Neural networks identify unstable systems with stability guarantees
Neural Closed-Loop Identification of Nonlinear Systems with Stability and Generalization Guarantees
Machine Learning
Summary
When machines or systems control themselves, it’s hard to understand their behavior because measuring their parts is tricky and often noisy. The authors show a new way for neural networks to learn about these systems safely, even when the system is unstable or noisy. Their method makes sure the learned model stays stable and predicts well, even with little data or in new situations.
What this means in practice
- •For control engineers: Identify models of unstable nonlinear systems from closed-loop operational data with guaranteed stability for safer and more accurate controller design.
- •For robotics developers: Use a stable identification framework to build predictive models of robotic systems that generalize well even under feedback and noise conditions.
Authors
Laura Meroi, Mahrokh G. Boroujeni, Leonardo Massai, Giancarlo Ferrari-Trecate
Abstract
Neural networks are expressive models of nonlinear dynamics, but identifying such systems from closed-loop data raises two difficulties: the feedback loop correlates inputs with measurement noise, biasing standard open-loop estimators, and the identified model must be stabilized by the data-collection controller, so that its closed-loop behavior matches the true plant's. We derive a complete parameterization of all nonlinear systems stabilized by a given controller, generalizing the classical dual-Youla parameterization to the nonlinear setting. Building on this characterization, we propose Internal Controller Identification (ICI), a computationally tractable framework for identifying potentially unstable systems while ensuring closed-loop stability by construction; in the linear case, our indirect method reduces to an open-loop identification problem, for which standard consistency results apply. The framework accommodates contextual information, letting a single certified model identify a family of systems, and supports a PAC-Bayesian training objective that, when data are scarce and prior knowledge is available, bounds the identified operator's expected prediction loss. Experiments show that ICI identifies open-loop unstable plants where uncertified baselines diverge, outperforms direct methods under weak excitation and feedback-correlated noise, generalizes zero-shot to environments unseen during training, and, with limited data, avoids the overfitting of empirical risk minimization while providing a non-vacuous generalization bound.