Asymptotic Solution of a Boundary-Value Problem for Linear Singularly-Perturbed Functional Differential Equations Arising in Optimal Control Theory

Author： Glizer V.Y.  

Publisher： Springer Publishing Company

ISSN： 0022-3239

Source： Journal of Optimization Theory and Applications, Vol.106, Iss.2, 2000-08, pp. : 309-335

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Abstract

The Hamiltonian boundary-value problem, associated with a singularly-perturbed linear-quadratic optimal control problem with delay in the state variables, is considered. A formal asymptotic solution of this boundary-value problem is constructed by application of the boundary function method. The justification of this asymptotic solution is done. The asymptotic solution of the Hamiltonian boundary-value problem is constructed and justified assuming boundary-layer stabilizability and detectability.

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