TY - JOUR
T1 - A mixed optimal control approach for upstream fish Migration
AU - Yoshioka, Hidekazu
AU - Shirai, Tomoyuki
AU - Tagami, Daisuke
N1 - Funding Information:
This research is funded by grants-in-aid for scientific research No. 17K15345, No. 16KT0018, and No. 15H06417 from the Japan Society for the Promotion of Science (JSPS) and Applied Ecology Research Grant No. 2016-02 from Water Resources Environment Center in Japan. A part of this research includes research results from the short-stay researcher projects in 2015, 2016, and 2017 of Institute of Mathematics for Industry, Kyushu University, Japan. The authors thank dr. Yumi Yoshioka of Tottori University for her support in creating a figure panel. The authors also thank all the participants of the Special Session: Math for Water, Soil, and Ecosystems in the international conference SDEWES2017 for their valuable comments and suggestions.
Publisher Copyright:
© 2019, International Centre for Sustainable Development of Energy, Water and Environment Systems SDEWES. All rights reserved.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - This paper proposes a simple mathematical model forupstream fish migration along rivers. The model describes the fish migration along a river based on a mixed optimal control approach having swimming velocity, school size, and stopping time of migration as control variables. The optimization problem reduces to a variational inequality. Its explicit “viscosity” solution is presented with the dependence of the fish migration on river environment. To prove uniqueness of the solution to the variational inequality requires a constructive argument not based on the conventional theorems. A novel finite difference scheme for solving the variational inequality is also proposed with its convergence results. An application example of the model discusses the upstream migration of Plecoglossus altivelis (Ayu) in Japan, which evaluates the dependence of the fish migration on the habitat quality and provides recommendations for managing river environment. This is an interdisciplinary research between environmental and mathematical fields.
AB - This paper proposes a simple mathematical model forupstream fish migration along rivers. The model describes the fish migration along a river based on a mixed optimal control approach having swimming velocity, school size, and stopping time of migration as control variables. The optimization problem reduces to a variational inequality. Its explicit “viscosity” solution is presented with the dependence of the fish migration on river environment. To prove uniqueness of the solution to the variational inequality requires a constructive argument not based on the conventional theorems. A novel finite difference scheme for solving the variational inequality is also proposed with its convergence results. An application example of the model discusses the upstream migration of Plecoglossus altivelis (Ayu) in Japan, which evaluates the dependence of the fish migration on the habitat quality and provides recommendations for managing river environment. This is an interdisciplinary research between environmental and mathematical fields.
UR - http://www.scopus.com/inward/record.url?scp=85057147382&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85057147382&partnerID=8YFLogxK
U2 - 10.13044/j.sdewes.d6.0221
DO - 10.13044/j.sdewes.d6.0221
M3 - Article
AN - SCOPUS:85057147382
SN - 1848-9257
VL - 7
SP - 101
EP - 121
JO - Journal of Sustainable Development of Energy, Water and Environment Systems
JF - Journal of Sustainable Development of Energy, Water and Environment Systems
IS - 1
ER -
