Approximate Synthesis of Optimal Deterministic Control Systems with Incomplete Feedback Based on Sufficient ε-Optimality Conditions

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Abstract

The problem of optimal control of deterministic dynamical systems in the absence of information about a part of the coordinates of the state vector is considered. Sufficient ε-optimality conditions based on the principle of expansion are formulated and proved. An algorithm is proposed for finding an a priori estimate of the proximity of the synthesized control law with incomplete feedback to the optimal one for a given set of initial states. The solution of the model example is given.

General Information

Keywords: sufficient optimality conditions, optimal synthesizing function, multi-agent algorithm, calculation of a priori estimation

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2024140109

Received: 01.03.2024

Accepted:

For citation: Panteleev A.V., Karane M.S. Approximate Synthesis of Optimal Deterministic Control Systems with Incomplete Feedback Based on Sufficient ε-Optimality Conditions. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2024. Vol. 14, no. 1, pp. 135–154. DOI: 10.17759/mda.2024140109. (In Russ., аbstr. in Engl.)

References

  1. Pontryagin L.S., Boltyansky V.G., Gamkrelidze R.V., Mishchenko E.F. Mathematical theory of optimal processes. M.: Nauka, 1983. (In Russ.).
  2. Fedorenko R.P. Approximate solution of optimal control problems. M.: Nauka, 1978. (In Russ.).
  3. Athans M., Falb P.L. Optimal Control: An Introduction to the Theory and Its Applications, Chelmsford, MA, USA: Courier Corporation, 2013.
  4. Gornov A.Yu. Computational technologies for solving optimal control problems. Novosibirsk: Nauka, 2009. (In Russ.).
  5. Srochko V.A. Iterative methods for solving optimal control problems. M. : Fizmatlit, 2000. (In Russ.).
  6. Dykhta V.A., Tyatyushkin A.I. Improvement methods in computational experiment. Novosibirsk: Nauka, 1988. (In Russ.).
  7. Kolmanovsky V.B., Nosov V.R. Approximate and numerical methods for solving problems of optical control. Moscow: MIEM, 1989. (In Russ.).
  8. Panteleev A.V., Karane M.M.S. Multi–agent and bio–inspired optimization methods for optimizing technical systems.– М.: Dobroe slovo & Co, 2024.– 336 p. (In Russ.).
  9. Krotov V.F., Gurman V.I. Methods and problems of optimal control. Moscow: Nauka, 1973. (In Russ.).
  10. Krotov V.F.Global methods in optimal control theory.  New York: Marcel Dekker, 1996.
  11. Gurman V.I. The principle of expansion in control problems. M.: Nauka, 1997. (In Russ.).
  12. Gurman V.I. Approximate synthesis of optimal control// Automation and Telemechanics, 1976. No.5. (In Russ.).
  13. Baturin V.A., Urbanovich D.E. Approximate methods of optimal control based on the principle of expansion. Novosibirsk : Nauka, 1997. (In Russ.).
  14. Weinstein S.E. Approximation of function of several variables // J. Approximation Theory. 1969. Vol. 2. P. 433–447.
  15. Panteleev A.V., Semenov V.V. Synthesis of optimal control systems with incomplete information. Moscow: MAI Publishing House, 1992. (In Russ.).
  16. Krotov V. F., Feldman N. N. Iterative method for solving optimal control problems // Izvestia of the USSR Academy of Sciences. Technical cybernetics. 1983. No. 2. pp. 160–168. (In Russ.).
  17. Khrustalev M.M. Necessary and sufficient conditions in the form of the Bellman equation // Reports of the USSR Academy of Sciences. 1978. Vol.242. No.5. pp. 1023–1026. (In Russ.).

Information About the Authors

Andrey V. Panteleev, Doctor of Physics and Matematics, Professor, Head of the Department of Mathematical Cybernetics, Institute of Information Technologies and Applied Mathematics, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0003-2493-3617, e-mail: avpanteleev@inbox.ru

Mary Magdalene S. Karane, Postgraduate Student of the Institute "Computer Science and Applied Mathematics", Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0002-8019-8613, e-mail: mmarselina@mail.ru

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