Ensuring stability, feasibility, robustness, and online tractability when integrating learned components into nonlinear control

Determine conditions and develop methods that guarantee stability, recursive feasibility, robustness, and online computational tractability for nonlinear control systems when incorporating learned components (such as learned dynamics models, cost functions, or constraints) into Model Predictive Control and related learning-based controllers, in order to reduce conservatism without sacrificing formal guarantees.

Background

The paper highlights that robust and stochastic MPC formulations can be overly conservative, limiting performance, and that learning-based approaches (e.g., differentiable MPC) can adapt constraints and costs from data to reduce conservatism. However, integrating learned elements into nonlinear control raises questions about maintaining feasibility, stability, robustness, and real-time solvability.

This open problem targets the theoretical and algorithmic foundations needed to endow learning-enhanced MPC formulations for nonlinear systems with the same rigorous guarantees traditionally available for purely model-based controllers, while ensuring practical online tractability.

References

However, ensuring stability, feasibility, robustness, and online computational tractability while incorporating learned components for nonlinear systems remains an open question.

— Safe Physics-Informed Machine Learning for Dynamics and Control  (2504.12952 - Drgona et al., 17 Apr 2025) in Section 6: Challenges and Opportunities

Learning-based control is developing rapidly, but raises questions regarding stability guarantees and certification that are still open.

— Dynamic Inversion: An Incrementally Evolving Methodology for Flight Control Design  (2608.23229 - Milz et al., 24 Aug 2026) in Conclusions

It is still unclear how much of the recent success in combining Koopman operator theory and MPC is due to the approximation capabilities of linear operators, as compared to the robustness of MPC to model-plant mismatch .

— Model predictive traction control system based on the Koopman operator  (2608.25753 - Hromatko et al., 26 Aug 2026) in Section “Results and discussion,” subsection “Comments”