# Modularity-in-Design of Dynamical Network Systems: Retrofit Control Approach

## TL;DR

This paper presents a modular, decentralized control design method for linear dynamical networks, enabling local controllers to be added without destabilizing the system, demonstrated on a power system example.

## Contribution

It introduces a constrained Youla parameterization for retrofit controllers, ensuring stability and performance improvements in modular network control design.

## Key findings

- Retrofit controllers maintain system stability under subsystem variations.
- Multiple retrofit controllers can enhance overall control performance.
- The method is validated on a power system frequency regulation example.

## Abstract

In this paper, we develop a modular design method of decentralized controllers for linear dynamical network systems, where multiple subcontroller designers aim at individually regulating their local control performance with accessibility only to their respective subsystem models. First, we derive a constrained version of the Youla parameterization that characterizes all retrofit controllers for a single subcontroller, defined as an add-on type subcontroller that manages a subsystem. The resultant feedback system is kept robustly stable for any variation in the neighboring subsystems, other than the subsystem of interest, provided that the original system is stable prior to implementing the retrofit control. Subsequently, we find out a unique internal structure of the retrofit controllers, assuming that the interaction input signal from the neighboring subsystems is measurable. Furthermore, we show that the simultaneous implementation of multiple retrofit controllers, designed by individual subcontroller designers, can improve the upper bound of the overall control performance. Finally, the practical significance of the method is demonstrated via an illustrative example of frequency regulation using the IEEE 68-bus power system model.