Trigonometric approximation of smooth optimal periodic control problems

Abstract

Trigonometric polynomials and penalty functions are used to approximate the constrained optimal periodic control problem for a system described by differential equations. The optimal control is assumed to be a smooth periodic function, i.e. it is continuously differentiate at least once. Sufficient conditions for the convergence of solutions of approximating problems to the optimal solution of the basic problem are given and the convergence rate is estimated. The particular usefulness of the approximation considered for singular optimal controls, which arise in chemical engineering, is emphasized.