arXiv subjects

Nicholas J. Watkins

Publications and source records attributed to Nicholas J. Watkins.

6 recordsLinked to original sources

arXiv2019

Robust Economic Model Predictive Control of Continuous-time Epidemic Processes

In this paper, we develop a robust economic model predictive controller for the containment of stochastic Susceptible-Exposed-Infected-Vigilant (SEIV) epidemic processes which drives the process to extinction quickly, while minimizing the rate at which control resources are used. The work we present here is significant in that it addresses the problem of efficiently controlling general stochastic epidemic systems without relying on mean-field approximation, which is an important issue in the theory of stochastic epidemic processes. This enables us to provide rigorous convergence guarantees on the stochastic epidemic model itself, improving over the mean-field type convergence results of most prior work. There are two primary technical difficulties addressed in treating this problem: (i) constructing a means of tractably approximating the evolution of the process, so that the designed approximation is robust to the modeling error introduced by the applied moment closure, and (ii) guaranteeing that the designed controller causes the closed-loop system to drive the SEIV process to extinction quickly. As an application, we use the developed framework for optimizing the use of quarantines in containing an SEIV epidemic outbreak.

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arXiv2018

Control of Generalized Discrete-time SIS Epidemics via Submodular Function Minimization

In this paper, we study a novel control method for a generalized SIS epidemic process. In particular, we use predictive control to design optimal protective resource distribution strategies which balance the need to eliminate the epidemic quickly against the need to limit the rate at which protective resources are used. We expect that such a controller may be useful in mitigating the spread of biological diseases which do not confer immunity to those who have been infected previously, with sexually transmitted infections being a prominent example of such. Technically, this paper provides a novel contribution in demonstrating that the particular combinatorial optimal control problem used to design resource allocations has an objective function which is submodular, and so can be solved in polynomial time despite its combinatorial nature. We test the performance of the proposed controller with numerical simulations, and provide some comments on directions for future work.

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arXiv2017

Stability of Control Systems with Feedback from Energy Harvesting Sensors

In this paper, we study the problem of certifying the stability of a closed loop system which receives feedback from an energy harvesting sensor. This is important, as energy harvesting sensors are recharged stochastically, and may only be able to provide feedback intermittently. Thus, stabilizing plants with feedback provided by energy harvesting sensors is challenging in that the feedback signal is only available stochastically, complicating the analysis of the closed-loop system. As the main contribution of the paper, we show that for a broad class of energy harvesting processes and transmission policies, the system can be modeled as a Markov jump linear system (MJLS), which thereby enables a rigorous stability analysis. We discuss the types of transmission policies and energy harvesting processes which can be accommodated in detail, demonstrating the generality of the results.

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arXiv2017

Inference, Prediction, and Control of Networked Epidemics

We develop a feedback control method for networked epidemic spreading processes. In contrast to most prior works which consider mean field, open-loop control schemes, the present work develops a novel framework for feedback control of epidemic processes which leverages incomplete observations of the stochastic epidemic process in order to control the exact dynamics of the epidemic outbreak. We develop an observation model for the epidemic process, and demonstrate that if the set of observed nodes is sufficiently well structured, then the random variables which denote the process' infections are conditionally independent given the observations. We then leverage the attained conditional independence property to construct tractable mechanisms for the inference and prediction of the process state, avoiding the need to use mean field approximations or combinatorial representations. We conclude by formulating a one-step lookahead controller for the discrete-time Susceptible-Infected-Susceptible (SIS) epidemic process which leverages the developed Bayesian inference and prediction mechanisms, and causes the epidemic to die out at a chosen rate.

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arXiv2015

Optimal resource allocation for competitive spreading processes on bilayer networks

This paper studies the SI1SI2S spreading model of two competing behaviors over a bilayer network. We address the problem of determining resource allocation strategies which design a spreading network so as to ensure the extinction of a selected process. Our discussion begins by extending the SI1SI2S model to edge-dependent infection and node-dependent recovery parameters with generalized graph topologies, which builds upon prior work that studies the homogeneous case. We then find conditions under which the mean-field approximation of a chosen epidemic process stabilizes to extinction exponentially quickly. Leveraging this result, we formulate and solve an optimal resource allocation problem in which we minimize the expenditure necessary to force a chosen epidemic process to become extinct as quickly as possible. In the case that the budget is not sufficient to ensure extinction of the desired process, we instead minimize a useful heuristic. We explore the efficacy of our methods by comparing simulations of the stochastic process to the mean-field model, and find that the mean-field methods developed work well for the optimal cost networks designed, but suffer from inaccuracy in other situations.

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arXiv2015

Deterministic Bounding Systems for Stochastic Compartmental Spreading Processes

This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly requiring a priori knowledge of non-negative (or non-positive) covariance between pairs of system variables. Moreover, we provide systems which provide both upper- and lower- bounds on the process moments. We then show that when system variables are shown to be non-negatively (or non-positively) correlated for all time in the system's evolution, we may leverage the knowledge to create better approximating systems. We then apply the technique to several previously studied compartmental spreading processes, and compare the bounding systems' performance to the standard approximations studied in prior literature.

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