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In this article we propose a shooting algorithm for partially-affine optimalcontrol problems, this is, systems in which the controls appear both linearlyand nonlinearly in the dynamics. Since the shooting system generally has moreequations than unknowns, the algorithm relies on the Gauss-Newton method. As aconsequence, the convergence is locally quadratic provided that the derivativeof the shooting function is injective and Lipschitz continuous at the optimalsolution. We provide a proof of the convergence for the proposed algorithmusing recently developed second order sufficient conditions for weak optimalityof partially-affine problems. We illustrate the applicability of the algorithmby solving an optimal treatment-vaccination epidemiological problem.

The shooting algorithm for partially control-affine problems with application to an SIRS epidemiological model