Optimal Control, Estimation, and Shape Design: Analysis and Applications

Abstract

This work considers applied optimization in several contexts.Generally, we consider the optimal design of Traveling Wave Tubes (TWTs) and electron guns and the application of optimal control to human immunodeficiency virus (HIV) treatment schedules.First, we consider the optimal design of electron guns using the 3D finite element code Beam Optics Analysis (BOA).Specifically, we consider the design of a Pierce gun that will be used in a 10MW multiple beam klystron at L-Band and a sheet beam gun (SBG).We consider various design considerations including beam shape, current, and electric field properties.Secondly, we consider the design of TWTs, which are vacuum electron devices used for the amplification of radio frequency power.We use the simulation code CHRISTINE-1D to consider the design of a linear, C-Band, helix TWT and a folded waveguide slow-wave circuit.Finally, we consider the problem of using optimal control methodology to design HIV treatment schedules.We first introduce a model describing HIV dynamics and study this model under optimal control based treatment strategies using a variety of sensitivity equations.We then study the Extended Kalman Filter (EKF) as a tool to filter data and estimate unknown states and model parameters.We then apply a Receding Horizon Control (RHC) methodology to the control of this model.This methodology is used in conjunction with the EKF, in the presence of noisy data, poor drug adherence and imperfectly known model parameters.We then study this methodology on a model of HIV dynamics that incorporates drug resistance.