Constrained Neural Ordinary Differential Equations with Stability Guarantees
This work addresses safety and performance in engineering systems by providing a method to incorporate stability into neural ODEs, though it is incremental as it builds on existing neural ODE frameworks.
The paper tackled the problem of modeling ordinary differential equations with neural networks while ensuring stability, by deriving stability guarantees from eigenvalue constraints and using barrier methods for inequality constraints, achieving prediction accuracy comparable to ground truth dynamics in open-loop simulations.
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches require domain expertise and are often difficult to tune or adapt to new systems. In this paper, we show how to model discrete ordinary differential equations (ODE) with algebraic nonlinearities as deep neural networks with varying degrees of prior knowledge. We derive the stability guarantees of the network layers based on the implicit constraints imposed on the weight's eigenvalues. Moreover, we show how to use barrier methods to generically handle additional inequality constraints. We demonstrate the prediction accuracy of learned neural ODEs evaluated on open-loop simulations compared to ground truth dynamics with bi-linear terms.