Synthesis of Optimal Control of a Group of Objects of Variable Dimension



The article deals with the problem of time-optimal control of a hybrid system of variable dimension. The problem of synthesis of optimal hybrid systems of variable dimension is of theoretical interest, since the problems under consideration differ from the classical problems of optimal control of deterministic systems, and methods for their solution have not been developed. The need for research is determined by modern problems of designing complex aviation and rocket and space systems, and the results obtained have a practical orientation and can be used in the creation of automatic control systems.

General Information

Keywords: hybrid systems of variable dimension, optimal control, switch systems, time-optimal operation

Journal rubric: Control Theory

Article type: scientific article


For citation: Bortakovskii A.S., Evdokimova E.A. Synthesis of Optimal Control of a Group of Objects of Variable Dimension. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2021. Vol. 11, no. 4, pp. 21–32. DOI: 10.17759/mda.2021110402. (In Russ., аbstr. in Engl.)


  1. Agrachev A.A., Sachkov U.L. Geometric control theory. Moscow: Physmathlit, 2005. 392 p.
  2. Bellman R. Dynamic programmimg. Moscow: Foreign literature, 1960. 400 p.
  3. Bortakovskii A.S. Sufficient optimality conditions for hybrid systems of variable dimension // Works of MIAN 308, 2020, P.88–100.
  4. Bortakovskii A.S., Evdokimova E.A. Synthesis of optimal hybrid systems for multipurpose time-optimal operation // Problems of mathematical analysis, ed. 109, 2021. P. 39–50.
  5. Mathematical theory of optimal processes / L.S. Pontryagin [and others] Moscow: Fizmatgiz, 1961. 393 p.
  6. Dmitruk A.V., Kaganovich A.M. The hybrid maximum principle is a consequence of Pontryagin maximum principle , Syst. Control Lett. 57, No. 11. P. 964–970 (2008).
  7. Sussmann H.J. A maximum principle for hybrid optimal control problems // Proc. of 38th IEEE Conference on Decision and Control, Phoenix, 1999.

Information About the Authors

Alexandr S. Bortakovskii, Doctor of Physics and Matematics, Associate Professor of the Department of Mathematics and Cybernetics, Institute of Information Technologies and Applied Mathematics, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID:, e-mail:

Ekaterina A. Evdokimova, 1st Category Mathematician, Federal Research Center «Informatics and Management», Russian Academy of Sciences (IPI RAS), Moscow, Russia, ORCID:, e-mail:



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