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Asymptotics of the Solution to the Minimization Problem of the Integral Quadratic Performance Index on Trajectories of a Quasi-Linear System

  • OPTIMAL CONTROL
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Abstract

The problem of minimizing an integral quadratic performance index on the trajectories of a quasi-linear dynamic system with a small parameter multiplying the nonlinearities subject to terminal constraints is considered. Asymptotic approximations of the optimal control in this problem in the form of open loop control and feedback are constructed. The computations are reduced to solving the unperturbed linear-quadratic problem, integrating systems of linear differential equations, and finding the roots of nonsingular linear algebraic systems.

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REFERENCES

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

    Google Scholar 

  2. Yu. N. Kiselev, “Asymptotic solution of the optimal performance problem for control systems close to linear,” Dokl. Akad. Nauk SSSR 182, 31–34 (1968).

    MathSciNet  Google Scholar 

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

    MATH  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. A. I. Kalinin, “Asymptotics of solutions of perturbed optimal control problems,” Izv. Akad. Nauk, Tekhn. Kibernet., No. 3, 104–114 (1994).

  6. A. I. Kalinin, Asymptotic Optimization Methods for Perturbed 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; Pergamon, Oxford, New York, 1964).

  8. A. I. Kalinin and L. I. Lavrinovich, “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 (2014).

    Article  MathSciNet  Google Scholar 

  9. R. Gabasov and F. M. Kirillova, Qualitative Theory of Optimal Processes (Nauka, Moscow, 1971) [in Russian].

    MATH  Google Scholar 

  10. A. I. Kalinin, “To the synthesis of optimal control systems,” Comput. Math. Math. Phys. 58, 378 (2018).

    Article  MathSciNet  Google Scholar 

  11. B. Sh. Mordukhovich, “The existence of optimal controls,” Itogi Nauki Tekh., Ser.: Sovrem. Probl. Mat. 6 (1976).

  12. Ph. Hartman, Ordinary Differential Equations (Soc. Ind. Appl. Math., Philadelphia, 1987).

    MATH  Google Scholar 

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

    MATH  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 or L. I. Lavrinovich.

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Translated by A. Klimontovich

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Kalinin, A.I., Lavrinovich, L.I. Asymptotics of the Solution to the Minimization Problem of the Integral Quadratic Performance Index on Trajectories of a Quasi-Linear System. J. Comput. Syst. Sci. Int. 58, 695–706 (2019). https://doi.org/10.1134/S1064230719050058

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  • DOI: https://doi.org/10.1134/S1064230719050058

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