Affiliation:
1. Institute for Nonlinear Mechanics University of Stuttgart Stuttgart Germany
2. Department of Mathematics National Technical University of Athens Athens Greece
3. Department of Mechanical and Aerospace Engineering University of California San Diego California USA
Abstract
AbstractFor population systems modeled by age‐structured hyperbolic partial differential equations (PDEs), we redesign the existing feedback laws, designed under the assumption that the dilution input is directly actuated, to the more realistic case where dilution is governed by actuation dynamics (modeled simply by an integrator). In addition to the standard constraint that the population density must remain positive, the dilution dynamics introduce constraints of not only positivity of dilution, but possibly of given positive lower and upper bounds on dilution. We present several designs, of varying complexity, and with various measurement requirements, which not only ensure global asymptotic (and local exponential) stabilization of a desired positive population density profile from all positive initial conditions, but do so without violating the constraints on the dilution state. To develop the results, we exploit the relation between first‐order hyperbolic PDEs and an equivalent representation in which a scalar input‐driven mode is decoupled from input‐free infinite‐dimensional internal dynamics represented by an integral delay system.
Funder
National Science Foundation
Air Force Office of Scientific Research
Subject
Electrical and Electronic Engineering,Industrial and Manufacturing Engineering,Mechanical Engineering,Aerospace Engineering,Biomedical Engineering,General Chemical Engineering,Control and Systems Engineering