A flatness based algorithm for optimal periodic control problems

Abstract

We present an algorithm for the efficient solution of optimal periodic control (OPC) problems using a differential flatness approach. Existing methods for OPC problems involve repeated integration of an ODE system to satisfy periodicy and have severe stability and/or accuracy problems. However, when the underlying dynamics is differentially flat, the differential equations as well as the periodic boundary conditions can be eliminated and the OPC problem can be reformulated as a nonlinear programming problem which is easier to solve. The algorithm is illustrated with two examples.