arXiv subjects

Claire Walton

Publications and source records attributed to Claire Walton.

5 recordsLinked to original sources

arXiv2026

Modeling Large-Scale Adversarial Swarm Engagements using Optimal Control

We study optimal control of large-scale autonomous systems under adversarial conditions in which agents may be probabilistically destroyed during an engagement. Because attrition changes the population that generates the spatial interaction dynamics, treating survival and motion independently can produce physically inconsistent solutions. We formulate a stochastic variable-population benchmark and examine three deterministic approximations that propagate agent survival probabilities from relative geometry. The models are applied to defense of a high-value unit against an attacking swarm and solved using direct optimal-control methods. Monte Carlo realizations of the stochastic benchmark show that deterministic models can reproduce engagement outcomes when attrition is coupled to spatial influence, whereas a decoupled formulation can exploit effectively destroyed defenders that continue to repel attackers, a failure mode we term ``ghost herding.'' Large-scale simulations and defender-number sweeps further show that this modeling choice can substantially alter predicted high-value-unit survival and inferred defensive resource requirements. The results provide a tractable framework for attrition-aware trajectory optimization and resource--survival analysis in adversarial autonomous systems.

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arXiv2024

Approximability of deep computations

This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of the series, we characterize deep computations that are bona fide computable, and prove the existence of deep equilibria, which hitherto have been found only empirically in deep learning. A subsequent paper will study the complexity of ultracomputations. Our approach adapts and combines technology from topology of function spaces, structural Ramsey theory, topological dynamics, and model theory.

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arXiv2021

Defense Against Adversarial Swarms with Parameter Uncertainty

This paper addresses the problem of optimal defense of a High Value Unit against a large-scale swarm attack. We show that the problem can be cast in the framework of uncertain parameter optimal control and derive a consistency result for the dual problem of this framework. We show that the dual can be computed numerically and apply these numerical results to derive optimal defender strategies against a 100 agent swarm attack.

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arXiv2021

Modeling and Control of Large-Scale Adversarial Swarm Engagements

We theoretically and numerically study the problem of optimal control of large-scale autonomous systems under explicitly adversarial conditions, including probabilistic destruction of agents during the simulation. Large-scale autonomous systems often include an adversarial component, where different agents or groups of agents explicitly compete with one another. An important component of these systems that is not included in current theory or modeling frameworks is random destruction of agents in time. In this case, the modeling and optimal control framework should consider the attrition of agents as well as their position. We propose and test three numerical modeling schemes, where survival probabilities of all agents are smoothly and continuously decreased in time, based on the relative positions of all agents during the simulation. In particular, we apply these schemes to the case of agents defending a high-value unit from an attacking swarm. We show that these models can be successfully used to model this situation, provided that attrition and spatial dynamics are coupled. Our results have relevance to an entire class of adversarial autonomy situations, where the positions of agents and their survival probabilities are both important.

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arXiv2018

Bernstein approximation of optimal control problems

Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been made. Perhaps they will find application when the properties of the approximant in the large are of more importance than the closeness of the approximation." -- has remarked P.J. Davis in his 1963 book Interpolation and Approximation. This paper presents a direct approximation method for nonlinear optimal control problems with mixed input and state constraints based on Bernstein polynomial approximation. We provide a rigorous analysis showing that the proposed method yields consistent approximations of time continuous optimal control problems. Furthermore, we demonstrate that the proposed method can also be used for costate estimation of the optimal control problems. This latter result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we explore the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the proposed approximation method through several numerical examples.

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