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Analytical Synthesis of an Amplitude-Constrained Controller

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Abstract

We consider a time-invariant optimal control problem of a new linear-quadratic type on the positive time axis with an amplitude constraint on the control. Using sufficient optimality conditions, we find an optimal positional control with a discontinuity on a subspace of the state space. The motion of the closed-loop system on the subspace in the sliding mode is investigated. The exponential stability of the closed-loop system is shown. Examples are given.

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REFERENCES

  1. Letov, A.M., Analytical controller synthesis: I, Avtom. Telemekh., 1960, no. 4, pp. 436–441.

  2. Kálmán R., On the general theory of control systems, in Tr. 1-go Mezhdunar. kongressa IFAK (Proc. 1st Int. IFAC Congr.), Moscow: Akad. Nauk SSSR, 1961. vol. 1. pp. 521–547.

  3. Letov, A.M., Analytical controller synthesis. Further problem development: V, Avtom. Telemekh., 1962, no. 11, pp. 1405–1413.

  4. Fuller, A.T., Optimization of linear control systems according to various quality criteria, in Tr. 1-go Mezhdunar. kongressa IFAK (Proc. 1st Int. IFAC Congr.), Moscow: Akad. Nauk SSSR, 1961, vol. 1, pp. 584–605.

  5. Gabasov, R., Kirillova, F.M., and Pavlenok, N.S., Constructing open-loop and closed-loop solutions of linear-quadratic optimal control problems, Comput. Math. Math. Phys., 2008, vol. 48, no. 10, pp. 1748–1779.

  6. Srochko, V.A., Iteratsionnye metody resheniya zadach optimal’nogo upravleniya (Iterative methods for solving optimal control problems), Moscow: Fizmatlit, 2000.

    Google Scholar 

  7. Antipin, A.S. and Khoroshilova, E.V., On a boundary value problem of terminal control with a quadratic performance criterion, Izv. Irkutsk. Gos. Univ., 2014, vol. 8, pp. 7–28.

    MATH  Google Scholar 

  8. Krotov, V.F., Bukreev, V.Z., and Gurman, V.I., Novye metody variatsionnogo ischisleniya v dinamike poleta (New Methods of Calculus of Variations in Flight Dynamics), Moscow: Mashinostroenie, 1969.

    Google Scholar 

  9. Utkin, V.I., Variable structure systems: research status and promise, Autom. Remote Control, 1983, vol. 44, no. 9, pp. 1105–1120.

    MATH  Google Scholar 

  10. Paraev, Yu.I., Uravneniya Lyapunova i Rikkati (Lyapunov and Riccati Equations), Tomsk: Tomsk. Univ., 1989.

    MATH  Google Scholar 

  11. Polyak, B.T., Vvedenie v optimizatsiyu (Introduction to Optimization), Moscow: Nauka, 1983.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Far Eastern Federal University, Vladivostok, 690090, Russia

    L. T. Ashchepkov

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  1. L. T. Ashchepkov
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Correspondence to L. T. Ashchepkov.

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Translated by V. Potapchouck

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Ashchepkov, L.T. Analytical Synthesis of an Amplitude-Constrained Controller. Autom Remote Control 83, 1050–1058 (2022). https://doi.org/10.1134/S0005117922070037

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