https://hal.inria.fr/hal-01075632Aubin, Jean-PierreJean-PierreAubinLASTRE - Laboratoire d'Applications des Systèmes Tychastiques Régulés - VIMADESRegulation of Viable and Optimal CohortsHAL CCSD2014[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Aubin, Jean-PierreSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - 2014-10-19 10:09:252020-08-10 15:46:032014-10-19 10:09:25enJournal articles10.1007/s00245-014-9277-x1This study deals with the evolution of (scalar) attributes (resources or income inevolutionary 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 numberof 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 viable} in the sense that the accumulations constraints} are satisfied at each instant, 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.