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Optimality Conditions for a Degenerate Problem of Analytical Design of Controllers

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Abstract

A degenerate problem of analytical design of optimal controllers is studied. For a nonlinear object and nonclassical functional with affine controls, necessary and sufficient conditions of local optimality are formulated. These conditions are useful in identifying a class of objects with singularities in minimizing the generalized work functional. An example is given.

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REFERENCES

  1. Kolmanovskii, V.B. and Miller, B.M., Modern Problems in Control Theory and Their Applications (Singular Solutions and Perturbations in Control Systems), Avtom. Telemekh., 1997, no. 7, p. 3.

  2. Gurman, V.I., Vyrozhdennye zadachi optimal'nogo upravleniya (Degenerate Optimal Control Problems), Moscow: Nauka, 1977.

    Google Scholar 

  3. Gabasov, R. and Kirillova, F.M., Osobye optimal'nye upravleniya (Singular Optimal Controls), Moscow: Nauka, 1973.

    Google Scholar 

  4. Miller, B.M., The Generalized Solutions of Nonlinear Optimization Problems with Impulse Control, SIAM J. Control Optimiz., 1996, no. 34, pp. 1420-1440.

  5. Dykhta, V.A., Optimality Conditions for Impulsive Processes and Its Applications, in Preprints 13 IFAC World Congress, Vol. D: Control Design II, Optimization, 1996, pp. 345-350.

  6. Pavlidis, T., Optimal Control of Pulse Frequency Modulated Systems, IEEE Trans. Autom. Control, 1966, vol. 11, no. 4, pp. 676-684.

    Google Scholar 

  7. Spavochnik po teorii avtomaticheskogo upravleniya (Automatic Control Theory: A Reference Guide), Krasovskii, A.A., Ed., Moscow: Nauka, 1987.

    Google Scholar 

  8. Bukov, V.N., Adaptivnye prognoziruyushchie sistemy upravleniya poletom (Adaptive Flight Control Prediction Systems), Moscow: Nauka, 1987.

    Google Scholar 

  9. Krasovskii, A.A., Nonclassical Objective Functionals and Problems in Optimal Control Theory: A Review, Izv. Akad. Nauk SSSR. Tekh. Kibern., 1992, no. 1, pp. 3-41.

  10. Bukov, V.N. and Sizykh, V.N., Approximate Optimal Control Design in Degenerate Problems of Analytical Design of Controllers, Avtom. Telemekh., 1999, no. 12, pp. 16-32.

  11. Gurman, V.I., Dykhta, V.A., and Kolokol'nikova, G.A., Nelokal'nye preobrazovaniya vyrozhdennykh zadach optimal'nogo upravleniya i impul'snye rezhimy (Nonlocal Transformations of Degenerate Optimal Control Problems and Pulse Modes), Irkutsk: Vychisl. Tsentr SO Akad. Nauk SSSR, 1990.

    Google Scholar 

  12. Jacobson, D.H., Totally Singular Quadratic Minimization Problems, IEEE Trans. Autom. Control, 1971, vol. 16, no. 6, pp. 651-658.

    Google Scholar 

  13. Moylan, P.J. and Moore, J.B., Generalizations of Singular Optimal Control, Automatica, 1971, vol. 7, no. 5, pp. 591-598.

    Google Scholar 

  14. Khutortsev, V.V., Design of an Optimal Control for Semidefinite Quality Functionals with Nonadditive Control Cost Functions, Avtom. Telemekh., 1998, no. 8, pp. 63-70.

  15. Moskalenko, A.I., Optimal'noe upravlenie modelyami ekonomicheskoi dinamiki (Optimal Control for Models of Economic Dynamics), Novosibirsk: Nauka, 1999.

    Google Scholar 

  16. Afanas'ev, V.N., Kolmanovskii, V.B., and Nosov, V.R., Matematicheskaya teoriya konstruirovaniya sistem upravleniya (Mathematical Theory of Control System Design), Moscow: Vysshaya Shkola, 1998.

    Google Scholar 

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Authors and Affiliations

  1. Military Aviation Technical University, Moscow, Russia

    V. N. Bukov

  2. Military Aviation Engineering Institute, Irkutsk, Russia

    V. N. Sizykh

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  1. V. N. Bukov
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  2. V. N. Sizykh
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Bukov, V.N., Sizykh, V.N. Optimality Conditions for a Degenerate Problem of Analytical Design of Controllers. Automation and Remote Control 62, 1078–1087 (2001). https://doi.org/10.1023/A:1010253725989

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