Lyapunov-Constrained Hybrid Modeling for Stable Parameter Learning in Nonlinear Systems

Hybrid modeling frameworks that integrate first-principles equations with data-driven corrections offer a promising approach for capturing complex, partially known system dynamics. However, ensuring the stability and physical realism of the learned correction terms remains a significant challenge, especially when using flexible function approximators such as neural networks. This work introduces a Lyapunov-constrained hybrid modeling framework that ensures the boundedness of a learned parameter dependent on the states. Leveraging tools from nonlinear control theory, we perform a Lie derivative analysis to extract relative-degree features, construct a reference map for the unknown parameter, and embed a Lyapunov decay constraint directly into the model’s training objective. We validate our method on a benchmark CSTR system with time-varying fouling, where the heat transfer coefficient is treated as an unmeasured and drifting parameter. Results show that the proposed hybrid model accurately reconstructs system trajectories and parameter profiles while enforcing bounded deviation from the precomputed reference manifold. The Lyapunov-based penalty ensures that the correction term remains physically plausible and stable across all operating conditions, even in open-loop simulations. This framework provides a rigorous foundation for deploying hybrid models in safety-critical process systems.