Networked Dynamical Systems: Privacy, Control, and Cognition

Many natural and man-made systems, ranging from thenervous system to power and transportation grids to societies, exhibitdynamic behaviors that evolve over a sparse and complex network. This networked aspect raises significant challenges and opportunities for the identification, analysis, and control of such dynamic behaviors. While some of these challenges emanate from the networked aspect \emph{per se} (such as the sparsity of connections between system components and the interplay between nodal \emph{communication} and network dynamics), various challenges arise from the specific application areas (such as privacy concerns in cyber-physical systems or the need for \emph{scalable} algorithm designs due to the large size of various biological and engineered networks). On the other hand, networked systems provide significant opportunities and allow for performance and robustness levels that are far beyond reach for centralized systems, with examples ranging from the Internet (of Things) to the smart grid and the brain. This dissertation aims to address several of these challenges and harness these opportunities. The dissertation is divided into three parts. In the first part, we study privacy concerns whose resolution is vital for the utility of networked cyber-physical systems. We study the problems of average consensus and convex optimization as two principal distributed computations occurring over networks and design algorithm with rigorous privacy guarantees that provide a \emph{best achievable} tradeoff between network utility and privacy. In the second part, we analyze networks with resource constraints. More specifically, we study three problems of stabilization under communication (bandwidth and latency) limitations in sensing and actuation, optimal time-varying control scheduling problem under limited number of actuators and control energy, and the structure identification problem of under-sensed networks (i.e., networks with latent nodes). Finally in the last part, we focus on the intersection of networked dynamical systems and neuroscience and draw connections between brain network dynamics and two extensively studied but yet not fully understood neuro-cognitive phenomena: goal-driven selective attention and neural oscillations. Using a novel axiomatic approach, we establish these connections in the form of necessary and/or sufficient conditions on the network structure that match the network output trajectories with experimentally observed brain activity

Parameterized Learning and Distillation with Vortex-encoded Spectral Correlations

Spectral computational methods leverage modal or nonlocal representations of data, and a physically realized approach to spectral computation pertains to encoded diffraction. Encoded diffraction offers a hybrid approach that pairs analog wave propagation with digital back-end electronics, however the intermediate sensor patterns are correlations rather than linear signal weights, which limits the development of robust and efficient downstream analyses. Here, with vortex encoders, we show that the solution for the signal field from sensor intensity adopts the form of polynomial regression, which is subsequently solved with a learned, linear transformation. This result establishes an analytic rationale for a spectral-methods paradigm in physically realized machine learning systems. To demonstrate this paradigm, we quantify the learning that is transferred with an image basis using speckle parameters, Singular-Value Decomposition Entropy ($H_{SVD}$) and Speckle-Analogue Density (SAD). We show that $H_{SVD}$, a proxy for image complexity, indicates the rate at which a model converges. Similarly, SAD, an averaged spatial frequency, marks a threshold for structurally similar reconstruction. With a vortex encoder, this approach with parameterized training may be extended to distill features. In fact, with images reconstructed with our models, we achieve classification accuracies that rival decade-old, state-of-the-art computer algorithms. This means that the process of learning compressed spectral correlations distills features to aid image classification, even when the goal images are feature-agnostic speckles. Our work highlights opportunities for analytic and axiom-driven machine-learning designs appropriate for real-time applications.Comment: Code is available at: https://github.com/altaiperry/Reconstruction23_Perr