Regulation of Viable and Optimal Cohorts

Regulation of Viable and Optimal Cohorts This study deals with the evolution of (scalar) attributes (resources or income in evolutionary demography or economics, position in traffic management, etc.) of a population of “mobiles” (economic agents, vehicles, etc.). The set of mobiles sharing the same attributes is regarded as an instantaneous cohort described by the number of its elements. The union of instantaneous cohorts during a mobile window between two attributes is a cohort . Given a measure defining the number of instantaneous cohorts, the accumulation of the mobile attributes on a evolving mobile window is the measure of the cohort on this temporal mobile window. Imposing accumulation constraints and departure conditions, this study is devoted to the regulation of the evolutions of the attributes which are 1. viable in the sense that the accumulations constraints are satisfied at each instant; 2. and, among them, optimal , in the sense that both the duration of the temporal mobile window is maximum and that the accumulation on this temporal mobile window is the largest viable one. This value is the “accumulation valuation” function. Viable and optimal evolutions under accumulation constraints are regulated by an “implicit Volterra integro-differential inclusion” built from the accumulation valuation function, solution to an Hamilton–Jacobi–Bellman partial differential equation under constraints which is constructed for this purpose. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Regulation of Viable and Optimal Cohorts

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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9277-x
Publisher site
See Article on Publisher Site

Abstract

This study deals with the evolution of (scalar) attributes (resources or income in evolutionary demography or economics, position in traffic management, etc.) of a population of “mobiles” (economic agents, vehicles, etc.). The set of mobiles sharing the same attributes is regarded as an instantaneous cohort described by the number of its elements. The union of instantaneous cohorts during a mobile window between two attributes is a cohort . Given a measure defining the number of instantaneous cohorts, the accumulation of the mobile attributes on a evolving mobile window is the measure of the cohort on this temporal mobile window. Imposing accumulation constraints and departure conditions, this study is devoted to the regulation of the evolutions of the attributes which are 1. viable in the sense that the accumulations constraints are satisfied at each instant; 2. and, among them, optimal , in the sense that both the duration of the temporal mobile window is maximum and that the accumulation on this temporal mobile window is the largest viable one. This value is the “accumulation valuation” function. Viable and optimal evolutions under accumulation constraints are regulated by an “implicit Volterra integro-differential inclusion” built from the accumulation valuation function, solution to an Hamilton–Jacobi–Bellman partial differential equation under constraints which is constructed for this purpose.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2015

References

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