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.
Similar content being viewed by others
References
Yu. Kondratenko, O. Gerasin, O. Kozlov, A. Topalov, and B. Kilimanov, “Inspection mobile robot’s control system with remote IoT-based data transmission,” J. of Mobile Multimedia, Vol. 17, Iss. 4, 499–526 (2021).
L. Balaji, A. Dhanalakshmi, and C. Chellaswamy, “A variance distortion rate control scheme for combined spatial-temporal scalable video coding,” J. of Mobile Multimedia, Vol. 12, No. 3–4, 277–290 (2017).
T. Inaba, D. Elmazi, S. Sakamoto, T. Oda, M. Ikeda, and L. Barolli, “A secure–aware call admission control scheme for wireless cellular networks using fuzzy logic and its performance evaluation,” J. of Mobile Multimedia, Vol. 11, Iss. 3–4, 213–222 (2015).
V. M. Kuntsevich, V. F. Gubarev, Y. P. Kondratenko, D. V. Lebedev, and V. P. Lysenko (eds.), Control Systems: Theory and Applications, Ser. in Automation, Control and Robotics, River Publishers, Delft (2018).
R. Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, John Wiley & Sons, New York (1965).
L. S. Pontryagin, Selected Scientific Works, Vol. 2 [in Russian], Nauka, Moscow (1988).
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).
A. A. Chikrii, Conflict Controlled Processes, Springer Sci. & Busines Media, Dordrecht–Boston–London (2013).
O. Hajek, Pursuit Games, Academic Press, New York (1975).
J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston–Basel–Berlin (1990).
Hu. S. Shouchuan and N. S. Papageorgiou, Handbook of Multivalued Analysis, Vol. 1: Theory, Springer, New York (1997).
À. S. Locke, Guidance, D. Van Nostrand Company, Princeton–New Jersey–New York (1957).
G. M. Siouris, Missile Guidance and Control Systems, Springer, New York (2004).
M. S. Nikol’skii, “On control problem for linear objects with disturbances in dynamics,” Trudy Inst. Mat. Mekh. UrO RAN, No. 3, 132–146 (1995).
J. Albus, A. Meystel, A. A. Chikrii, A. A. Belousov, and A. I. Kozlov, “Analytical method for solution of the game problem of soft landing for moving objects,” Cybern. Syst. Analysis, Vol. 37, No. 1, 75–91 (2001). https://doi.org/10.1023/A:1016620201241.
V. N. Ushakov, V. I. Ukhobotov, and I. V. Izmest’ev, “On a problem of impulse control under disturbance and possible breakdown,” Trudy Inst. Mat. i Mekh. UrO RAN, Vol. 27, No. 2, 249–263 (2021).
S. D. Zemlyakov, V. Y. Rutkovskij, and A. V. Silaev, “Reconfiguration of control systems in case of failures,” Avtomatika i Telemekhanika, No. 1, 3–20 (1996).
G. Ts. Chikrii, “Principle of time stretching for motion control in condition of conflict,” in: Y. P. Kondratenko, V. M. Kuntsevich, A. A. Chikrii, and V. F. Gubarev (eds.), Advanced Control Systems: Theory and Applications, River Publishers Ser. in Automation, Control and Robotics, New York (2021), pp. 53–82.
G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, Inc., New York–Toronto–London (1961).
A. A. Chikrii and S. D. Eidel’man, “Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order,” Cybern. Syst. Analysis, Vol. 36, No. 3, 315–338 (2000). https://doi.org/10.1007/BF02732983.
M. S. Nikol’skii, “Stroboscopic strategies and first direct method of L. S. Pontryagin in quasi-linear non-stationary differential games of pursuit-evasion,” Problemy Upravlen. Teor. Inform., Vol. 11, No. 5, 373–377 (1982).
Yu. B. Pilipenko and A. A. Chikrii, “Oscillatory conflict-control processes,” J. Appl. Math. Mech., Vol. 57, No. 3, 407–417 (1993).
A. Chikrii, R. Petryshyn, I. Cherevko, and Y. Bigun, “Method of resolving function in the theory of conflict-controlled processes,” in: Y. Kondratenko, V. Kuntsevich, A. Chikrii, and V. Gubarev (eds.), Advanced Control Systems: Theory and Applications, Springer, Vol. 203 (2019), pp. 3–33.
R. J. Aumann, “Integrals of set-valued functions,” J. Math. Anal. Appl., Vol. 12, 1–12 (1965).
A. D. Joffe and V. M. Tikhomirov, Theory of Extreme Problems [in Russian], Nauka, Moscow (1974).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2023, pp. 146–157.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Voskolovych, O.I., Chikrii, K.A. Failure of Control Devices Under Conflict Conditions. Cybern Syst Anal 59, 306–316 (2023). https://doi.org/10.1007/s10559-023-00564-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-023-00564-4