Trigonometric approximation of optimal periodic control problems for systems with inertial controllers

A constrained optimal periodic control (OPC) problem for nonlinear systems with inertial controllers is considered. A sequence of approximate problems containing trigonometric polynomials for approximation of the state, control, and functions in the state equations and in the optimality criterion is formulated. Sufficient conditions for a sequence of nearly optimal solutions of approximate problems to be norm-convergent to the basic problem optimal solution are derived. It is pointed out that the direct approximation approach in the space of state and control combined with the finite-dimensional optimization methods such as the space covering and gradient-type methods makes probable the finding of the global optimum for OPC problems.