ASYMPTOTIC APPROXIMATION TO A SOLUTION OF A SINGULARLY PERTURBED LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEM WITH SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION OF STATE VARIABLE

摘要

The direct scheme method is applied to construct an asymptotic approximation of any order to a solution of a singularly perturbed optimal problem with scalar state, controlled via a second-order linear ODE and two fixed end points. The error estimates for state and control variables and for the functional are obtained. An illustrative example is given.