# A Complexity Analysis of Event-Triggered Model Predictive Control on Industrial Hardware

## TL;DR

This paper evaluates the practical implementation of event-triggered model predictive control on industrial hardware, analyzing computational and bandwidth trade-offs through theoretical and empirical methods.

## Contribution

It provides a detailed complexity analysis of different implementation variants, combining theoretical insights with real-world hardware experiments.

## Key findings

- Bandwidth is minimized when transmitting only active constraints.
- Computational cost scales nearly linearly with problem size in practice.
- Implementation results confirm theoretical complexity analysis.

## Abstract

We implement a recently proposed event-triggered networked MPC approach on industrial hardware to analyze its practical relevance. There exist several alternatives for such an implementation that differ with respect to the distribution of computational load between local and central nodes, and with respect to network bandwidth requirements. These alternatives have been analyzed theoretically before, but when implemented it becomes evident that their usefulness cannot be predicted based on theoretical considerations alone. It is the purpose of the present paper to account for both practical and theoretical aspects in determining which alternative is most appropriate for an implementation on industrial hardware. The smallest possible bandwidth is known to result for a variant in which only the active set of constraints is transmitted from the central to the local nodes. Since local nodes must determine the control law from the active set in this case, which requires matrix inversions, an unattractive computational cost results at first sight. Somewhat surprisingly, the computational cost scales practically linearly in the problem size when implemented. We confirm this result with a more detailed theoretical complexity analysis than given in previous papers. All results are illustrated with data obtained with an implementation on industrial hardware components.