Аннотация:

We consider the optimal control problem with integral convex performance index for a linear system in the class of piecewise continuous controls with smooth geometric constraints on the control. Such problems are called cheap control problems. We study the case where the optimal control of the limit problem remains unchanged, whereas for the original problem there are two points at which the control form is changed. Using the auxiliary parameter method, we show that the solution may have expansion in the Poincare sense in any asymptotic sequence of rational functions of the small parameter or its logarithms.