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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.16754 |
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| _version_ | 1866914571742085120 |
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| author | Pouladi, Syed |
| author_facet | Pouladi, Syed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable Fiber-Koopman Residual Dynamics for Environment-Constrained Robust Control Pouladi, Syed Systems and Control 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. |
| title | Stable Fiber-Koopman Residual Dynamics for Environment-Constrained Robust Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.16754 |