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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics$
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G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Print publication date: 2012

Print ISBN-13: 9780691142173

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142173.001.0001

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(p.263) Chapter Thirteen Controllability
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Princeton University Press

This chapter addresses the problem of controllability for stochastic complex electromagnetic media. The starting point is the stochastic integrodifferential equations that model the evolution of the fields, with a control procedure to be selected so that the system is driven to a desired final state. The controllability problem for stochastic media is more complicated than that for deterministic media and includes subtleties that must be addressed to reach a satisfactory answer. Hence, this chapter sets the model and then discusses the subtle issues introduced by the stochasticity in the controllability problem. It then proposes two different approaches towards controllability: an approach using PDEs with random coefficients and an approach using backward stochastic evolution equations (BSEEs). Afterward, the chapter lists several comments concerning boundary controllability and optimal control.

Keywords:   controllability, stochastic complex electromagnetic media, stochastic integrodifferential equations, stochasticity, controllability problem, random coefficients, backward stochastic evolution equations, boundary controllability, optimal control

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