Parameterization of Retrofit Controllers

TL;DR

This paper presents a generalized parameterization framework for retrofit controllers, enabling modular control design in complex network systems without stability or measurability assumptions, by extending existing theories to unstable systems.

Contribution

It extends the Youla parameterization approach for retrofit controllers to unstable systems and provides an explicit geometric control theory-based description, removing previous technical assumptions.

Findings

Retrofit controllers can be designed for unstable systems.

The framework allows modular control design without stability assumptions.

Explicit geometric descriptions facilitate controller synthesis.

Abstract

This study investigates a parameterization of all retrofit controllers. Retrofit control can accomplish modular design of control systems, i.e., independent design of subcontrollers only with its corresponding subsystem model in a dynamical network system. In the retrofit control framework, the network system to be controlled is regarded as an interconnected system composed of the subsystem of interest and an environment. Existing studies have revealed that all retrofit controllers can be characterized as a constrained Youla parameterization under the technical assumption that the subsystem of interest is stable. It has also been discovered that all of the retrofit controllers that belong to a particular tractable class have a distinctive internal structure composed of a rectifier and an internal controller under the additional technical assumption that the interconnection signal from the environment to the subsystem of interest is measurable or that the internal state of the subsystem of interest is measurable. Due to the internal structure, the retrofit controller design problem under the assumptions can be reduced to a standard controller design problem to which existing controller synthesis techniques can be applied. The aim of this paper is to extend the above results without the technical assumptions. It is found that the existing developments can naturally be generalized through the Youla parameterization for unstable systems and an explicit description of the inverse system with the geometric control theory. The result leads to the conclusion that retrofit controllers can readily be designed even in the general case.