On the shooting algorithm for partially affine control problems

Abstract

In this thesis we propose a shooting algorithm for partially affine optimal control problems, this is, systems in which the controls appear both linearly and nonlinearly in the dynamics. Since the shooting system generally has more equations than unknowns, the algorithm relies on the Gauss-Newton method. As a consequence, the convergence is locally quadratic provided that the derivative of the shooting function is Lipschitz continuous at the optimal solution. We provide a proof of the convergence for the proposed algorithm using recently developed second order conditions for weak optimality of partially affine problems. We illustrate the applicability of the algorithm by solving an optimal treatment-vaccination epidemiological problem.