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Application of the perturbation method for the minimization of an integral quadratic functional on the trajectories of a quasilinear system

  • Optimal Control
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Abstract

The problem of optimization of the transient process in a quasilinear system containing a small parameter multiplying the nonlinearities is considered. This problem is to find a feasible control with the minimal value of the integral quadratic performance index. Asymptotic approximations to the optimal open-loop control and optimal feedback are constructed. Computations are reduced to the solution of the undisturbed linear-quadratic problem, integration of systems of linear differential equations, and solving linear algebraic systems of equations.

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References

  1. N. N. Krasovskii, Theory of Control of Motion (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  2. Yu. N. Kiselev, “Asymptotic solution of the time-optimal control problem for almost linear systems,” Dokl. Akad. Nauk SSSR 182(1) (1968).

    Google Scholar 

  3. P. L. Falb and J. L. Jong, Some Successive Approximation Methods on Control and Oscillation Theory (Academic, New York, 1969).

    Google Scholar 

  4. F. L. Chernous’ko, L. D., Akulenko, and B. N. Sokolov, Control of Oscillations (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  5. L. D. Akulenko, Asymptotic Methods in Optimal Control (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  6. A. I. Kalinin, Asymptotic Methods for Optimization of Disturbed Dynamical Systems (Ekoperspektiva, Minsk, 2000) [in Russian].

    Google Scholar 

  7. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Interscience, New York, 1962; Gordon and Breach, New York, 1986).

    MATH  Google Scholar 

  8. P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964; Mir, Moscow, 1970).

    MATH  Google Scholar 

  9. B. Sh. Mordukhovich, “Existence of Optimal Controls,” in Itogi Nauki I Tekhniki. Sovremennye Problemy Matematiki (1976), Vol. 6.

    Google Scholar 

  10. R. Gabasov and F. M. Kirillova, Constructive Optimization Methods. Part 2. Control Problems (Universitetskoe, Minsk, 1984) [in Russian].

    MATH  Google Scholar 

  11. M. Athans and P. Falb, Optimal Control: An Introduction to the Theory and Its Applications (McGraw-Hill, New York, 1966; Mashinostroenie, Moscow, 1968).

    Google Scholar 

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Authors and Affiliations

  1. Belarussian State University, Minsk, Belarus

    A. I. Kalinin & L. I. Lavrinovich

Authors
  1. A. I. Kalinin
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  2. L. I. Lavrinovich
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Correspondence to A. I. Kalinin.

Additional information

Original Russian Text © A.I. Kalinin, L.I. Lavrinovich, 2014, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2014, No. 2, pp. 3–12.

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Kalinin, A.I., Lavrinovich, L.I. Application of the perturbation method for the minimization of an integral quadratic functional on the trajectories of a quasilinear system. J. Comput. Syst. Sci. Int. 53, 149–158 (2014). https://doi.org/10.1134/S1064230714020117

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  • DOI: https://doi.org/10.1134/S1064230714020117

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