Jonathan Frey

University of Freiburg

Friday, September 25, 2026, 14:00 - 16:00

SR 02-016/18, Geb. 101

Nonlinear model predictive control (NMPC) has become a popular feedback control strategy in applications that require the systematic treatment of nonlinear dynamics, constraints, and performance objectives. Its underlying optimal control problems provide a flexible modeling framework for systems in various fields, such as mobility, energy, industrial processes, and robotics. At the same time, the practical deployment of NMPC depends on algorithms that can solve these problems fast and reliably, often under strict real-time requirements. This challenge is particularly pronounced in embedded applications, where high feedback rates must be achieved despite limited computational resources and where delays directly affect closed-loop performance. The resulting need for efficient algorithms, suitable formulations, and accessible implementations motivates the developments presented in this thesis.

This thesis investigates several directions that improve the applicability and performance of optimization-based control, in particular NMPC. A recurring theme is the entanglement between algorithms and problem formulations, and synergies along both dimensions are explored throughout. Most contributions are accompanied by efficient implementations in the open-source software package acados, which provides fast solvers for embedded optimization and whose development was led by the author during the timeframe of this thesis.

First, the thesis studies advanced problem formulations and discretization schemes that go beyond standard single-phase formulations and basic control parameterizations. In particular, it introduces efficient techniques for long-horizon optimal control, including a Gauss-Newton Runge-Kutta cost integration scheme, and develops multi-phase formulations that allow the combination of models with different fidelity, varying polynomial control parameterizations, and closed-loop cost descriptions. It is shown how such advanced formulations can be treated with structure-exploiting algorithms, yielding better trade-offs between computational complexity and closed-loop performance than standard formulations.

Second, the thesis contributes to real-time algorithms that reduce feedback delay in NMPC. It revisits the real-time iteration method and advanced-step ideas, and studies advanced-step real-time iteration (AS-RTI) schemes with four iteration levels that provide a transparent trade-off between computational effort and solution accuracy. A unified local convergence analysis for all four variants is established, and an efficient implementation within acados is presented.

Third, the thesis addresses differentiable solution methods for nonlinear programming and optimal control. It studies the computation of approximate solutions with interior-point methods and their sensitivities under active-set changes, and introduces sequential barrier quadratic programming (SBQP) as a new algorithm that combines favorable properties of sequential quadratic programming and interior-point methods. Building on that, the algorithm is equipped with efficient forward and adjoint sensitivity computations that exploit the structure of optimal control problems, enabling, for instance, the use of NMPC formulations as differentiable layers within machine learning pipelines.

The implementations in acados make all of these advances available for practical NMPC applications. Because the methods are realized within a common software environment, they can be used not only individually but also in combination within a single solver. This combination of methodological developments and efficient open-source implementations has enabled the application of various algorithmic novelties studied in this thesis to real-world control systems.