Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Review of Modern Methods and Technologies for Delayed Dynamical System D.A. GAVRILOV, A.YU. GORNOV, E.A. TATARINOVA, V.E. BUZDIN, O.A. POTKIN The article presents the results of a review of modern methods and technologies of control in the presence of delays (delay) in a dynamic system. A distinctive feature for systems with a deviating argument is that the state at each moment of time is understood as an element of a functional infinite space. A distinctive feature for ordinary systems of differential features is that it is a finite-dimensional vector. Research ideological foundations of the scientifi c direction, fundamental results are analyzed. Theoretical formulations of problems are excluded, the analysis of the geography of the use of works, the temporary division of annotated works, practical approaches to solving problems, the structure of the main tasks are carried out. Attention is paid to the study of systemic differential predilections with a deviating argument both in phase coordinates and in control ones conducted both in Russia and abroad. The search for solutions in modern formulations is complicated by large dimensions and the possible presence of interference and noise in the initial data, it is planned to search for control, stability from the trajectory of a dynamic system. The most common patterns of occurrence with deviating factors are linear systems with a delay in phase coordinates. Methods processing classical Pontryagin principles remain the most popular among the most popular approaches to their number. Keywords: Nonlinear Adaptive Control, Optimal Control Problem, Methodological And Algorithmic Support, Dynamic System With Delay. DOI: 10.25791/pribor.2.2023.1389 Pp. 44-51.