Scheduling and control over networks using MPC with time-varying terminal ingredients: extended version

TL;DR

This paper introduces a novel MPC approach with time-varying terminal ingredients for networked control systems, reducing computational complexity and increasing robustness compared to traditional rollout methods.

Contribution

It proposes a periodically time-varying terminal region and cost in MPC, applicable to resource-constrained networks, with proven convergence guarantees for specific network setups.

Findings

Enhanced stability with lower computational complexity

Demonstrated improved robustness in numerical examples

Applicable to token bucket and actuator scheduling networks

Abstract

Rollout approaches are an effective tool to address the problem of co-designing the transmission schedule and the corresponding input values, when the controller is connected to the plant via a resource-constrained communication network. These approaches typically employ an MPC, activated at multiples of the period length of a base transmission schedule. Using multi-step invariant terminal regions and a prediction horizon longer than the base period, stability can be ensured. This strategy, however, suffers from intrinsic shortcomings, such as a high computational complexity and low robustness. We aim to resolve these drawbacks by proposing an MPC with periodically time-varying terminal region and cost for the rollout setup, where the controller is activated at each time instant and features an arbitrary but fixed prediction horizon. We consider in more detail two specific setups from the literature on Networked Control Systems, namely the token bucket network and actuator scheduling. For both setups, we provide conditions for which convergence under application of the time-varying MPC can be guaranteed. In two numerical examples, we demonstrate the benefits of the proposed method.