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On Technical Controllability and Decomposition of the Lagrangian Systems with Bounded Controls

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Abstract

Consideration was given to control of the plant obeying the second-order Lagrange equations. Stringent requirements on the dynamic characteristics of motion under bounded control actions were placed on the control system of this plant. The notions of technical controllability of the closed-loop system and autonomous technical controllability of the plant were defined. The conditions for autonomous technical controllability of the plant were established and used to prove that the mathematical model of plant motion can be decomposed into individual subsystems. The decomposable mathematical model underlies a control algorithm providing technical controllability of the closed-loop system in terms of the given set of technical requirements.

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REFERENCES

  1. Pyatnitskii, E.S., Controllability of Classes of Lagrangian Systems with Bounded Controls, Avtom.Telemekh., 1996, no. 12, pp. 29–37.

  2. Kulakov, F.M., Supervizornoe upravlenie manipulyatsionnymi robotami (Supervisory Control of Manipulation Robots), Moscow: Nauka, 1980.

    Google Scholar 

  3. Pyatnitskii, E.S., Decomposition Principle in Control of Mechanical Systems, Dokl.Ross.Akad.Nauk, 1988, vol. 300, no. 2, pp. 300–303.

    Google Scholar 

  4. Chernous'ko, F.L., Decomposition and Suboptimal Control in Dynamic Systems, Prikl.Mat.Mekh., 1990, vol. 54, no. 6, pp. 883–893.

    Google Scholar 

  5. Matyukhin, V.I., Universal'nye zakony upravleniya mekhanicheskimi sistemami (Universal Control Laws for Mechanical Systems), Moscow: MAKS Press, 2001.

    Google Scholar 

  6. Anan'evskii, I.M., Two Approaches to Control of a Mechanical System with Unknown Parameters, Izv.Ross.Akad.Nauk, Teor.Sist.Upravlen., 2001, no. 2, pp. 39–47.

  7. Pyatnitskii, E.S., Control of Mechanical Black Box, Avtom.Telemekh., 1999, no. 3, pp. 202–212.

  8. Raushenbakh, B.V. and Tokar', E.N., Upravlenie orientatsiei kosmicheskikh apparatov (Control of Spacecraft Orientation), Moscow: Nauka, 1974.

    Google Scholar 

  9. Shevyakov, A.A., Mart'yanova, T.S., Rutkovskii, V.Yu., et al., Optimizatsiya mnogomernykh sistem upravleniya gazoturbinnykh dvigatelei letatel'nykh apparatov (Optimization of Multidimensional Control Systems of Turbine Engines of Flight Vehicles), Moscow: Mashinostroenie, 1989.

    Google Scholar 

  10. Spravochnik po teorii avtomaticheskogo upravleniya (Handbook on the Theory of Automatic Control), Krasovskii, A.A., Ed., Moscow: Nauka, 1987.

    Google Scholar 

  11. Bogomolov, V.P., Rutkovskii, V.Yu., and Sukhanov V.M., Design of the Optimal Mechanical Structure of Free-Flyer as a Controlled Plant. I, II, Avtom.Telemekh., 1998, no. 5, pp. 27–40, no. 6, pp. 75–88.

  12. Zemlyakov, S.D. and Rutkovskii, V.Yu., On a Case of Monotone and Speed-reliable Control of Nonlinear Multivariable Plant, Dokl.Ross.Akad.Nauk, 2002, vol. 383, no. 6, pp. 750–753.

    Google Scholar 

  13. Glumov, V.M., Zemlyakov, S.D., Rutkovskii, V.Yu., and Sukhanov, V.M., Technical Controllability of the Free-Flying Automated Space Module, Avtom.Telemekh., 2001, no. 3, pp. 31–44.

  14. Lur'e, A.I., Analiticheskaya mekhanika (Analytical Mechanics), Moscow: Fizmatgiz, 1961.

    Google Scholar 

  15. Voevodin, V.V. and Kuznetsov, Yu.A., Matritsy i vychisleniya (Matrices and Computations), Moscow: Nauka, 1984.

    Google Scholar 

  16. Voronov, A.A., Osnovy teorii avtomaticheskogo upravleniya (Fundamentals of the Theory of Automatic Control), Moscow: Energiya, 1965.

    Google Scholar 

  17. Gantmakher, F. R., Teoriya matrits (Theory ofMatrices), Moscow: Nauka, 1988. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.

    Google Scholar 

  18. Boltyanskii, V.G., Matematicheskie metody optimal'nogo upravleniya (MathematicalMethods of Optimal Control), Moscow: Nauka, 1969.

    Google Scholar 

  19. Emel'yanov, S.V., Sistemy avtomaticheskogo upravleniya s peremennoi strukturoi (Variable-Structure Automatic Control Systems), Moscow: Nauka, 1967.

    Google Scholar 

  20. Utkin, V.I., Skol'zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.

    Google Scholar 

  21. Golub, G. and Van Loan, Ch., Matrix Computations, Baltimor: John Hopkins Univ. Press, 1989. Translated under the title Matrichnye vychisleniya, Moscow: Mir, 1999.

    Google Scholar 

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. M. Glumov, S. D. Zemlyakov, V. Yu. Rutkovskii & V. M. Sukhanov

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  1. V. M. Glumov
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  2. S. D. Zemlyakov
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  3. V. Yu. Rutkovskii
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  4. V. M. Sukhanov
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Glumov, V.M., Zemlyakov, S.D., Rutkovskii, V.Y. et al. On Technical Controllability and Decomposition of the Lagrangian Systems with Bounded Controls. Automation and Remote Control 63, 1546–1564 (2002). https://doi.org/10.1023/A:1020440527734

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