Distributed MPC with ALADIN -- A Tutorial

Abstract

This paper consists of a tutorial on the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) and its application to distributed model predictive control (MPC). The focus is - for simplicity of presentation - on convex quadratic programming (QP) formulations of MPC. It is explained how ALADIN can be used to synthesize sparse QP solvers for large-scale linear-quadratic optimal control by combining ideas from augmented Lagrangian methods, sequential quadratic programming, as well as barrier or interior point methods. The highlight of this tutorial is a real-time ALADIN variant that can be implemented with a few lines of code yet arriving at a sparse QP solver that can compete with mature open-source and commercial QP solvers in terms of both run-time as well as numerical accuracy. It is discussed why this observation could have far reaching consequences on the future of algorithm and software development in the field of large-scale optimization and MPC.