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Automation and Remote Control

, Volume 77, Issue 7, pp 1163–1179 | Cite as

Quasi-optimal control of dynamic systems

  • V. M. AleksandrovEmail author
Nonlinear Systems
  • 43 Downloads

Abstract

For linear systems under bounded control, consideration was given to a pair of methods for approximate solution of the speed problem. Independence of the initial conditions for the switching moments of the quasi-optimal control and their constancy for systems with constant parameters were proved. A domain of initial conditions where the control constraints are not violated was determined. The properties and distinctions of the quasi-optimal control were established. A way to approximate a quasi-optimal control to the optimal one was considered, and the closeness estimate was given.

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References

  1. 1.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1976.Google Scholar
  2. 2.
    Fedorenko, R.P., Priblizhennoe reshenie zadach optimal’nogo upravleniya (Approximate Solution of the Optimal Control Problem), Moscow: Nauka, 1976.zbMATHGoogle Scholar
  3. 3.
    Lyubushin, A.A., On Using Modifications of the Method of Successive Approximations to Solve the Problem of Optimal Control, Zh. Vychisl. Mat. Mat. Fiz., 1982, vol. 22, no. 1, pp. 30–35.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Grachev, N.I. and Evtushenko, Yu.G., Library of Programs to Solve the Optimal Control Problems, Zh. Vychisl. Mat. Mat. Fiz., 1979, vol. 19, no. 2, pp. 367–387.MathSciNetGoogle Scholar
  5. 5.
    Srochko, V.A., Iteratsionnye metody resheniya zadach optimal’nogo upravleniya (Iterative Methods to Solve Optimal Control Problems), Moscow: Fizmatlit, 2000.Google Scholar
  6. 6.
    Osipov, Yu.S., Program Packages: An Approach to Solution of the Problems of Positional Control with Incomplete Information, Usp. Mat. Nauk, 2006, vol. 61, no. 4, pp. 25–76.CrossRefGoogle Scholar
  7. 7.
    Aleksandrov, V.M., A Numerical Method of Solving the Linear Speed Problem, Zh. Vychisl. Mat. Mat. Fiz., 1998, vol. 38, no. 6, pp. 918–931.MathSciNetGoogle Scholar
  8. 8.
    Shevchenko, G.V., Problem of Minimizing Convex Functional for the Linear System of Differential Delay Equations with Fixed Ends, Zh. Vychisl. Mat. Mat. Fiz., 2013, vol. 53, no. 6, pp. 867–877.MathSciNetzbMATHGoogle Scholar
  9. 9.
    Aleksandrov, V.M., Computation of the Real Time Optimal Control, Zh. Vychisl. Mat. Mat. Fiz., 2012, vol. 52, no. 10, pp. 1778–1800.MathSciNetzbMATHGoogle Scholar
  10. 10.
    Aleksandrov, V.M., Definition of the Initial Approximation and the Method to Calculate the Optimal Control, Sib. Elektron. Mat. Izv., 2014, vol. 11, pp. 87–118, http://semrmathnscru/v11/p87-118pdf.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsSiberian Branch of Russian Academy of SciencesNovosibirskRussia

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