Singular stochastic control model for algae growth management in dam downstream

Abstract

A stochastic control model for finding an ecologically sound, fit-for-purpose dam operation policy to suppress bloom of attached algae in its downstream is presented. A singular exactly solvable and a more realistic regular-singular cases are analysed in terms of a Hamilton–Jacobi–Bellman equation. Regularity and consistency of the value function are analysed and its classical verification theorem is established. Practical implications of the mathematical analysis results are discussed focusing on parameter dependence of the optimal controls. An asymptotic analysis with a numerical computation reveals solution behaviour of the Hamilton–Jacobi–Bellman equation near the origin, namely at the early stage of algae growth.

Keywords

• stochastic differential equation
• singular control
• regular-singular control
• attached algae
• hamilton–jacobi–bellman equation