Parametrization of the regular equivalences of the canonical controller and its applications

TL;DR

This paper provides a parametrization of all regular controllers equivalent to the canonical controller in linear systems, enabling solutions to control design problems with minimal control channels and specific input-output constraints.

Contribution

It introduces a novel parametrization of regular controllers equivalent to the canonical controller, facilitating new control design algorithms.

Findings

Parametrization of all regular controllers equivalent to the canonical controller.

Algorithms for designing controllers with minimal control channels.

Algorithms for controllers satisfying input-output partitioning constraints.

Abstract

We study control problems for linear systems in the behavioral framework. Our focus is a class of regular controllers that are equivalent to the canonical controller. The canonical controller is a particular controller that is guaranteed to be a solution whenever a solution exists. However, it has been shown that in most cases, the canonical controller is not regular. The main result of the paper is a parametrization of all regular controllers that are equivalent to the canonical controller. The parametrization is then used to solve two control problems. The first problem is related to designing a regular controller that uses as few control channels as possible. The second problem is to design a regular controller that satisfies a predefined input-output partitioning constraint. In both problems, based on the parametrization, we present algorithms that does the controller design.