Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness

2021/04/13 by Max Revay, Ruigang Wang, Revay, Max +3 · 15 citations
Computer Science · Engineering · #Advanced Memory and Neural Computing #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Neural Networks and Reservoir Computing #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2104.05942

openalex publication_date 2021/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees of stability and robustness. All models in the proposed class are contracting -- a strong form of nonlinear stability -- and models can satisfy prescribed incremental integral quadratic constraints (IQC), including Lipschitz bounds and incremental passivity. RENs are otherwise very flexible: they can represent all stable linear systems, all previously-known sets of contracting recurrent neural networks and echo state networks, all deep feedforward neural networks, and all stable Wiener/Hammerstein models, and can approximate all fading-memory and contracting nonlinear systems. RENs are parameterized directly by a vector in R^N, i.e. stability and robustness are ensured without parameter constraints, which simplifies learning since \HLgeneric methods for unconstrained optimization such as stochastic gradient descent and its variants can be used. The performance and robustness of the new model set is evaluated on benchmark nonlinear system identification problems, and the paper also presents applications in data-driven nonlinear observer design and control with stability guarantees.

Cited by

• Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches
• Resilient AFE Drive Control using Neural Networks with Tracking Guarantees
• PAC-Bayesian Optimal Control with Stability and Generalization Guarantees
• Development of a velocity form for a class of RNNs, with application to offset-free nonlinear MPC design
• Orthogonal-by-construction augmentation of physics-based input-output models
• Learning stabilising policies for constrained nonlinear systems
• Funnel-Based Online Recovery Control for Nonlinear Systems With Unknown Dynamics
• Constrained Performance Boosting Control for Nonlinear Systems via ADMM
• Contributions to Semialgebraic-Set-Based Stability Verification of Dynamical Systems with Neural-Network-Based Controllers
• Learning Robust Agile Flight Control with Stability Guarantees
• Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructions
• Circuit realization and hardware linearization of monotone operator equilibrium networks
• Predictability Enables Parallelization of Nonlinear State Space Models
• Passive nonlinear FIR filters for data-driven control
• State dimension reduction of recurrent equilibrium networks with contraction and robustness preservation

Related

• Recurrent Equilibrium Networks: Flexible Dynamic Models With Guaranteed Stability and Robustness
• Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System
• State dimension reduction of recurrent equilibrium networks with contraction and robustness preservation
• R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networks
• Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guarantees