Author

Syed Pouladi

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Preprint Aug 2026

Adaptive Stability-Constrained Neural Differential Equations for Controlled Dynamical Systems with Unknown Inputs

Continuous-time neural models are attractive for identifying nonlinear systems, but a small one-step error can grow rapidly when a learned vector field is rolled out under inputs that differ from those used for training. This paper develops an adaptive stability-constrained neural differential equation (AS-NDE) for systems with measured controls and unmatched, unknown perturbations. The nominal vector field and a state--input-dependent Riemannian metric are learned jointly. Positive definiteness is enforced by construction, while a sampled differential inequality penalizes violations of a prescribed contraction rate. An incremental input-to-state bound is derived: the distance between two trajectories decays exponentially up to gains determined by differences in their controls and disturbances. The statement explicitly accounts for the time derivative of an input-dependent metric, a term that is easily omitted in heuristic stability regularizers. We give a reproducible evaluation protocol for a forced Duffing oscillator and a permanent-magnet synchronous motor (PMSM) model. Because no measured data or executed training runs accompany this draft, all numerical curves and tables are clearly identified as illustrative synthetic placeholders; their PGFPlots coordinates are embedded in the source for direct replacement. The resulting manuscript is intended as a technically consistent starting point, not as evidence of empirical superiority before the prescribed experiments are run.

Syed Pouladi · 0 citations

Preprint Jul 2026

Learning Stable Controlled Dynamical Systems via Input-Contraction Neural Differential Models

Learning continuous-time representations of dynamical systems from observation data has emerged as a cornerstone of data-driven control and scientific machine learning. However, existing neural differential equations either treat external control inputs heuristically without providing strict structural guarantees, or enforce stability properties under the restrictive assumption of constant or vanishing inputs. This paper proposes the Input-Contraction Neural Differential Model (ICNDM), a novel deep learning framework that seamlessly incorporates time-varying control inputs while ensuring incremental exponential convergence via input-dependent contraction regularization. By leveraging an embedded input encoder and a parameterized metric network, the proposed architecture learns both the non-autonomous neural vector fields and a generalized Riemannian contraction metric simultaneously. We derive sufficient conditions for input-dependent contraction and formally establish an input-to-state contraction property under bounded external excitations. Extensive numerical evaluations on highly nonlinear chaotic oscillators and experimental data from a Permanent Magnet Synchronous Motor (PMSM) drive system demonstrate that ICNDM yields substantial reductions in long-horizon rollout errors and exhibits superior structural robustness against input perturbations compared with state-of-the-art neural differential benchmarks.

Syed Pouladi · 0 citations