# Distributed Model Predictive Control Under Inexact Primal-Dual Gradient Optimization Based on Contraction Analysis

## TL;DR

This paper proposes a distributed model predictive control approach for linear systems with coupled constraints, utilizing primal-dual gradient optimization and contraction analysis to ensure convergence, stability, and reduced computation.

## Contribution

It introduces a novel DMPC method based on inexact primal-dual gradient optimization with contraction analysis for convergence and stability guarantees.

## Key findings

- Ensures recursive feasibility and stability under inexact solutions.
- Uses contraction theory for convergence analysis of primal-dual methods.
- Validates the approach with numerical simulation results.

## Abstract

This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all subsystems, which is solved by means of the primal-dual gradient optimization in a distributed manner using Laplacian consensus. To reduce the computational burden, the constraint tightening method is utilized to provide a capability of premature termination with guaranteeing the convergence of the DMPC optimization. The contraction theory is first adopted in the convergence analysis of the primal-dual gradient optimization under discrete-time updating dynamics towards a nonlinear objective function. Under some reasonable assumptions, the recursive feasibility and stability of the closed-loop system can be established under the inexact solution. A numerical simulation is given to verify the performance of the proposed strategy.