A structure exploiting algorithm for approximate robust optimal control with application to power generating kites

In the present paper we discuss numerical solution strategies for robust optimal control problems. Here, our motivation is to optimize the dynamic open-loop behaviour of a kite, which is affected by unknown wind turbulence. After reviewing some existing strategies for robust optimal control, we specialize on a particular approach which uses a Lyapunov differential equation in order to approximate the influence of the uncertainties on the state of the dynamic system and to guarantee stability of periodic systems. We propose strategies to exploit the structure of the corresponding formulation and provide an open-source implementation of the algorithm. The practical advantage of this implementation is illustrated by applying it to a robustness and stability optimization problem for a power generating kite system. Here, the model equations and system parameters are inspired from a real-world application.