Online Computation of Terminal Ingredients in Distributed Model Predictive Control for Reference Tracking

TL;DR

This paper introduces a distributed model predictive control scheme that reconfigures the terminal set online without centralized computations, using an SDP approximation scalable for distributed optimization, demonstrated on a power network example.

Contribution

It proposes a novel distributed MPC scheme with online terminal set reconfiguration and an SDP approximation method for scalable distributed optimization.

Findings

Fixing the terminal controller improves performance.

The scheme achieves large feasible regions without centralized computations.

The approximate SDP method reduces computational costs.

Abstract

A distributed model predictive control scheme is developed for tracking piecewise constant references where the terminal set is reconfigured online, whereas the terminal controller is computed offline. Unlike many standard existing schemes, this scheme yields large feasible regions without performing offline centralized computations. Although the resulting optimal control problem (OCP) is a semidefinite program (SDP), an SDP scalability method based on diagonal dominance is used to approximate the derived SDP by a second-order cone program. The OCPs of the proposed scheme and its approximation are amenable to distributed optimization. Both schemes are evaluated using a power network example and compared to a scheme where the terminal controller is reconfigured online as well. It is found that fixing the terminal controller results in better performance, noticeable reduction in computational cost and similar feasible region compared to the case in which this controller is reconfigured online.