Towards scalable dynamical models: data-driven modeling, reduction, and control
File(s)
Author(s)
Mao, Junyu
Type
Thesis
Abstract
At the core of scientific discovery and engineering design lies a fundamental tension: real-world unfolds through complex, noisy, and high-dimensional dynamics, yet our ability to comprehend, predict, optimize and control such systems hinges on multiple layers of abstraction and simplification. Model reduction acts as one of the methodologies that empower us to systematically approximate and simplify dynamical systems, adjusting their dimensionality and complexity to align with available computational power, or conversely, scaling nowadays technical solutions to address large and intricate engineering challenges.
This thesis investigates problems in scalable system representation and control, offering several theoretical and methodological contributions. The thesis is structured into three main parts. The first part advances model reduction by moment matching. It extends classical results to Fornasini-Marchesini two-dimensional systems, where states evolve along multiple axes, and introduces a new characterization of moments via an explicit representation of interpolation conditions using a swapped interconnection, forming a dual perspective to existing theory. The second part adopts a data-centric approach, focusing on constructing reduced-order models directly from time-domain data without assuming full system knowledge. A theoretical foundation is developed for approximating moments through a swapped interconnection, which improves computational efficiency. Building on this, a complete pipeline is proposed to obtain a unique two-sided moment matching model from empirical data for linear time-invariant systems. This framework is further generalized to settings where interconnection behavior is preserved under inputs generated by systems beyond the linear class. Finally, the last part develops a unified framework for addressing a range of data-driven design problems for cascade systems from a behavioral perspective. This framework enables the exact computation of reduced-order models directly from system trajectories and extends naturally to other fundamental control problems, including output regulation and cascade stabilization.
This thesis investigates problems in scalable system representation and control, offering several theoretical and methodological contributions. The thesis is structured into three main parts. The first part advances model reduction by moment matching. It extends classical results to Fornasini-Marchesini two-dimensional systems, where states evolve along multiple axes, and introduces a new characterization of moments via an explicit representation of interpolation conditions using a swapped interconnection, forming a dual perspective to existing theory. The second part adopts a data-centric approach, focusing on constructing reduced-order models directly from time-domain data without assuming full system knowledge. A theoretical foundation is developed for approximating moments through a swapped interconnection, which improves computational efficiency. Building on this, a complete pipeline is proposed to obtain a unique two-sided moment matching model from empirical data for linear time-invariant systems. This framework is further generalized to settings where interconnection behavior is preserved under inputs generated by systems beyond the linear class. Finally, the last part develops a unified framework for addressing a range of data-driven design problems for cascade systems from a behavioral perspective. This framework enables the exact computation of reduced-order models directly from system trajectories and extends naturally to other fundamental control problems, including output regulation and cascade stabilization.
Version
Open Access
Date Issued
2025-12-14
Date Awarded
2026-05-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Scarciotti, Giordano
Publisher Department
Department of Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)