HJB and Fokker-Planck equations for river environmental management based on stochastic impulse control with discrete and random observation
| Autor: | Motoh Tsujimura, Kunihiko Hamagami, Yumi Yoshioka, Yuta Yaegashi, Hidekazu Yoshioka |
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| Rok vydání: | 2021 |
| Předmět: |
education.field_of_study
Population Dirac (software) Hamilton–Jacobi–Bellman equation Probability density function Numerical Analysis (math.NA) Systems and Control (eess.SY) Electrical Engineering and Systems Science - Systems and Control Computational Mathematics Stochastic differential equation Computational Theory and Mathematics Optimization and Control (math.OC) Modeling and Simulation Bellman equation FOS: Mathematics FOS: Electrical engineering electronic engineering information engineering Jump Applied mathematics Fokker–Planck equation Mathematics - Numerical Analysis education Mathematics - Optimization and Control Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 96:131-154 |
| ISSN: | 0898-1221 |
| Popis: | We formulate a new two-variable river environmental restoration problem based on jump stochastic differential equations (SDEs) governing the sediment storage and nuisance benthic algae population dynamics in a dam-downstream river. Controlling the dynamics is carried out through impulsive sediment replenishment with discrete and random observation/intervention to avoid sediment depletion and thick algae growth. We consider a cost-efficient management problem of the SDEs to achieve the objectives whose resolution reduces to solving a Hamilton-Jacobi-Bellman (HJB) equation. We also consider a Fokker-Planck (FP) equation governing the probability density function of the controlled dynamics. The HJB equation has a discontinuous solution, while the FP equation has a Dirac's delta along boundaries. We show that the value function, the optimized objective function, is governed by the HJB equation in the simplified case and further that a threshold-type control is optimal. We demonstrate that simple numerical schemes can handle these equations. Finally, we numerically analyze the optimal controls and the resulting probability density functions. Comment: Accepted manuscript |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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