Math. Model. Nat. Phenom.
Volume 9, Number 4, 2014Optimal control
|Page(s)||20 - 37|
|Published online||20 June 2014|
Constant Versus Periodic Fishing: Age Structured Optimal Control Approach
ORCOS, Vienna University of Technology
2 Institute of Mechanics, Lomonosov Moscow State University
⋆ Corresponding author. E-mail: email@example.com
The paper investigates an age-structured infinite-horizon optimal control model of harvesting a biological resource, interpreted as fish. Time and age are considered as continuum variables. The main result shows that in case of selective fishing, where only fish of prescribed sizes is harvested, it may be advantageous in the log run to implement a periodic fishing effort, rather than constant (the latter suggested by single-fish models that disregard the age-heterogeneity). Thus taking into account the age-structure of the fish may qualitatively change the theoretically optimal fishing mode. This result is obtained by developing a technique for reliable numerical verification of second order necessary optimality conditions for the considered problem. This technique could be useful for other optimal control problems of periodic age-structured systems.
Mathematics Subject Classification: 49N20 / 35F46
Key words: age-structured systems / periodic control / optimal fishing / properness test
© EDP Sciences, 2014
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