, 19-08-00487.

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Authors and Affiliations

  1. Moscow Research Television Institute, Moscow, 105094, Russia

    V. A. Bukhalev

  2. State Research Institute of Aviation Systems (GosNIIAS), Moscow, 125167, Russia

    A. A. Skrynnikov

  3. Moscow Aviation Institute, Moscow, 125993, Russia

    A. A. Skrynnikov & V. A. Boldinov

Authors
  1. V. A. Bukhalev
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  2. A. A. Skrynnikov
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  3. V. A. Boldinov
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Corresponding authors

Correspondence to V. A. Bukhalev, A. A. Skrynnikov or V. A. Boldinov.

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Translated by V. Potapchouck

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Bukhalev, V.A., Skrynnikov, A.A. & Boldinov, V.A. Game Minimax Control of Automatic System Bandwidth under Information Counteraction. Autom Remote Control 83, 282–290 (2022). https://doi.org/10.1134/S0005117922020102

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  • DOI: https://doi.org/10.1134/S0005117922020102

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