H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback

TL;DR

This paper presents a comprehensive state-space method for designing H_2-optimal decentralized controllers for poset-causal systems with state-feedback, leveraging problem separability for efficient computation and revealing structural controller insights.

Contribution

It introduces a novel state-space solution exploiting separability, providing explicit controller structure and degree bounds based on poset structure.

Findings

Efficient controller computation via uncoupled Riccati equations

Structural insights into controller degree bounds

Numerical example demonstrating the approach

Abstract

We develop a complete state-space solution to H_2-optimal decentralized control of poset-causal systems with state-feedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a remarkable pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to prediction of the state along the different paths on the poset. The results are illustrated by a numerical example.