Mamba Sequence Modeling meets Model Predictive Control

TL;DR

This paper introduces Mamba neural networks for Model Predictive Control, demonstrating superior speed and accuracy over LSTM-based methods in various dynamical system control tasks, including physical experiments.

Contribution

The paper develops a novel Mamba neural network architecture for MPC, providing a complete mathematical description and demonstrating its advantages over LSTM-MPC in speed and performance.

Findings

Mamba-MPC outperforms LSTM-MPC in predictive accuracy.

Mamba-MPC is significantly faster computationally.

Mamba-MPC successfully stabilizes and tracks references in physical systems.

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.