Two new papers that advance the application of control theory in machine learning have been accepted at the IFAC World Congress and the International Journal of Control. Both works address critical challenges in nonlinear system identification: ensuring neural network models behave reliably and safely, even beyond their immediate training conditions.
Certifying Regional Stability in RNNsThe first paper[1], accepted at the upcoming IFAC World Congress, presents a method for learning a regionally stable recurrent neural network (RNN) from input-output data generated by unknown dynamical systems. Traditional learning methods often either impose a global form of stability, which can be overly conservative, or use no stability constraints at all, leading to unpredictable behavior.To bridge this gap, we developed a novel method that certifies regional stability. By utilizing generalized sector conditions on the deadzone activation function and linear matrix inequality constraints, the proposed learning method equips models with a certificate of forward invariance within a specific subset of the state space. Numerical evaluations demonstrate that this regionally constrained approach successfully identifies systems that global methods fail to identify.
Enhancing Generalization Through DissipativityThe second paper[2], accepted for publication in the International Journal of Control, addresses the generalization problem in neural networks during inference. While standard models can achieve high prediction accuracy on in-distribution data, they frequently fail when excited by unseen input trajectories.To solve this, we propose a hybrid residual model that guarantees input-output stability. The method enhances a baseline linear approximation with an RNN to capture complex residual dynamics. Crucially, by imposing constraints on the learnable parameters to ensure dissipativity—an intrinsic property of most physical systems—the resulting models exhibit improved generalization on out-of-distribution (OOD) data.
[1] Frank, D., Shakib, M.F., and Staab, S. (2026). Learning the dynamics of nonlinear systems with regional stability guarantees through linear matrix inequality constraints. In Proceedings of the 23rd IFAC World Congress. (Provisional link: https://arxiv.org/pdf/2605.18292).
[2] Frank, D., Holicki, T., Scherer, C. W., & Staab, S. (2026). Regularised neural network-based nonlinear system identification with prior system knowledge. International Journal of Control, 1–29. https://doi.org/10.1080/00207179.2026.2679228
