ISS-BKNO framework guarantees stable learning of controlled dynamics under constraints

Lin Feng's ISS-BKNO (Input-to-State Stable Bundle Koopman Neural ODEs) tackles a fundamental challenge in learning-controlled dynamics: how to guarantee stability and safety under environmental constraints without sacrificing flexibility. Traditional approaches address either stability or extrinsic inputs in isolation, but ISS-BKNO unifies Koopman operator identification (for global linearization), Neural ODEs (for continuous-time modeling), fiber bundle geometry (to separate environment-specific dynamics), and input-to-state stability certification. The architecture uses a three-stage lifting pipeline: a bundle-aware encoder that preserves fiber structure, an environment-conditioned Koopman matrix with eigenvalues forced into the left half-plane, and a residual neural ODE whose Jacobian satisfies a quadratic sector bound. Lyapunov-based ISS regularization turns the stability requirement into a differentiable penalty, jointly optimized with prediction loss. Theoretical results prove fiber invariance, an explicit ISS gain formula, and approximation error bounded by the EDMD residual.

Experiments on four diverse tasks—a pendulum, cart-pole, unicycle navigation, and a Franka Emika robot arm—demonstrate the framework's effectiveness. ISS-BKNO significantly outperforms standard Neural ODE and Koopman baselines (like EDMD and deep Koopman models) in both prediction accuracy and robustness to matched disturbances. The stability guarantees are not just theoretical: the explicit ISS gain formula provides a computable safety margin for real-time control. This work is particularly relevant for robotics, autonomous navigation, and any domain where learned dynamics must operate safely under changing conditions. By integrating geometric structure with stability certification, ISS-BKNO offers a principled path toward reliable learning-based control systems.