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- B M Adams, H T Banks, Hee-Dae Kwon, Hien T Tran
- Mathematical biosciences and engineering : MBE
- 2004

We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug "cocktail " therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) in… (More)

We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by innnite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial diierential equations with unbounded input and unbounded observation operators are included as special cases… (More)

- H. T. Banks, B. M. Lewis, H. T. Tran
- Comp. Opt. and Appl.
- 2007

State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design and synthesis methods of nonlinear feedback controllers and estimators for a broad class of nonlinear regulator problems. In essence, the SDRE approach involves mimicking standard linear quadratic regulator (LQR) formulation for linear systems. In particular, the… (More)

We consider classes of functional differential equation models which arise in attempts to describe temporal delays in HIV pathogenesis. In particular, we develop methods for incorporating arbitrary variability (i.e., general probability distributions) for these delays into systems that cannot readily be reduced to a finite number of coupled ordinary… (More)

- H. T. Banks, Ricardo C. H. del Rosario, Ralph C. Smith
- IEEE Trans. Automat. Contr.
- 2000

Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actua-tors. Donnell-Mushtari equations, modiied to include Kelvin-Voigt damping, are used to… (More)

- H. T. Banks, M. Davidian
- 2007

We discuss statistical and computational aspects of inverse or parameter estimation problems based on Ordinary Least Squares and Generalized Least Squares with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the topics included here are mathematical model, statistical model… (More)

- H T Banks, Karyn L Sutton, +4 authors Andreas Meyerhans
- Bulletin of mathematical biology
- 2011

Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57-89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1-26, 2007) contain a mathematical model with fluorescence intensity as a structure… (More)

- H T Banks, Kathleen Holm, Franz Kappel
- Inverse problems
- 2011

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according… (More)

- R A Albanese, H T Banks, M V Evans, L K Potter
- Bulletin of mathematical biology
- 2002

In this paper we present three physiologically based pharmacokinetic (PBPK) models for the systemic transport of trichloroethylene (TCE), with a focus on the adipose, or fat tissue. TCE is a widespread environmental contaminant, and has been shown to produce toxic effects in both animals and humans. A key characteristic of TCE is its tendency to accumulate… (More)