A diffusion process model for the optimal operation of a reservoir system

The water level in a reservoir is modelled as a controlled diffusion process on a compact interval of the real line. The problem is to control the water discharge rate so as to minimise the expected costs, which depend upon the histories of the water levels and release rates. The form of the optimal control is studied for two general classes of reservoir control problems.

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Methods of the Real-time Runoff Account under the Conditions of the Bed Silting (the Matyra River in the village of Krutoye range as a study case)

Water sector of Russia: problems, technologies, management - Методы оценки и механизмы регулирования водопользования в современных условиях ◽

10.35567/1999-4508-2017-2-6 ◽

2017 ◽

Author(s):

Keyword(s):

Real Time ◽

Discharge Rate ◽

Water Discharge ◽

Water Levels ◽

Accounting Data ◽

The Real ◽

Discharge Rates ◽

Auto Correlation Function ◽

The Village ◽

Adequate Reliability

This paper presents the updated method of the real-time runoff calculation in conditions of river channel silting based on the method of optimal extrapolation. The Matyra river used as the example. The results of the analysis of the data obtained by observations of the Matyra River water regime during the period from 1994 to 2013 have been presented. We have analyzed all specific features of the hydrologic regime characteristics alterations under the influence of meteorological factors over the periods of the bed silting. The proposed decisions for real-time runoff account employ basic many-year dependence of the water discharge rates on water levels that have been exactly defined by the latest measurements of the water discharge rate through introduction of corrections that characterize changing of the bed passage ability of the year under consideration. These changes are calculated by the method of optimal extrapolation of the series of relative deviations from many-year water discharge curve calculated over the year under consideration. Assessment of the statistic characteristics of the relative deviation series such as auto-correlation function, dispersion and expectation value has been done to calculate weight coefficients in the optimal extrapolation formulas. Assessment of the proposals effectiveness has been carried out on the basis of the data of realtime and regime runoff accounting over the 2008-2013 period. Root mean square deviations from the regime accounting data were 5–10 %. The obtained results enable to make a conclusion on adequate reliability of the real-time runoff accounting data obtained with the use of the developed methods and to recommend it for real-time accounting of the small and medium-sized considerably silted rivers runoff.

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Optimal Control of a PDE Model of an Invasive Species in a River

Mathematics ◽

10.3390/math7100975 ◽

2019 ◽

Vol 7 (10) ◽

pp. 975

Author(s):

Rebecca Pettit ◽

Suzanne Lenhart

Keyword(s):

Optimal Control ◽

Invasive Species ◽

Management Strategy ◽

Discharge Rate ◽

Water Discharge ◽

Invasive Population ◽

Cross Sectional ◽

Flow Rates ◽

Pde Model ◽

The Cost

Managing invasive species in rivers can be assisted by appropriate adjustment of flow rates. Using a partial differential equation (PDE) model representing an invasive population in a river, we investigate controlling the water discharge rate as a management strategy. Our goal is to see how controlling the water discharge rate will affect the invasive population, and more specifically how water discharges may force the invasive population downstream. We complete the analysis of a flow control problem, which seeks to minimize the invasive population upstream while minimizing the cost of this management. Using an optimality system, consisting of our population PDE, an adjoint PDE, and corresponding optimal control characterization, we illustrate some numerical simulations in which parameters are varied to determine how far upstream the invasive population reaches. We also change the river’s cross-sectional area to investigate its impact on the optimal control.

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Time-optimal control of a linear diffusion process

Proceedings of the Institution of Electrical Engineers ◽

10.1049/piee.1965.0093 ◽

1965 ◽

Vol 112 (3) ◽

pp. 543 ◽

Cited By ~ 2

Author(s):

I. McCausland

Keyword(s):

Optimal Control ◽

Diffusion Process ◽

Time Optimal Control ◽

Linear Diffusion ◽

Time Optimal

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On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2019057 ◽

2020 ◽

Vol 26 ◽

pp. 41

Author(s):

Tianxiao Wang

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Optimal Control Problems ◽

Mean Field ◽

Open Loop ◽

Time Inconsistency ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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