Asynchronous Splitting Design for Model Predictive Control

TL;DR

This paper introduces an asynchronous dual solver with variance reduction for embedded model predictive control, demonstrating geometric convergence and improved estimate quality through probabilistic update tuning.

Contribution

It presents a novel stochastic AMA algorithm with VR tailored for asynchronous MPC, enabling better convergence and flexibility in update scheduling.

Findings

Geometric convergence to a suboptimal solution demonstrated.

Enhanced estimate quality via probabilistic asynchronous updates.

Preliminary results on aircraft longitudinal control application.

Abstract

This paper focuses on the design of an asynchronous dual solver suitable for embedded model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the context of stochastic proximal gradient methods, and on the alternating minimization algorithm (AMA). The resultant algorithm, a stochastic AMA with VR, shows geometric convergence (in the expectation) to a suboptimal solution of the MPC problem and, compared to other state-of-the-art dual asynchronous algorithms, allows to tune the probability of the asynchronous updates to improve the quality of the estimates. We apply the proposed algorithm to a specific class of splitting methods, i.e., the decomposition along the length of the prediction horizon, and provide preliminary numerical results on a practical application, the longitudinal control of an Airbus passenger aircraft.