Bilinear Mamba-Koopman Neural MPC for Varying Dynamics

TL;DR

This paper introduces Bilinear Mamba-Koopman Neural MPC, an extension that incorporates control-dependent dynamics to improve adaptation and robustness in time-varying systems, with minimal added complexity.

Contribution

It proposes a bilinear extension to Koopman-based neural MPC that enables control-dependent latent dynamics, enhancing adaptability and robustness in varying conditions.

Findings

Matches or improves forecasting accuracy across benchmarks.

Enhances stability and robustness in time-varying scenarios.

Degrades more gracefully under stale-plan execution.

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.