An Optimal Controller Architecture for Poset-Causal Systems

TL;DR

This paper introduces a new decentralized control architecture for poset-structured systems, leveraging Moebius inversion, and proves its optimality in the H_2 sense, with simple separation properties and decoupled analysis.

Contribution

It presents a novel controller architecture based on poset theory, connecting order theory with control, and proves its H_2 optimality for poset-structured systems.

Findings

The proposed architecture simplifies analysis via decoupled subsystems.

It establishes a deep connection between order theory and control concepts.

The H_2-optimal controller inherently has the proposed structure.

Abstract

We propose a novel and natural architecture for decentralized control that is applicable whenever the underlying system has the structure of a partially ordered set (poset). This controller architecture is based on the concept of Moebius inversion for posets, and enjoys simple and appealing separation properties, since the closed-loop dynamics can be analyzed in terms of decoupled subsystems. The controller structure provides rich and interesting connections between concepts from order theory such as Moebius inversion and control-theoretic concepts such as state prediction, correction, and separability. In addition, using our earlier results on H_2-optimal decentralized control for arbitrary posets, we prove that the H_2-optimal controller in fact possesses the proposed structure, thereby establishing the optimality of the new controller architecture.