JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (7): 21-29.doi: 10.6040/j.issn.1671-9352.0.2017.604

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Optimal control for inputting rate of a size-structure competitive system

SHEN Liu-xiao, ZHAO Chun*   

  1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2017-11-24 Online:2018-07-20 Published:2018-07-03

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Abstract: Inputting rate control problems of a size-structure competitive system is studied in this paper. First of all, the existence and uniqueness of the solution of the competitive system are proved with the help of the fixed point theorem. Then by using characteristic method, the continuous dependence of solution on control variable is obtained. Secondly, the existence and uniqueness of the optimal control are discussed by Ekeland variational principle. Finally, the necessary conditions of the optimal control are established by the conception of tangent and normal cone.

Key words: necessary conditions, size-structure, optimal inputting rate, fixed point theorem

CLC Number: 

  • O232
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