RESEARCH PAPERS: Papers on Bilinear Control

The Bilinear, Modal State Equations for Age-Dependent Growth Control

[+] Author and Article Information
J. W. Brewer

University of California, Davis, Calif. 95616

J. Dyn. Sys., Meas., Control 103(2), 89-94 (Jun 01, 1981) (6 pages) doi:10.1115/1.3139660 History: Received August 28, 1980; Online July 21, 2009


There have been previous attempts to model biological processes as bilinear systems [4,9,10]. In these early studies any member of a population was taken to be quite like any other so that the variation of fertility and susceptibility to mortality with age was ignored. In this paper, however, the age-dependent nature of biological growth [5] is accounted for. The modal (eigenfunction) analysis of the basic partial differential equation of age-dependent growth is shown to result in a system of bilinear equations. (The basic mathematical model is a non-self-adjoint operator with a discrete spectrum and the modes are coupled by the control term.) The impulse control of a truncated version of this system of equations is then discussed. It is anticipated that the results presented here will aid planning for optimal amounts of pesticides to agro-ecosystems or for optimal amounts of drugs (or radiations) to unwanted cell populations.

Copyright © 1981 by ASME
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