Bridging Abstraction-Based Hierarchical Control and Moment Matching: A Conceptual Unification
Zirui Niu, Mohammad Fahim Shakib, Giordano Scarciotti
TL;DR
The paper tackles the computational burden of large-scale dynamical systems by linking moment matching with ASHC, recasting ASHC's bounded-output discrepancy and M-relations as moment-matching constraints via Sylvester equations and interconnections. It demonstrates one-to-one moment relationships in direct interconnections, offers Sylvester-equation conditions for M-relations, and validates the framework on a two-spring-two-mass example. This conceptual unification enables cross-pollination of methods between moment matching and ASHC and suggests extensions to nonlinear, time-delay, and data-driven settings. The work points to rich future directions where such cross-pollination yields computationally efficient, verifiable approaches for complex dynamics.
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.