A mixed optimal control approach for upstream fish Migration

Hidekazu Yoshioka, Tomoyuki Shirai, Daisuke Tagami

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)101-121
Number of pages21
JournalJournal of Sustainable Development of Energy, Water and Environment Systems
Issue number1
Publication statusPublished - Mar 1 2019

All Science Journal Classification (ASJC) codes

  • Renewable Energy, Sustainability and the Environment
  • Environmental Science (miscellaneous)
  • Water Science and Technology
  • Energy Engineering and Power Technology


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