Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 867-880.

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Optimal Boundary Control for a Hierarchical Size-Structured Population Model with Delay

Zerong He(),Yimeng Dou,Mengjie Han   

  1. Institute of Operational Research and Cybernetics. Hangzhou Dianzi University, Hangzhou 310018
  • Received:2021-04-16 Online:2022-06-26 Published:2022-05-09
  • Supported by:
    the NSFC(11871185)


In this article, we formulate a population control model, which is based upon the hierarchical size-structure and the incubation delay. For a given ideal population distribution, we investigate the optimal input problem: How to choose a inflow way such that the sum of the deviation between the terminal state and the given one and the total costs is minimal. The well-posedness is established by the method of characteristics, the existence of unique optimal policy is shown by the Ekeland variational principle, and the optimal policy is exactly described by a normal cone and an adjoint system. These results set a foundational framework for practical applications.

Key words: Hierarchy of body size, Delay, Optimal control, Normal cone, Variational principle

CLC Number: 

  • O211.4