Solutions and Challenges in Computing FBSDEs with Large Jumps for Dam and Reservoir System Operation

Yoshioka, Hidekazu

doi:10.1007/978-3-030-77980-1_40

Cited by 1 publication

(5 citation statements)

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“…Similar basis works without convergence problems for simpler non-LQ systems having a liner inflow SDE with the computational period of 120 (day). 60 This peculiar behavior of the numerical solution with 𝒮 NLQ1 is considered due to the longer computational period (360 (day)) in the present case where the convergence condition of the relaxed Picard iteration (small T with sufficiently regular coefficients) may not be satisfied numerically. 64 We did not find similar peculiar behavior with the basis 𝒮 NLQ2 .…”

Section: F I G U R E 14mentioning

confidence: 92%

“…We tackle this issue by considering sub-optimal controls imposing the constraint only in the forward dynamics. 60 Sub-optimal controls can be used effectively if they are feasible and more easily computable than the optimal ones 61,62 ; both are satisfied in our case.…”

Section: Objectives and Contributionsmentioning

confidence: 99%

“…In this case, it seems difficult to apply a conventional stochastic maximum principle in the earlier section because of the state-constraint that induces a boundary discontinuity of the control. 42 Instead, as in Yoshioka, 60 we couple the constrained state dynamics with the BSDE of that obtained in the previous section ( 23)-( 26) with an additional assumption (8) to find sub-optimal controls with which the constraint is still activated. Namely, we only change the forward system dynamics and the admissible set of controls.…”

Section: Constrained Casementioning

confidence: 99%

“…In fact, no regularization was necessary in Yoshioka. 60 Another cause of this difference of the convergence rates would be attributed to the fact that the TSOU process is driven by state-independent jumps while the CBI process by state-dependent jumps. The state-dependence prevented us from employing the exact discretization of tempered stable jumps as a low variance numerical method.…”

Section: Lq Case: Comparison With the Exact Solutionmentioning

confidence: 99%

“…) ) are worse than nearly 1 observed for FBSDEs with a TSOU process. 60 This is possibly because of using a positive regularization parameter 𝜆 with which numerical solutions do not strictly converge to the exact solution TA B L E 4 l 1 and l 2 errors of the coefficient E = E t of the adjoint variable p (q) with different 𝜆. due to regularization errors. In fact, no regularization was necessary in Yoshioka.…”

Section: Lq Case: Comparison With the Exact Solutionmentioning

confidence: 99%

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

Yoshioka

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.

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Section: F I G U R E 14mentioning

confidence: 92%