Stable Fiber-Koopman Residual Dynamics for Environment-Constrained Robust Control
For autonomous vehicle control under varying environmental conditions, SFKD provides a method that simultaneously ensures stability guarantees and high predictive accuracy, addressing a key tension in learning-based dynamical models.
The paper introduces Stable Fiber-Koopman Residual Dynamics (SFKD), a framework that combines environment-aware geometric consistency, latent-space stability certification, and bounded residual perturbation propagation for robust control. In autonomous vehicle path tracking experiments, SFKD achieved a 31% reduction in tracking RMSE and a 44% improvement in control smoothness compared to five baselines.
Learning-based dynamical models face a persistent tension between expressiveness and formal guarantees: richer model classes improve predictive accuracy, but their stability properties are typically verified only empirically, if at all. This paper proposes \emph{Stable Fiber-Koopman Residual Dynamics} (SFKD), a unified framework that simultaneously addresses environment-aware geometric consistency, latent-space stability certification, and bounded residual perturbation propagation. Concretely, SFKD constructs a fiber bundle latent manifold whose fibers encode environment-specific dynamics; an environment-conditioned Koopman operator governs the dominant linear evolution on each fiber; and a contraction-constrained residual neural network captures unmodeled nonlinear effects while admitting an explicit input-to-state stability (ISS) certificate. The resulting model is embedded in a sampling-based MPPI controller for autonomous vehicle path tracking under variable surface conditions and wind disturbances. Theoretical analysis establishes ISS of the latent dynamics and a finite ultimate bound on tracking error. Numerical experiments against five baselines -- Koopman MPC, Neural ODE, ICODE, ControlSynth, and ICODE-MPPI -- demonstrate a 31\% reduction in tracking RMSE, a 44\% improvement in control smoothness, and near-zero latent stability violation rate across environment-switching scenarios.