Abstract
Asymptotic estimates are given for processes of terminal control with respect to a small parameter at a higher derivative of control processes. The problem given is connected to the problem of “turning point,”which does not allow the application of general methods of asymptotic expansions of solutions of differential equations. To solve the problem, special analytic methods and the asymptotic Laplace method are used.
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A. T. Barabanov, V. G. Kozyrev, and A. T. Chalaya, Analytic Theory of Processes in Electric Chains with a Disconnecting Arc [in Russian], Priborostroienie,23, 36–40 (1977).
M. A. Lavrentev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1965).
Methods of Study of Nonlinear Systems of Automatic Regulations [in Russian], Nauka, Moscow (1975).
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Translated from Dinamicheskie Sistemy, No. 7, pp. 84–89, 1988.
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Barabanov, A.T., Kozyrev, V.G. Asymptotic approximations of processes in systems of terminal control with singular perturbations. J Math Sci 65, 1555–1558 (1993). https://doi.org/10.1007/BF01097663
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DOI: https://doi.org/10.1007/BF01097663