A recursive algorithm based on the maximum principle of pontryagin

This article reports findings in designing a conceptual optimal control algorithm based on the maximum principle of Pontryagin and of the steepest descent type for a relaxed version of the original problem. Allowing the relaxation of initial condition in order to rewrite the two boundary value problem as one with boundary conditions in the same endpoint, key properties of this algorithm are proved. Then, some results are obtained by using an optimization algorithm of the same type for which off-the-shelf routines taking into account the numerical issues, which are always tricky for infinite dimensional problems. © 2018 IEEE.