Abstract
The problem of minimax control synthesis for objects that are described by a two-dimensional heat conduction equation of parabolic type is solved. It is assumed that the control object functions under uncertainty conditions, and the perturbations acting on the object belong to some given hyperelipsoid. The problem of constructing a regulator in the state of an object for cases of point and mobile limit control is considered in accordance with the integral-quadratic quality criterion. In the work, for the first time, a minimax approach was used to control the objects described by the two-dimensional parabolic type thermal conductivity equation; the theoretical positions of synthesis of minimax regulators for cases of lumped boundary (point) and moving regulators are considered; algorithmic software is developed that allows to simulate the dynamics of the constructed minimax-regulators and to investigate the corresponding transients.
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References
Butkovsky, A.G.: Metodi control systems with distributed parameters, 568 p. Moskva, Nauka (1975). (in Russian)
Butkovsky, A.G., Darinsky, Yu.V., Pustylnikov, L.M.: Mobile control systems with distributed parameters. Autom. Remote Control 2, 15–25 (1976). (in Russian)
Butkovsky, A.G., Pustylnikov, L.M.: The theory of mobile control systems with distributed parameters, 397 p. Moskva, Nauka (1980, in Russian)
Korobiichuk, I., Siumachenko, D., Smityuh, Y., Shumyhai, D.: Research on automatic controllers for plants with significant delay. Advances in Intelligent Systems and Computing, vol. 519, pp. 449–457 (2017). https://doi.org/10.1007/978-3-319-46490-9_60
Korobiichuk, I., Ladanyuk, A., Shumyhai, D., Boyko, R., Reshetiuk, V., Kamiński, M.: How to increase efficiency of automatic control of complex plants by development and implementation of coordination control system. In: Recent Advances in Systems, Control and Information Technology. Advances in Intelligent Systems and Computing, vol. 543, pp. 189–195 (2017). https://doi.org/10.1007/978-3-319-48923-0_23
Korobiichuk, I., Lutskaya, N., Ladanyuk, A., Naku, S., Kachniarz, M., Nowicki, M., Szewczyk, R.: Synthesis of optimal robust regulator for food processing facilities. Advances in Intelligent Systems and Computing, vol. 550, pp. 58–66 (2017). https://doi.org/10.1007/978-3-319-54042-9_5
Baloev, A.A.: Synthesis of suboptimal control with incomplete measurement for systems with distributed parameters. Soviet Aeronautics (English translation of Izvestiya VUZ, Aviatsionnaya Tekhnika), vol. 27, no. 1, pp. 66–71 (1984)
Khamis, A., Subbaram Naidu, D.: Real-time algorithm for nonlinear systems with incomplete state information using finite-horizon optimal control technique. In: 7th International Symposium on Resilient Control Systems, ISRCS 2014, 6900094 (2014)
Lions, J.L.: Optimal control of systems described by partial differential equations, 414 p. Moskva, Mir (1972). (in Russian)
Ladyzhenskaya, O.A., Uraltseva, N.N., Solonnikov, V.A.: Linear and quasilinear equations of parabolic type, 736 p. Moskva, Nauka (1967). (in Russian)
Lobok, O.P., Goncharenko, B.M., Savitska, N.M.: Minimax control in linear systems of dynamic systems with distributed parameters. J. Naukovi pratsi NUHT 21(6), 16–26 (2015). (in Ukrainian)
Kirichenko, N.F.: Minimax control and estimation in dynamic systems. Autom. Remote Control 1, 32–39 (1982). (in Russian)
Lobok, O.P.: Minimax regulators in systems with distributed parameters. In: Modeling and Optimization of Complex Systems, no. 2, pp. 62–67 (1983). (in Russian)
Vasiliev, F.P.: Methods for solving extremal problems, 400 p. Moskva, Nauka (1981). (in Russian)
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Korobiichuk, I., Lobok, A., Goncharenko, B., Savitska, N., Sych, M., Vihrova, L. (2020). The Problem of the Optimal Strategy of Minimax Control by Objects with Distributed Parameters. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2019. AUTOMATION 2019. Advances in Intelligent Systems and Computing, vol 920. Springer, Cham. https://doi.org/10.1007/978-3-030-13273-6_8
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DOI: https://doi.org/10.1007/978-3-030-13273-6_8
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