# Weak Interactions Based System Partitioning Using Integer Linear Programming

## TL;DR

This paper presents a method for system partitioning based on minimizing weak interactions between subsystems using linear integer programming, aiding in controller design by identifying controllable subsystem groupings.

## Contribution

The paper introduces a novel linear integer programming approach to system partitioning that minimizes interactions and ensures controllability of subsystems.

## Key findings

- Effective partitioning with minimal interactions demonstrated
- Method ensures controllability of resulting subsystems
- Two example applications validate the approach

## Abstract

The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given partitioning, the total magnitude of the interactions between subsystem models is evaluated. Therefore, the partitioning problem seeking for weak interactions can be posed as a minimization problem. Initially, the problem is formulated as a non-linear integer minimization that is then relaxed into a linear integer programming problem. It is shown within this paper that cuts can be applied to the initial search space in order to find the least interacting partitioning; only composed of controllable subsystems. Two examples are given to demonstrate the methodology.