Koopman-based Modeling for Rocket Landing

Abstract

The rocket landing problem has been one of the main interests of the space sector in the last decades and, more recently, the need for a fast and efficient way to solve precisely the guidance problem has emerged as crucial for reusability purposes. In this context, Koopman Operator Theory is promising because of its ability to globally linearize an un- controlled autonomous system, by lifting the state onto a set of observables. In general, the conditions to include the control in a linear way are quite restrictive, but a bilinear model can be obtained with almost no further approximations. Well-established methods employ a fixed dictionary of observables, but more recent studies show that it is beneficial, in terms of accuracy, to learn a dictionary through neural network optimization. In this work, the atmospheric, fuel-optimal, rocket landing problem is addressed with the aim of assessing if a Koopman model can be used to successfully solve the Optimal Control Prob- lem and if it is computationally advantageous. The main contributions of this thesis are the extension of dictionary learning techniques to include control and the formulation of a new framework to estimate a bilinear control model, after obtaining the equivalent linear modeling of the free dynamics. It is shown that dictionary learning methods provide more accurate linear control models than standard methods. The resulting dynamical model is used to build a Linear Program that can be solved efficiently; on the other hand, when a Koopman bilinear model is used, a solution can be found, but with poor computational efficiency.