Environment-Aware Stable Neural Koopman Dynamics Learning for Input-Driven Systems under Environmental Constraints

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Article Summary

Constructing predictive models of nonlinear dynamical systems from measurement data is a longstanding problem in systems identification and control. Although Neural ordinary differential equations~(Neural ODEs), Koopman operator approximations, and input-aware architectures have each moved the field forward, none simultaneously addresses environment-varying operating conditions, rigorous stability guarantees, and input-to-state stability (ISS) certification within a unified trainable framework. This paper introduces Environment-Aware Stable Neural Koopman Dynamics Learning (ESNKD), which integrates four components: (i)~a bundle-structured encoder that maps environmental observations to a geometrically regularized latent manifold, drawing on the fiber bundle framework; (ii)~an input-conditioned Neural ODE whose residual term handles arbitrary external signals, extending the input concomitant philosophy; (iii)~a contraction synthesis layer enforcing convergence via Persidskii-type tractable linear inequalities, analogous to the certification mechanism; and (iv)~a Koopman lifting stage with LMI-based ISS verification that follows the theoretical pipeline of. Theoretical guarantees cover solution existence and uniqueness, incremental exponential stability, ISS with explicit gain bounds, and robustness to environmental perturbation. Experiments on five benchmark systems, including two robotic manipulation platforms, show consistent improvements over five competitive baselines in both prediction accuracy and safety certification rates.

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