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Social Optimal mean field control problem for population growth model
Author(s) -
Yu Wenguang,
Wang Fei,
Huang Yujuan,
Liu Haodong
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2164
Subject(s) - optimal control , population , mathematical optimization , mathematics , brownian motion , field (mathematics) , population model , mean field theory , control (management) , state (computer science) , class (philosophy) , control theory (sociology) , mathematical economics , computer science , statistics , demography , artificial intelligence , physics , pure mathematics , algorithm , quantum mechanics , sociology
In this paper, we consider a class of social optimal mean field control problem of the population growth model. Suppose a fishpond has N ‐fish schools, the population of each of them is described by a geometry Brownian motion, the fisherman is on one hand to minimize the total nourishment investments and on another hand to minimize the expected population level measured by the state average of the population of all fish schools. By solving an optimal control problem involved N ‐controls and approximating the state average appearing in the adjoint equation, a series of decentralized controls is designed which have a property of asymptotic social optimality. Finally, a simulation example is given.