On a Canonical Distributed Controller in the Behavioral Framework

TL;DR

This paper introduces a canonical distributed controller within the behavioral framework, enabling decentralized control of interconnected systems without predefined input-output roles, and establishes conditions for regular interconnections.

Contribution

It presents a novel canonical distributed controller for behavioral systems and provides conditions for regular interconnections in decentralized control design.

Findings

The canonical distributed controller can implement desired interconnected behaviors.

Conditions for regularity of interconnections are established.

Interconnection regularity of subsystems is characterized by the plant and behavior interconnections.

Abstract

Control in a classical transfer function or state-space setting typically views a controller as a signal processor: sensor outputs are mapped to actuator inputs. In behavioral system theory, control is simply viewed as interconnection; the interconnection of a plant with a controller. In this paper we consider the problem of control of interconnected systems in a behavioral setting. The behavioral setting is especially fit for modelling interconnected systems, because it allows for the interconnection of subsystems without imposing inputs and outputs. We introduce a so-called canonical distributed controller that implements a given interconnected behavior that is desired, provided that necessary and sufficient conditions hold true. The controller design can be performed in a decentralized manner, in the sense that a local controller only depends on the local system behavior. Regularity of interconnections is an important property in behavioral control that yields feedback interconnections. We provide conditions under which the interconnection of this distributed controller with the plant is regular. Furthermore, we show that the interconnections of subsystems of the canonical distributed controller are regular if and only if the interconnections of the plant and desired behavior are regular.