Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem
https://doi.org/10.18255/1818-1015-2015-1-85-104
Abstract
This paper is devoted to the construction of a zero-order approximation of the solution of a three-time scale singular perturbed linear-quadratic optimal control problem with the help of the direct scheme method. The algorithm of the method consists in immediate substituting a postulated asymptotic expansion of solution into the problem condition and constructing a family of control problems to define the terms of the asymptotic expansion. Asymptotic approximation of the solution contains regular functions and four boundary ones of exponential type which are determined from the five linearquadratic optimal control problems. It is shown, that the system of equations for a zero-order approximation appeared from control optimality conditions of the initial perturbed problem corresponds to control optimality conditions appeared in respective five optimal control problems constructed for finding zero-order asymptotic approximation with the help of the direct scheme method. An illustrative example is given.
About the Author
M. A. Kalashnikova
Voronezh State University
Russian Federation
Russian Federation
аспирант кафедры математического анализа,
Universitetskaya pl., 1, Voronezh, 394006, Russia
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Review
For citations:
Kalashnikova M.A. Zero-order Approximation of Three-time Scale Singular Linear-quadratic Optimal Control Problem. Modeling and Analysis of Information Systems. 2015;22(1):85-104. (In Russ.) https://doi.org/10.18255/1818-1015-2015-1-85-104
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