Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments

• Published in: Applied mathematical modelling Vol. 116; pp. 490 - 509
• Main Authors: Yoshioka, Hidekazu, Tanaka, Tomohiro, Yoshioka, Yumi, Hashiguchi, Ayumi
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2023
• Subjects: Markovian lift; River discharge; Static ergodic control; Superposition of affine jump processes; Superposition of affine jump processes; Markovian lift; Static ergodic control; River discharge
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2022.11.009

•A cost-constrained optimization problem of river discharge is considered.•It is based on a novel stochastic model to generate subexponential autocorrelation.•The Markovian lift allows for efficiently resolving its non-Markovian nature.•The stochastic model is identified at each point in an existing river reach.•The control problem is finally applied to the water abstraction in the river. We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that generates realistic subexponential autocorrelation functions, and the “static” nature of the control originates from a realistic observability assumption in the system. The Markovian lift was effectively used to discretize the system into a finite-dimensional process, which is easier to analyze. The resolution of the problem is based on backward Kolmogorov equations and a quadratic solution ansatz. The control problem has a closed-form solution, and the variance has both strict upper and lower bounds, indicating that the variance cannot take an arbitrary value even when it is subject to a high control cost. The correspondence between the discretized system based on the Markovian lift and the original infinite-dimensional one is discussed. Then, a convergent Markovian lift is presented to approximate the infinite-dimensional system. Finally, the control problem was applied to real cases using available data for a river reach. An extended problem subject to an additional constraint on maintaining the flow variability was also analyzed without significantly degrading the tractability of the proposed framework.