Robust Neural IDA-PBC: Passivity-based stabilization under approximations

We revisit and extend the Neural Interconnection and Damping Assignment Passivity-Based Control (Neural IDA-PBC) framework, which recasts IDA-PBC design as an optimization problem using Physics-Informed Neural Networks (PINNs). Despite its promise, the stability and robustness of the resulting closed-loop systems under approximate matching have remained unaddressed. We fill this gap by formally analyzing the effects of approximation residuals as additive perturbations and deriving conditions for ultimate boundedness, practical and asymptotic stability. Building on this, we introduce a renewed design pipeline with two key features: (i) a composite loss that incorporates residuals targeting passivity, dissipation, and robustness guarantees; (ii) a modular NN parameterization of the desired dynamics, allowing for structural priors such as skew-symmetry, convexity, and momentum damping. This modular approach enables learning controllers that preserve the physical structure of energy-based systems and allows fine-tuning of closed-loop transients post-training. We validate the method on a 3D underactuated quadrotor with 12 state variables, demonstrating stable energy-shaping control and structure-preserving convergence using only numerical approximations.