{"references": ["Pihnastyi O. M. Overview of models of controlled production processes of production line production lines / \u041e.M.Pihnastyi // Scientific bulletins of the Belgorod State University. Belgorod: BSU. - 2015. - No. 34/1. P.137-152. http://doi.org/10.5281/zenodo.2647598", "Pihnastyi O.M. Statistical theory of control systems of the flow production / O.M. Pihnastyi. \u2013LAP LAMBERT Academic Publishing. \u2013 2018. - 436 p. ISBN: 978-613-9-95512-1", "Malkin I.G. The theory of stability of motion / I.G. Malkin. - Moscow: Nauka, 1966 .- P. 531", "Pihnastyi O. M. Analysis of models of transition processes controlled manufacturing / O. M. Pihnastyi / Scientific Bulletins of the Belgorod State University. Belgorod: BSU. - 2015. - No. 35/1. - P. 133-144 https://doi.org/10.5281/zenodo.2595561", "Lyapunov A.M. General problem of motion stability / A.M. Lyapunov. - M .: Gostekhizdat, 1950 .-- P. 395", "Pihnastyi O. M. On the relationship between micro-and macro-description of production and technical systems / O.M. Pihnastyi, V. Zaruba // Management of large systems: proceedings of the International Scientific and Practical Conference (Moscow, November 17-19, 2009). - Moscow: IPU RAN, 2009.- P. 255-258. http://doi.org/10.5281/zenodo.4731141", "Sinitsa L.M. Organization of production. / L.M. Tit. - Minsk: UP IVC Minfin, 2003. \u2013C. 512", "Pihnastyi O.M. Analytical methods for designing technological trajectories of the object of labour in a phase space of states / O.M.Pihnastyi // Scientific bulletin of National Mining University. \u2013 Dnipro: State Higher Educational Institution \u00abNational Mining University\u00bb. \u20132017. n.4. P. 104\u2013111. http://nvngu.in.ua/index.php/en/component/jdownloads/viewdownload/69/8679", "Khodusov V.D. The use of physical kinetics methods for studying oscillations of the parameters of a production line / V.D. Khodusov, O.M. Pihnastyi // East european journal of physics. - 2014. - Vol. 1, Num. 4. - S. 88-95. http://nbuv.gov.ua/UJRN/eejph_2014_1_4_12", "Korobetsky Yu.P. Simulation models in flexible systems. / Yu.P. Korobetsky, S.K. Ramazanov. - Lugansk: Ed. VNU, 2003. - P. 280", "Kempf K. Optimization models for production planning. Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook. / K.Kempf, P.Keskinocak, R.Uzsoy \u2013Springer-Verlag, New York, 2010. \u2013 P. 587", "Pihnastyi O.M. To the question of similarity of technological processes of production and technical systems / NA Azarenkov, OM Pihnastiy, VD Khodusov // Reports of the National Academy of Sciences of Ukraine. -Kiev: Akademperiodika Publishing House. - 2011. \u2013\u21162\u2013P. 29-35. doi.org/10.13140/RG.2.2.13585.53600"]}

The problem of designing a system for optimal operational control of random deviations in the productivity of technological equipment is considered. To construct an algorithm for optimal control of the performance of technological equipment, a PDE model of a production flow line was used. The Lyapunov functions method was used to determine the value of the optimal control of the technological equipment performance. The production line is considered by a distributed dynamic system. Equations are written for the flow parameters of the production line in small perturbations. A criterion for the quality control of the performance of technological equipment of a production flow line has been introduced. Based on this criterion, the Lyapunov function is determined for the considered production system. Taking into account the form of the Lyapunov function, control actions are obtained that correct the performance of the technological equipment. The introduced control made it possible to ensure the synchronization of the productivity of the technological equipment of the production line and the asymptotic stability of the given planned state of the flow parameters of the production line for the steady and transient operation mode.