Numerical solution of the optimal periodic control problem using differential flatness

Optimal periodic control (OPC) is of interest in many engineering applications. In practice, the numerical solution of the OPC problem has been found to be quite challenging. In this note, we present a method which uses differential flatness for the solution of OPC problems. The OPC problem is reformulated using the flatness of the underlying dynamical system to eliminate the differential equations and the periodicity constraints, resulting in simpler and generally more efficient computation. The effect of point-wise constraints and the analytical computation of the Jacobian matrix are also discussed. The approach is demonstrated using two examples.