mlsanityData to 7 Oct 2026

Bilinear Mamba-Koopman Neural MPC for Varying Dynamics

arXiv 2605.04793 ↗First posted 6 May 2026cs.LG math.OCcited by 0

On the map: State-space sequence models (S4, Mamba) → Time series forecasting with SSMs

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba). Builds on 9 of its 30 references that are in the map. First posted on arXiv 6 May 2026.

Builds on

9 of 30 references.

References · 9

  1. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  4. 2017OSQP: An Operator Splitting Solver for Quadratic Programscited by 156
  5. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 139
  6. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  7. 2019Learning Compositional Koopman Operators for Model-Based Controlcited by 67
  8. 2022Deep Koopman Learning of Nonlinear Time-Varying Systemscited by 10
  9. 2018Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problemscited by 7

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  6. 2026Principled Koopman Representations with Kalman Inference for Efficient Time-Series Prediction
  7. 2024State-space models are accurate and efficient neural operators for dynamical systems
  8. 2026From Gradients to Riccati Geometry: Kalman World Models for Single-Pass Learning