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Suboptimal control of logical-dynamic systems under parametric uncertainty conditions

  • Control of Systems
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Abstract

Sufficient optimality conditions of logical-dynamic systems are obtained, the logical portion of which models the operation of a memory-equipped automaton. Equations are derived for the definition of the optimal programmed control and full feedback control. Optimal processes with multiple switchings of the logical (automaton) portion at fixed instants of time are investigated. On the basis of sufficient conditions, algorithms are suggested for the development of the suboptimal control of logical-dynamic systems under parametric uncertainty conditions. The use of optimality and suboptimality conditions is illustrated by examples.

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References

  1. Semenov, V.V., Dynamic Programming in Synthesis of Logical-Dynamic Systems, Priborostroenie, 1984, no. 9, pp. 71–77.

  2. Bortakovskii, A.S., Sufficient Conditions of Optimality of the Automaton Portion of the Logical-Dynamic System, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2006, no. 6, pp. 77–92.

  3. Panteleev, A.V. and Bortakovskii, A.S., Teoriya upravleniya v primerakh i zadachakh (Theory of Control in Examples and Problems), Moscow: Vysshaya Shkola, 2003.

    Google Scholar 

  4. Vasil’ev, S.N., Zherlov, A.K., Fedosov, E.A., et al., Intellektnoe upravlenie dinamicheskimi sistemami (Intellectual Control of Dynamic Systems), Moscow: Fizmatlit, 2000.

    Google Scholar 

  5. IFAC Workshop: Modelling and Analysis of Logic Controlled Dynamic Systems, Irkutsk, 2003.

  6. Hybrid Systems, Grossman, R.L., Nerode, A., Ravn, A.P., and Rischel, H., Eds., Berlin: Springer-Verlag, 1993, vol. 736.

    Google Scholar 

  7. Hybrid Systems, Alur, A., Henzinger, T.A., and Sontag, E.D., Eds., Berlin: Springer-Verlag, 1996.

    Google Scholar 

  8. Hybrid Systems, Ahtsaklis, P., Kohn, W., Lemmon, M., Nerode, A., and Sastry, S., Eds., Berlin: Springer-Verlag, 1998.

    Google Scholar 

  9. Matveev, A.S., Qualitative Theory of Hybrid Dynamical Systems, New York: Springer, 2000.

    MATH  Google Scholar 

  10. Cassandras, C.G., Peryne, D.L., and Wardi, Y., Optimal Control of a Class of Hybrid Systems, IEEE Trans. Automat. Control, 2001, vol. 46, no. 3, pp. 398–415.

    Article  MATH  MathSciNet  Google Scholar 

  11. Savkin, A.V. and Evans, R.J., Hybrid Dynamical Systems: Controller and Sensor Switching Problems, New York: Springer, 2003.

    Google Scholar 

  12. Krotov, V.F. and Gurman, V.I., Motody i zadachi optimal’nogo upravleniya (Methods and Problems of Optimal Control), Moscow: Nauka, 1973.

    Google Scholar 

  13. Liberson, D. and Morse, A.S., Basic Problems in Stability and Switched Systems, IEEE Control Syst. Magaz., 1999, vol. 19, no. 5, pp. 59–70.

    Article  Google Scholar 

  14. Miller, B.M. and Rubinovich, E.Ya., Impulsive Control in Continuous and Discrete-continuous Systems, New York: Kluwer, 2003.

    MATH  Google Scholar 

  15. Li, Z., Soh, Y., and Wen, C., Switched and Impulsive Systems: Analysis, Design and Applications, New York: Springer, 2005.

    MATH  Google Scholar 

  16. Bortakovskii, A.S. and Panteleev, A.V., Sufficient Optimality Conditions of Control of Continuously Discrete Systems, Avtom. Telemekh., 1987, no. 7, pp. 57–66.

  17. Bortakovskii, A.S. and Pegachkova, E.A., Optimal Control of Linear Logical-Dynamic Systems with the Quadratic Quality Criterion, in Theoreticheskie voprosy vychislitel’noi tekhniki i programmnogo obespecheniya (Theoretical Problems of Computer Engineering and Software), Moscow: Mosk. Inst. Radiotekhn. Elektron. Avtom., 2006, pp. 56–61.

    Google Scholar 

  18. Letov, A.M., Dinamika poleta i upravlenie (Dynamics of Flight and Control), Moscow: Nauka, 1973.

    Google Scholar 

  19. Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Uncertainty Conditions), Moscow: Nauka, 1977.

    Google Scholar 

  20. Ovsyannikov, D.A., Matematicheskie metody upravleniya puchkami (Mathematical Methods of Control of Bundles), Leningrad: Leningr. Univ., 1980.

    Google Scholar 

  21. Bortakovskii, A.S., Control of Determinate Systems under Uncertainty Conditions at Optimality of Effective Controls, in Upravlenie i navigatsiya LA v usloviyakh parametricheskoi neopredelennosti (Control and Navigation of Flying Vehicles under Parametric Uncertainty Conditions), Moscow: Mosk. Aviats. Inst., 1991.

    Google Scholar 

  22. Dem’yanov, V.F. and Rubin, A.M., Osnovy negladkogo analiza i kvazidifferentsial’noe ischislenie (Bases of Rough Analysis and Quasidifferential Calculus), Moscow: Nauka, 1990.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow State Aviation Institute, Moscow, Russia

    A. S. Bortakovskii

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  1. A. S. Bortakovskii
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Original Russian Text © A.S. Bortakovskii, 2007, published in Avtomatika i Telemekhanika, 2007, No. 11, pp. 105–121.

This work was supported by the Russian Foundation for Basic Research, projects nos. 05-01-00458 and 06-08-00882.

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Bortakovskii, A.S. Suboptimal control of logical-dynamic systems under parametric uncertainty conditions. Autom Remote Control 68, 1986–2001 (2007). https://doi.org/10.1134/S0005117907110082

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  • DOI: https://doi.org/10.1134/S0005117907110082

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