Bilinear Mamba-Koopman Neural MPC for Varying Dynamics
Abstract
Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.
Related
- Contraction-Based Model Predictive Control using Bilinear Koopman Realizations with Proportional Error Bounds
- On the stability of eigenvalues of varying bilinear forms in abstract Hilbertian settings and applications
- Scalable Mamba-Based Message-Passing Neural Decoder for Error-Correcting Codes
- Data-driven Koopman mode approximation: A neural power iteration algorithm
- Measure-free Koopman-von Neumann dynamics and noncommutative Geometry
BibTeX
@misc{pagi2026bilinear,
title = {{Bilinear Mamba-Koopman Neural MPC for Varying Dynamics}},
author = {Matan Pagi and Zohar Sorek},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.04793},
eprint = {2605.04793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04793},
}
RIS
TY - UNPB
TI - Bilinear Mamba-Koopman Neural MPC for Varying Dynamics
AU - Matan Pagi
AU - Zohar Sorek
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2605.04793
UR - https://arxiv.org/abs/2605.04793
AB - Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.
ER -