- João Miguel P. Anastácio Machado
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 nonlin-early 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 have also developed an efficient methodology to automate the computation of singular arcs. The applicability of our algorithm is illustrated by solving an optimal treatment-vaccination epidemiological problem.
*Texto enviado pelo aluno.
Membros da banca:
- María Soledad Aronna (orientadora) - FGV EMAp
- Roberto Guglielmi - University of Waterloo
- Joseph Frédéric Bonnans - Inria and Ecole Polytechnique