Bridging Abstraction-Based Hierarchical Control and Moment Matching: A Conceptual Unification

TL;DR

This paper unifies hierarchical control and moment matching frameworks by establishing a conceptual connection, especially in linear systems, enabling cross-disciplinary insights and advancements.

Contribution

It provides a theoretical link between approximate-simulation-based hierarchical control and moment matching, enhancing understanding and potential integration of these methods.

Findings

Both frameworks' key requirements can be interpreted via moment matching.

The connection is explicitly demonstrated for linear time-invariant systems.

This unification facilitates cross-pollination of ideas between control and system identification.

Abstract

In this paper, we establish a relation between approximate-simulation-based hierarchical control (ASHC) and moment matching techniques, and build a conceptual bridge between these two frameworks. To this end, we study the two key requirements of the ASHC technique, namely the bounded output discrepancy and the $M$-relation, through the lens of moment matching. We show that, in the linear time-invariant case, both requirements can be interpreted in the moment matching perspective through certain system interconnection structures. Building this conceptual bridge provides a foundation for cross-pollination of ideas between these two frameworks.