Stability of model-free predictive control (MFPC)

Establish stability of the closed-loop system controlled by model-free predictive control (MFPC), formulated via the ultra-local model dot y = F + α u with online estimation and receding-horizon implementation, when applied to the Dubins' car planar robot for trajectory tracking.

Background

The paper compares two control approaches for collision avoidance with a Dubins' car: a model-based flatness-plus-HEOL scheme and a model-free predictive control (MFPC) scheme based on the ultra-local model with online disturbance estimation and a predictive optimization step. The authors report strong empirical performance and robustness for both approaches.

While local stability for the flatness-plus-HEOL approach is stated to be straightforward, the authors explicitly acknowledge that theoretical stability results for MFPC have not yet been demonstrated. This leaves the stability analysis of the MFPC closed loop as an open issue in the presented context.

References

One example is stability. In the case of the combination of flatness-based control and HEOL, local stability is straightforward. However, nothing has been demonstrated yet for MFPC.

— Avoidance of an unexpected obstacle without reinforcement learning: Why not using advanced control-theoretic tools?  (2509.03721 - Join et al., 3 Sep 2025) in Section 5, Conclusion