A direct solution approach for multi timescale optimal control problems

In high fidelity optimal control problems, a commonly appearing problem emerges from different timescales inherent to the model, resulting in stiff differential equations. When solving these problems using direct discretization, the selection of the discretization nodes for all States is driven by the States associated with the fast dynamics, no matter how strong their influence on the solution is. In this paper, a novel discretization scheme is presented that uses direct collocation for the slow States while the fast States of the model are represented based on a direct multiple shooting scheme. This way, different grids may be chosen for the States, resulting in a slight decoupling of the timescales. A high fidelity air race trajectory optimization problem is implemented to demonstrate how the dimensions of the discretized problem can be significantly decreased by the method, resulting in improved computational performance during the solution process.