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Asymptotic solution of a boundary-value problem for linear singularly-perturbed functional differential equations arising in optimal control theory. (English) Zbl 1001.49036
Summary: 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.
MSC:
49N10Linear-quadratic optimal control problems
35B37PDE in connection with control problems (MSC2000)
35R10Partial functional-differential equations
93C70Time-scale analysis and singular perturbations