This book addresses the controllability problems of composite linear dynamic systems and systems with multipoint intermediate conditions. It investigates the motion of controlled composite systems and constructs an explicit form of the motion for controlled composite linear systems. Particular attention is devoted to the necessary and sufficient conditions for complete controllability and observability of composite linear systems, which, in the stationary case, are comparable in completeness to the Kalman conditions. The qualitative properties of controllability and observability of composite systems, as well as of the controllability of composite systems using a dynamic controller, are explored. Constructive methods are proposed for solving control problems of composite systems, systems with non-separated multipoint intermediate conditions, and systems with constraints on the values of different parts of the phase vector coordinates at intermediate times. Explicit solutions to control problems, optimal control, and stabilization are constructed as applications to specific problems in composite systems and dynamic systems with multipoint intermediate conditions. The mathematical models of these systems are described by both ordinary differential equations and partial differential equations.

The volume is intended for a broad range of specialists in applied mathematics and theoretical mechanics working in control and observation theory, mathematical modeling, systems analysis, and their applications, as well as for graduate and undergraduate students specializing in these fields.

Vanya Rafaelovich Barseghyan, Doctor of Physical and Mathematical Sciences, Professor, Leading Researcher at the Institute of Mechanics of the National Academy of Sciences of the Republic of Armenia, Professor at the Department of Mechanics of Yerevan State University. He is the author of about 200 scientific works, 6 educational and methodological manuals, and the monograph “Control of composite dynamic systems and systems with multipoint intermediate conditions” (Moscow, Russia: Nauka Publ., 2016). V.R. Barseghyan is a laureate of the President of the Republic of Armenia Award (2012).

Svetlana Vitalievna Solodusha, Doctor of Technical Sciences, Associate Professor, Chief Researcher at the Melentiev Energy Systems Institute of the Siberian Branch of the Russian Academy of Sciences. She is the author of more than 150 scientific works, organizer of the conference on unstable problems in computational mathematics, and guest editor of the journal Mathematics (MDPI).