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

Abstract

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.

References in corpus (3)

• Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control
• Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments
• Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge

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