ICNDM: New neural differential model guarantees stable control with time-varying inputs

Learning stable continuous-time representations of dynamical systems is critical for data-driven control, but existing neural ODEs either lack strict guarantees for external inputs or only work under restrictive assumptions like constant inputs. Syed Pouladi's new paper proposes the Input-Contraction Neural Differential Model (ICNDM) to address this gap. The framework learns both the non-autonomous neural vector field and a generalized Riemannian contraction metric simultaneously, using an embedded input encoder and a parameterized network. This allows ICNDM to enforce incremental exponential convergence through input-dependent contraction regularization, even when control signals are time-varying. The authors derive sufficient conditions for input-dependent contraction and establish an input-to-state contraction property under bounded external excitations, providing formal stability guarantees.

Empirically, ICNDM was evaluated on highly nonlinear chaotic oscillators and experimental data from a Permanent Magnet Synchronous Motor (PMSM) drive system. The results show substantial reductions in long-horizon rollout errors compared to state-of-the-art neural differential benchmarks. The model also exhibits superior structural robustness against input perturbations, making it particularly promising for safety-critical control applications in robotics, autonomous vehicles, and industrial automation. By bridging the gap between theoretical stability and practical data-driven modeling, ICNDM offers a principled approach for learning controllers that are both expressive and provably stable.