Suboptimal MPC with a Computation Governor: Stability, Recursive Feasibility, and Applications to ADMM

TL;DR

This paper introduces a computational governor strategy for linear-quadratic MPC using inexact optimization methods like ADMM, ensuring stability and feasibility despite limited computation time.

Contribution

It develops conditions and procedures for adjusting reference commands and constraint tightening to guarantee stability and recursive feasibility in suboptimal MPC.

Findings

Ensures recursive feasibility with inexact optimization

Guarantees closed-loop stability under computation constraints

Provides an online method for reference adjustment and terminal set construction

Abstract

The paper considers a computational governor strategy to facilitate the implementation of Model Predictive Control (MPC) based on inexact optimization when the time available to compute the solution may be insufficient. In the setting of linear-quadratic MPC and a class of optimizers that includes Alternating Direction Method of Multipliers (ADMM), we derive conditions on the reference command adjustment by the computational governor and on a constraint tightening strategy which ensure recursive feasibility, convergence of the modified reference command, and closed-loop stability. An online procedure to select the modified reference command and construct an implicit terminal set is also proposed. A simulation example is reported which illustrates the developed procedures.