Structure Exploiting Integrators for Model Predictive Control

Master Thesis Presentation

Jonathan Frey

Wednesday, November 21, 2018, 11:00 - 11:50

"Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany"

Abstract

Optimization based control strategies, such as Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE), have become popular techniques for real-time control of various physical systems. However, in the context of embedded optimization, systems with fast dynamics are still a challenge. The simulation of the model and its sensitivity propagation are key tasks that have to be carried out frequently within most NMPC algorithms.
Thus, it is critical for an optimal control software package to have efficient algorithms for these tasks available.
A software package for optimal control, that was recently developed by the team of Prof. Moritz Diehl, is acados. The development of integration schemes in acados, also called integrators, constitutes a major part of this thesis. In the following, the main contributions of this thesis are summarized.
The Implicit Runge-Kutta (IRK) integrator is maintained and extended to support differential-algebraic equations (DAE) and the option to propagate exact second order sensitivities.
The previous works on structure exploitation within IRK methods are presented and compared. A dynamic system structure, which can also treat index-1 DAEs and is called "Generalized Nonlinear Static Feedback" (GNSF), combines the approaches that exploit linear dependencies within the dynamic model.
An efficient IRK scheme that exploits the GNSF structure, thus called GNSF-IRK, was derived and implemented in acados with the option to efficiently propagate forward and adjoint first order sensitivities.
Additionally, an algorithm is proposed that can automatically transcribe most index-1 DAE systems into the presented GNSF structure, such that the GNSF-IRK scheme can be used conveniently.
Within numerical experiments, both the transcription algorithm and GNSF-IRK are applied to various dynamic models, of which some correspond to industrial wind turbines.
The analysis of the experiments shows how the algorithms should be used and how GNSF-IRK can outperform the standard IRK method.