Regime-switching constrained viscosity solutions approach for controlling dam–reservoir systems

2022

Adv Control Appl

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We deal with a new maximum principle‐based stochastic control model for river management through operating a dam and reservoir system. The model is based on coupled forward–backward stochastic differential equations (FBSDEs) derived from jump‐driven streamflow dynamics and reservoir water balance. A continuous‐time branching process with immigration driven by a tempered stable subordinator efficiently describes clustered inflow streamflow dynamics. This is a completely new attempt in hydrology and control engineering. Applying a stochastic maximum principle to the dynamics based on an objective functional for designing cost‐efficient control of dam and reservoir systems leads to the FBSDEs as a system of optimality equations. The FBSDEs under a linear‐quadratic ansatz lead to a tractable model, while they are solved numerically in the other cases using a least‐squares Monte‐Carlo method. Optimal controls are found in the former, while only sub‐optimal ones are computable in the latter due to a hard state constraint. Model parameters are successfully identified from a real data of a river in Japan having a dam and reservoir system. We also show that the linear‐quadratic case can capture the real operation data of the system with underestimation of the outflow discharge. More complex cases with a realistic time horizon are analyzed numerically to investigate impacts of considering the environmental flows and seasonal operational purposes. Key challenges towards more sophisticated modeling and analysis with jump‐driven FBSDEs are discussed as well.

Section: Mathematical Backgroundmentioning

confidence: 99%

Section: Numerical Computationmentioning

confidence: 99%

Section: Study Sitementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

2022

Adv Control Appl

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“…Modeling streamflow itself is not a goal but rather a pathway toward streamflow management as dynamic optimization problems like dam and hydropower management [6][7]. Stochastic control based on the dynamic programming with SDEs [8] is a versatile tool for dynamic optimization under uncertainty.…”

Section: Introductionmentioning

confidence: 99%

A Simple Model on Streamflow Management with a Dynamic Risk Measure

Proceedings of the Seventh International Conference on Mathematics and Computing

2022

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We present an exactly-solvable risk-minimizing stochastic differential game for flood management in rivers. The streamflow dynamics follow stochastic differential equations driven by a Lévy process. An entropic dynamic risk measure is employed to evaluate a flood risk under model uncertainty. The problem is solved via a Hamilton-Jacobi-Bellman-Isaacs equation. We explicitly derive an optimal flood mitigation policy along with its existence criteria and the worst-case probability measure. A backward stochastic differential representation as an alternative formulation is also presented.

Stochastic Control of Dam Discharges

Wiley StatsRef: Statistics Reference Online

2021

Dam is a dynamical system receiving stochastic inflows while releasing controlled outflows. Its optimal control requires considering a state constraint on the stored water volume and should use an objective function considering both human activities and downstream environmental management. In addition, the system dynamics are not always known exactly. We briefly explain a robust modeling framework of dam discharges based on a dynamic programming approach and constrained viscosity solutions with a demonstrative computational example. We focus on a single problem rather than reviewing diverse examples because it has key features that stochastic control in real applications encounters.