Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1181-1191.

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Optimal Control of Initial Distributions in a Hierarchical Size-Structured Population System with Delay

Zerong He(),Mengjie Han   

  1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2020-06-08 Online:2021-08-26 Published:2021-08-09
  • Supported by:
    the NSFC(11871185);the NSF of Zhejiang Province(LY18A010010)


This article is concerned with an optimal control problem for a hierarchical size-dependent population model with delay, the control function is the initial distribution. It is expected that the difference between the terminal state and the given target can be minimized in a least costs. The uniform continuity of states in controls is established by the method of characteristic lines and priori estimates, the minimal principle is derived by the construction of a normal cone and an adjoint system, and the existence of unique optimal strategy is proved by means of the Ekeland variational theorem and fixed-point approach. These results pave the way to applications.

Key words: Hierarchy of size, Integro-partial differential equations, Optimal control, Normal cones, Variational principle

CLC Number: 

  • O211.4