Controlled dynamic systems and Carleman operator
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Controlled dynamic systems on a compact set and thus with invariant measure are considered. This allows reducing differential dynamic systems to Fredholm-type integral equations. An algorithm of constructing a vector field of maximum descent rate along a trajectory is presented. The algorithm is reduced to a numerical moment-type procedure.
Keywordsdynamic system compact set control stability Hilbert-Schmidt and Carleman operators measure
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- 1.V. I. Arnol’d, Ordinary Differential Equations [in Russian], Nauka, Moscow (1971).Google Scholar
- 4.P. R. Halmos and V. S. Sander, Bounded Integral Operators on L 2 Spaces, Springer-Verlag (1979).Google Scholar
- 5.N. N. Krasovskii, Problems of Stabilization of Controlled Motion, Supplement IV to the monograph I. G. Malkin, Theory of Motion Stability [in Russian], Nauka, Moscow (1966).Google Scholar
- 6.V. I. Zubov, Mathematical Methods for Analysis of Automatic Control Systems [in Russian], Mashinostroenie, Leningrad (1974).Google Scholar
- 7.N. N. Bogolyubov, Complete Works [in Russian], Vol. 2, Naukova Dumka, Kyiv (1976).Google Scholar
- 8.K. Moren, Methods in Hilbert Space [Russian translation], Mir, Moscow (1965).Google Scholar
- 10.V. I. Zubov, “Integral equations for the Lyapunov function,” Dokl. AN SSSR, 314, No. 4, 780–782 (1990).Google Scholar
- 11.I. G. Petrovskii, Lectures on the Theory of Integral Equations [in Russian], Nauka, Moscow (1965).Google Scholar
- 12.M. G. Krein and A. A. Nudel’man, Markov Moment Problem and Extremum Problems [in Russian], Nauka, Moscow (1978).Google Scholar