  This paper introduces and analyses a continuous optimization approach to
solve optimal control problems involving ordinary differential equations (ODEs)
and tracking type objectives. Our aim is to determine control or input
functions, and potentially uncertain model parameters, for a dynamical system
described by an ODE. We establish the mathematical framework and define the
optimal control problem with a tracking functional, incorporating
regularization terms and box-constraints for model parameters and input
functions. Treating the problem as an infinite-dimensional optimization
problem, we employ a Gauss-Newton method within a suitable function space
framework. This leads to an iterative process where, at each step, we solve a
linearization of the problem by considering a linear surrogate model around the
current solution estimate. The resulting linear auxiliary problem resembles a
linear-quadratic ODE optimal tracking control problem, which we tackle using
either a gradient descent method in function spaces or a Riccati-based
approach. Finally, we present and analyze the efficacy of our method through
numerical experiments.
