A construction-free coordinate-descent augmented-Lagrangian method for embedded linear MPC based on ARX models

TL;DR

This paper introduces a construction-free, matrix-free coordinate-descent augmented-Lagrangian algorithm tailored for embedded linear MPC using ARX models, enabling efficient online adaptation without explicit QP construction.

Contribution

The paper develops a novel construction-free algorithm for ARX-based MPC that avoids explicit QP formulation, suitable for embedded and adaptive control applications.

Findings

Demonstrates efficiency in numerical examples compared to traditional QP solvers.

Enables online model adaptation with low computational cost.

Suitable for deployment in industrial embedded platforms.

Abstract

This paper proposes a construction-free algorithm for solving linear MPC problems based on autoregressive with exogenous terms (ARX) input-output models. The solution algorithm relies on a coordinate-descent augmented Lagrangian (CDAL) method previously proposed by the authors, which we adapt here to exploit the special structure of ARX-based MPC. The CDAL-ARX algorithm enjoys the construction-free feature, in that it avoids explicitly constructing the quadratic programming (QP) problem associated with MPC, which would eliminate construction cost when the ARX model changes/adapts online. For example, the ARX model parameters are dependent on linear parameter-varying (LPV) scheduling signals, or recursively adapted from streaming input-output data with cheap computation cost, which make the ARX model widely used in adaptive control. Moreover, the implementation of the resulting CDAL-ARX algorithm is matrix-free and library-free, and hence amenable for deployment in industrial embedded platforms. We show the efficiency of CDAL-ARX in two numerical examples, also in comparison with MPC implementations based on other general-purpose quadratic programming solvers.