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Sean Warnick

Sean Warnick appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Systems and Controlmath.OCArtificial IntelligenceMachine LearningQuantitative Methods

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Published work

6 published item(s)

preprint2026arXiv

A Generalized Singular Value Theory for Neural Networks

Building on the abstract Generalized Singular Value Decomposition (GSVD) theory of Brown et al. [2025], we prove that most modern neural architectures admit a generalized SVD representation in which they are left-invertible before a final linear layer, with no change in input-output behavior. Furthermore, the left-invertible nonlinear portion of the input-output behavior can be made to be \emph{norm preserving}, meaning that perturbations in the left-invertible ``embedding'' (the activations prior to the final linear layer in this representation) correspond proportionally to changes in the input, i.e., distance in feature space can be calibrated directly to distance in input space. We provide a data-driven algorithm for estimating this representation from trained models and propose a model architecture that naturally facilitates the decomposition. We then provide a proof-of-concept that the learned representation can be used to identify adversarial perturbations to model inputs, and develop the theory necessary for future applications to areas such as model bias and invertibility.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Optimal distributed control for platooning via sparse coprime factorizations

We introduce a novel distributed control architecture for heterogeneous platoons of linear time--invariant autonomous vehicles. Our approach is based on a generalization of the concept of {\em leader--follower} controllers for which we provide a Youla--like parameterization while the sparsity constraints are imposed on the controller's left coprime factors, outlying a new concept of structural constraints in distributed control. The proposed scheme is amenable to optimal controller design via norm based costs, it guarantees string stability and eliminates the accordion effect from the behavior of the platoon. We also introduce a synchronization mechanism for the exact compensation of the time delays induced by the wireless broadcasting of information.

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preprint2014arXiv

Meanings and Applications of Structure in Networks of Dynamic Systems

This chapter reviews four notions of system structure, three of which are contextual and classic (i.e. the complete computational structure linked to a state space model, the sparsity pattern of a transfer function, and the interconnection of subsystems) and one which is relatively new (i.e. the signal structure of a system's dynamical structure function). Although each of these structural concepts apply to the nonlinear and stochastic setting, this work will focus on linear time invariant systems to distill the key concepts and make their relationships clear. We then discusses three applications of the newest structural form (the signal structure of a system's dynamical structure function): network reconstruction, vulnerability analysis, and a recent result in distributed control that guarantees the synthesis of a stabilizing controller with a specified structure or proves that no such controller exists.

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preprint2013arXiv

A Novel Description of Linear Time--Invariant Networks via Structured Coprime Factorizations

In this paper we study state-space realizations of Linear and Time-Invariant (LTI) systems. Motivated by biochemical reaction networks, Gonçalves and Warnick have recently introduced the notion of a {\em Dynamical Structure Functions} (DSF), a particular factorization of the system's transfer function matrix that elucidates the interconnection structure in dependencies between manifest variables. We build onto this work by showing an intrinsic connection between a DSF and certain sparse left coprime factorizations. By establishing this link, we provide an interesting systems theoretic interpretation of sparsity patterns of coprime factors. In particular we show how the sparsity of these coprime factors allows for a given LTI system to be implemented as a network of LTI sub-systems. We examine possible applications in distributed control such as the design of a LTI controller that can be implemented over a network with a pre-specified topology.

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preprint2012arXiv

A Technique for Designing Stabilizing Distributed Controllers with Arbitrary Signal Structure Constraints

This paper presents a new approach to distributed controller design that exploits a partial-structure representation of linear time invariant systems to characterize the structure of a system. This partial-structure representation, called the dynamical structure function, characterizes the {\em signal structure}, or open-loop causal dependencies among manifest variables, capturing a significantly richer notion of structure than the sparsity pattern of the transfer function. The design technique sequentially constructs each link in an arbitrary controller signal structure, and the main result proves that the resulting controller is either stabilizing or no controller with the desired structure can stabilize the system.

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preprint2012arXiv

Minimal realization of the dynamical structure function and its application to network reconstruction

Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the minimal number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the minimal number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterizes minimal order state-space realizations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing an algorithm to explicitly obtain such a minimal realization.

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