TY - GEN

T1 - A Hamilton-jacobi equation for evaluating eemi propagation in a computing system

AU - Valbuena, Luis

AU - Heileman, Gregory L.

AU - Hemmady, Sameer

AU - Schamiloglu, Edl

N1 - Publisher Copyright: © 2019 IEEE.

PY - 2019/9

Y1 - 2019/9

N2 - In this paper, we present a theoretical framework for modeling the empirically observed cascading of software failures on a complicated computing system exposed to extreme electromagnetic interference (EEMI). Our approach is to treat the temporal evolution of the electromagnetic coupling and the resultant cascading series of electromagnetic-induced faults as the 'flow' in a dynamic fluid-mechanical system and thereby utilize aspects of the Navier Stokes and Hamilton-Jacobi equations to predict the rate of this flow. Therefore, inspired by the concepts of fluid dynamics [1], we include a diffusion term in the Hamilton-Jacobi-Isaacs (HJI) equation. We have considered two approaches. In one we apply a Taylor expansion to the optimality principle and consider additional terms; in the other scenario, we simply add a diffusion term in the form of a Laplacian applied to the cost function H(mathbf{x},ldots) and some constant mathbf{c}, as it is present in the Navier-Stokes equation for incompressible flow. We provide numerical comparisons for both approaches with respect to the original HJI equation where the dynamical vector field corresponds to analytical models of a NOR logic gate. This model is a second-order differential equation that describes the behavior of the gate that incorporates a new term accounting for EEMI injection.

AB - In this paper, we present a theoretical framework for modeling the empirically observed cascading of software failures on a complicated computing system exposed to extreme electromagnetic interference (EEMI). Our approach is to treat the temporal evolution of the electromagnetic coupling and the resultant cascading series of electromagnetic-induced faults as the 'flow' in a dynamic fluid-mechanical system and thereby utilize aspects of the Navier Stokes and Hamilton-Jacobi equations to predict the rate of this flow. Therefore, inspired by the concepts of fluid dynamics [1], we include a diffusion term in the Hamilton-Jacobi-Isaacs (HJI) equation. We have considered two approaches. In one we apply a Taylor expansion to the optimality principle and consider additional terms; in the other scenario, we simply add a diffusion term in the form of a Laplacian applied to the cost function H(mathbf{x},ldots) and some constant mathbf{c}, as it is present in the Navier-Stokes equation for incompressible flow. We provide numerical comparisons for both approaches with respect to the original HJI equation where the dynamical vector field corresponds to analytical models of a NOR logic gate. This model is a second-order differential equation that describes the behavior of the gate that incorporates a new term accounting for EEMI injection.

KW - EEMI

KW - Electromagnetics

KW - Hamilton-Jacobi-Isaacs

UR - http://www.scopus.com/inward/record.url?scp=85074924404&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074924404&partnerID=8YFLogxK

U2 - 10.1109/ICEAA.2019.8879393

DO - 10.1109/ICEAA.2019.8879393

M3 - Conference contribution

T3 - Proceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

SP - 851

EP - 856

BT - Proceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

Y2 - 9 September 2019 through 13 September 2019

ER -