Mamba Sequence Modeling meets Model Predictive Control

Abstract

In this paper, we consider the design of Model Predictive Control (MPC) algorithms based on Mamba neural networks. Mamba is a neural network architecture capable of sub-quadratic computational scaling in sequence length with state-of-the-art modeling capabilities. We provide a consistent and complete mathematical description of the Mamba neural network is provided. Then, adjustments and optimizations are made to construct a decoder-only Mamba multi-step predictor for MPC and an input-output formulation is given for sequence-to-sequence modeling of dynamical systems. The performance of Mamba-MPC is evaluated on several numerical examples and compared to a Long-Short-Term-Memory based MPC (LSTM-MPC) equivalent. First, a Single-Input-Single-Output (SISO) Van der Pol oscillator is considered, where stability, reference tracking, and noise robustness are evaluated. Then, a MIMO Four Tank setup is introduced where Multiple-Input-Multiple-Output (MIMO) reference tracking is evaluated. Lastly, Mamba-MPC is implemented on a physical Quanser Aero2 setup for closed-loop reference tracking. The results demonstrate that Mamba-MPC is able to stabilize and track a reference for SISO and MIMO systems, both in simulation and on a physical setup. Moreover, Mamba-MPC consistently outperforms LSTM-MPC in predictive control and is significantly computationally faster.

v2: corrected 3 misreported hyperparameters, result are unchanged. Updated to OJCSYS version, added Transformer comparison, computational cost scaling comparison, stateful vs stateless training, towards Towards Stability Guarantees for Mamba-MPC section. Cleaned up textual errors and outdated references