An Efficient Algorithm for Tube-based Robust Nonlinear Optimal Control with Optimal Linear Feedback
Florian Messerer, Moritz Diehl
Abstract
We propose an algorithm for solving tube-based robust nonlinear optimal control problems based on the approximate propagation of ellipsoidal uncertainty tubes. Crucially, the algorithm does not only optimize the nominal control trajectory, but the decision variables include linear feedback gains for each time step. In consequence, the resulting trajectories do not suffer from the unrealistically large uncertainty sets of open-loop robust trajectories, but are able to approximately capture the feedback behavior implicit to model predictive control. The proposed algorithm iterates by alternatingly performing a Riccati recursion and solving a perturbed nominal optimal control problem. We provide a theoretical analysis of the local convergence behavior and demonstrate its basic applicability on the example problem of controlling a towing kite.