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Volume 59 >>> № 2 MARCH — APRIL 2023

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UDC 517.9

О.І. Voskolovych¹, K.A. Chikrii²

¹ Krut Heroes Military Institute of Telecommunications and Information Technologies, Kyiv, Ukraine

olexii.voskolovych@viti.edu.ua

² V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

c.kirill@gmail.com

FAILURE OF CONTROL DEVICES UNDER CONFLICT CONDITIONS

Abstract. The authors consider a nonstationary game problem of control of moving objects in the case of violations in their dynamics caused by a breakdown or failure of the control devices. A game situation is analyzed where the moment of failure of control devices is a priori unknown, and the time required to eliminate it is given. The sufficient conditions for bringing the trajectory of the conflict-controlled process to the terminal set in a certain finite time are established. The results are illustrated using a model example with simple motion.

Keywords: conflict-controlled process, set-valued mapping, resolving function, failure of control devices, stroboscopic strategy, Pontryagin’s condition, Aumann’s integral.

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REFERENCES

Kondratenko Yu., Gerasin O, Kozlov O., Topalov A., Kilimanov B. Inspection mobile robot’s control system remote IoT-based data transmission. Journal of Mobile Multimedia. 2021. Vol. 17, Iss. 4. P. 499–526.

Balaji L., Dhanalakshmi A., Chellaswamy C. A variance distortion rate Control scheme for combined spatial-temporal sealable Video coding. Journal of Mobile Multimedia. 2017. Vol. 12, No 3–4. P. 277–290.

Inaba T., Elmazi D., Sakamoto S., Oda T., Ikeda M., Barolli L. A secure–aware Call Admission Control scheme for a wireless cellular network using fuzzy logic and its performance evolution. Journal of Mobile Multimedia. 2015. Vol. 11, Iss. 3–4. P. 213–222.

Kuntsevich V.M., Gubarev V.F., Kondratenko Y.P., Lebedev D.V., Lysenko V.P. (Eds). Control Systems: Theory and Applications. Series in Automation, Control and Robotics. Gistrup; Delft: River Publishers, 2018. 329 p.

Isaacs R. Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. New York: John Wiley Sons, 1965. 479 p.

Pontryagin L.S. Selected Scientific Works. Moscow: Nauka, 1988. Vol. 2. 576 p. (in Russian).

Krasovskii N.N., Subbotin A.I. Positional Differential Games. Moscow: Nauka, 1974. 420 p. (in Russian).

Chikrii A.A. Conflict Controlled Processes. Dordrecht; Boston; London: Springer Science and Busines Media, 2013. 424 p.

Hajek O. Pursuit Games. New York: Academic Press, 1975. 266 p.

Aubin J.-P., Frankowska H. Set-valued Analysis. Boston; Basel; Berlin: Birkhauser, 1990. 461 p.

Shouchuan Hu.S., Papageorgiou N.S. Handbook of Multivalued Analysis: Vol.1: Theory. New York: Springer, 1997. 980 p.

Locke А.S. Guidance. Princeton, New Jersey; New York: D. Van Nostrand Company, 1957. 775 p.

Siouris G.M. Missile Guidance and Control Systems. New York: Springer, 2004. 666 p.

Nikol’skii M.S. On control problem for linear objects with disturbances in dynamics. Trudy Inst. Mat. Mekh UrO RAN. 1995. № 3. P.132–146. (in Russian).

Albus J., Meystel A., Chikrii A.A., Belousov A.A., Kozlov A.I. Analytical method for solution of the game problem of soft meeting for moving objects. Cybernetics and Systems Analysis. 2001. Vol. 37, N 1. P. 75–91. URL: https://link.springer.com/article/10.1023/A:1016620201241.

Ushakov V.N., Ukhobotov V.I., Izmest’ev I.V. On a problem of impulse control under disturbance and possible breakdown. Trudy Instituta Mat. I Mekh. UrO RAN. 2021. Vol. 27, N 2. P. 249–263. (in Russian).

Zemlyakov S.D., Rutkovskij V.Y., Silaev A.V. Reconfiguration of control systems in case of failures. Avtomatika I Telemekhanika. 1996. N 1. P. 3–20. (in Russian).

Chikrii G.Ts. Principle of time stretching for motion control in condition of conflict. In: Advanced Control Systems: Theory and Applications. Series in Automation, Control and Robotics. Kondratenko Y.P., Kuntsevich V.M., Chikrii A.A., Gubarev V.F. (Eds.). New York: River Publishers, 2021. P. 53–82.

Korn G., Korn T. Mathematical Handbook for Scientists and Engineers. New York; Toronto; London: McGraw-Hill, Inc., 1961. 720 p.

Chikrij A.A., Eidelman S.D. Generalized Mittag Leffler functions in game problems for evolution equations of fractional order. Kibernetika i Systemnyj Analiz. 2000. Vol. 36, N 3. P. 3–32 (in Russian).

Nikol’skii M.S. Stroboscopic strategies and first direct method of L.S. Pontryagin in quasi-linear non-stationary differential games of pursuit-evasion. Problems of Control and Information Theory. 1992. Vol. 11, N 5. P. 373–377.

Pilipenko Yu.V, Chikrij A.A. The oscillation processes of conflict control. Prikladnaya Mathematika I Mekhanika. 1993. Vol. 57, N 3. P. –14.

Chikrii A., Petryshyn R., Cherevko I., Bigun Y. Method of resolving function in the theory of conflict-controlled processes. In: Advanced Control Technique Systems: Theory and Applications. Series Studies in Systems, Decision and Control. Kondratenko Y., Kuntsevich V., Chikrii A., Gubarev V. (Eds.). Springer, 2019. Vol. 203. P. 3–33.

Aumann R.J. Integrals of set-valued functions. J. Math. Anal. Appl. 1965. Vol. 12. P. 1–12.

Joffe A.D., Tikhomirov V.M. Theory of Extreme Problems. Moscow: Nauka, 1974. 480 p. (in Russian).