A Unified Framework for Dynamics Modeling and Control Design Using Deep Learning With Side Information on Stabilizability

This article presents a unified framework for dynamics modeling and control design using deep learning, focusing on incorporating prior side information on stabilizability. Control theory provides systematic techniques for designing feedback systems while ensuring fundamental properties such as stabilizability, which are crucial for practical control applications. However, conventional data-driven approaches often overlook or struggle to explicitly incorporate such control properties into learned models. To address this, we introduce a novel neural network (NN)-based approach that concurrently learns the system dynamics, a stabilizing feedback controller, and a Lyapunov function for the closed-loop system, thus explicitly guaranteeing stabilizability in the learned model. Our proposed deep learning framework is versatile and applicable across a wide range of control problems, including safety control, $L_{2}$ -gain control, passivation, and solutions to Hamilton-Jacobi inequalities. By embedding stabilizability as a core property within the learning process, our method allows for the development of learned models that are not only data-driven but also grounded in control-theoretic guarantees, greatly enhancing their utility in real-world control applications. This article includes examples that demonstrate the effectiveness of this approach, showcasing the stability and control performance improvements achieved in various control scenarios. The methods proposed in this article can be easily applied to modeling without control design. The code has been open-sourced and is available at https://github.com/kashctrl/Deep_Stabilizable_Models.