Input-to-State Stable Bundle Koopman Neural ODEs for Learning Controlled Dynamics under Environmental Constraints

Abstract

We propose ISS-BKNO, a unified framework that integrates Koopman operator identification, Neural ordinary differential equations (ODEs), fiber bundle geometry, and input-to-state stability (ISS) certification. Unlike prior approaches that address stability, extrinsic inputs, or environmental constraints in isolation, the proposed framework simultaneously learns controlled nonlinear dynamics while guaranteeing global convergence and a computable ISS gain. The architecture introduces a three-stage lifting pipeline: a bundle-aware encoder that separates environment-specific fibers, an environment-conditioned Koopman backbone whose matrix spectrum is constrained to lie in the left half-plane, and a residual neural ODE correction whose Jacobian satisfies a quadratic sector bound. Lyapunov-based ISS regularization turns the stability requirement into a differentiable penalty that is jointly optimized with the prediction objective. Theoretical results establish fiber invariance, ISS with an explicit gain formula, and an approximation error bound that scales with the EDMD residual. Experiments on a pendulum, cart-pole, a unicycle-based navigation task, and a Franka Emika manipulator demonstrate substantially improved prediction accuracy and robustness under matched disturbances compared with existing Neural ODE and Koopman baselines.