Geodesic
On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 1, pp. 93-116

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The paper deals with a formalism of constructing a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients. This formalism is based on immediate substituting a postulated asymptotic expansion of boundary layer type for the solution into the problem condition and on defining four optimal control problems for finding asymptotics terms. The unique solvability of the problems, the solutions of which form the zero order approximation for the asymptotic solution, is proven. An illustrative example is given.
Keywords: linear-quadratic optimal control problem, discontinuous coefficients, asymptotic expansion.
Mots-clés : singular perturbations 
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     author = {G. A. Kurina and Nguy\^en Thi Ho\`ai},
     title = {On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients},
     journal = {Modelirovanie i analiz informacionnyh sistem},
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     url = {http://geodesic.mathdoc.fr/item/MAIS_2010_17_1_a7/}
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G. A. Kurina; Nguyên Thi Hoài. On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 1, pp. 93-116. http://geodesic.mathdoc.fr/item/MAIS_2010_17_1_a7/