Abstract

Precise and robust manipulation of large populations of structurally identical dynamical systems with heterogeneous dynamics, known as ensemble systems, is a central challenge in many emerging applications. These systems are often difficult to analyze and control because of the inherent nonlinearities, high dimensionality, heterogeneity, and incomplete knowledge of the underlying dynamics. To address these challenges, this thesis develops structured and interpretable representations for the analysis, control, and learning of nonlinear ensemble systems. Its central objective is to transform complex heterogeneous dynamics into representations that preserve essential structural and dynamical properties while enabling tractable computation and effective control design. First, the Exact Bilinearization Iterative Form is introduced as a systematic framework for determining when nonlinear control-affine systems admit exact finite-dimensional bilinear representations. This framework is then used in applications to feedback stabilization, algebraic- and zonotope-based reachability analysis, and geometric optimal control. Second, a moment-kernelization framework is developed for studying ensemble systems, transforming infinite-dimensional parameterized dynamics into moment representations suitable for finite-dimensional approximation. This framework facilitates fundamental system tasks such as tracking, steering, and stabilization, and enables a range of diverse quantum ensemble control applications, including robust spin manipulation, coherence transfer, and control of Bose-Einstein condensates in the presence of parameter inhomogeneity. Finally, reservoir-computing-based methods are developed for data-driven control and learning in settings where models are unknown or data are incomplete, yielding causal operator representations for nonlinear ensemble control and iterative learning algorithms for irregular time-series reconstruction. By combining exact bilinear embeddings, moment representations, and reservoir-induced operators, this thesis provides concrete tools for analyzing nonlinear systems, designing robust controls for heterogeneous quantum ensembles, and learning control and reconstruction maps directly from dynamic data.

Committee Chair

Jr-Shin Li

Committee Members

Andrew Clark; Shen Zeng; Vignesh Narayanan; Xudong Chen

Degree

Doctor of Philosophy (PhD)

Author's Department

Electrical & Systems Engineering

Author's School

McKelvey School of Engineering

Document Type

Dissertation

Date of Award

8-19-2026

Language

English (en)

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