Andrea Ghezzi

University of Freiburg

Monday, September 28, 2026, 14:00 - 16:00

SR 02-016/18, Geb. 101

Abstract

This thesis studies constrained decision-making in nonlinear systems from two complementary perspectives: the development of derivative-based optimization algorithms and the construction of learning-based approximations of optimal controllers.

On the optimization side, the thesis addresses mixed-integer nonlinear programs (MINLPs) and mixed-integer optimal control problems (MIOCPs), which arise when nonlinear dynamics are coupled with discrete decisions such as switching and logical constraints. A new algorithm, S-B-MIQP, is proposed by combining ideas from generalized Benders decomposition, outer approximation, and sequential quadratic programming. For convex MINLPs, the method is globally convergent and can certify infeasibility, while a heuristic cut-correction strategy extends its applicability to nonconvex problems. The method is implemented in the open-source CAMINO toolbox and evaluated on benchmark instances from MINLPLib as well as on mixed-integer optimal control problems.

The thesis further investigates decision-making problems with logical structure, formulated either as MINLPs or as mathematical programs with vanishing constraints (MPVCs). Through aerospace trajectory-planning case studies, including Mars landing with divert-feasible regions, it is shown that MPVCs can be advantageous when the number of logical decisions is limited, whereas MINLPs are generally more robust when the number of logical decisions increases.

On the learning side, the thesis develops methods to reduce the computational burden of nonlinear model predictive control (MPC). First, imitation learning from MPC is formulated using a Q-loss that evaluates policies with respect to the underlying optimal control problem (OCP) rather than a surrogate behavioral metric. In this way, the Q-loss directly embeds performance objective and constraint satisfaction of the MPC. However, the evaluation of the Q-loss requires the solution of an OCP for each sample. To alleviate the computation burden, we devise a second Q-loss based on the Gauss-Newton approximation of the OCP.

Second, a rollout-then-optimize strategy is introduced, in which a learned policy generates a nominal trajectory that is refined online by a single Riccati-based Newton correction within a real-time iteration MPC framework. Theoretical analysis and numerical experiments on a quadrotor tracking problem show that this approach can substantially improve learned policies while retaining low online computational cost.

Taken together, these results show that constrained nonlinear decision-making can be made more tractable either by specialized algorithms for MINLPs or by reducing the online cost of MPC through learning-based approximation.

Examination committee

1st examiner: Prof. Dr. Moritz Diehl, University of Freiburg

2nd examiner: Dr. Sven Leyffer, Argonne National Laboratory

Observer: JProf. Dr. Edoardo Milana, University of Freiburg

President: Prof. Dr. Joschka Boedecker, University of Freiburg