ADMM for MPC with state and input constraints, and input nonlinearity

TL;DR

This paper introduces an ADMM-based algorithm for solving nonconvex MPC problems with constraints and nonlinear input maps, aiming for real-time hybrid vehicle control, demonstrating effective approximate solutions with some limitations.

Contribution

The paper develops a novel ADMM algorithm tailored for nonconvex constrained MPC problems with nonlinearities, providing convergence proofs and practical insights.

Findings

Effective for approximate solutions in real-time applications

Converges to points satisfying necessary optimality conditions

Limitations observed when exact solutions are needed

Abstract

In this paper we propose an Alternating Direction Method of Multipliers (ADMM) algorithm for solving a Model Predictive Control (MPC) optimization problem, in which the system has state and input constraints and a nonlinear input map. The resulting optimization is nonconvex, and we provide a proof of convergence to a point satisfying necessary conditions for optimality. This general method is proposed as a solution for blended mode control of hybrid electric vehicles, to allow optimization in real time. To demonstrate the properties of the algorithm we conduct numerical experiments on randomly generated problems, and show that the algorithm is effective for achieving an approximate solution, but has limitations when an exact solution is required.