arXiv subjects

Hidekazu Yoshioka

Publications and source records attributed to Hidekazu Yoshioka.

47 records · Page 3Linked to original sources

arXiv2022

Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge

We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is a superposition of Ornstein-Uhlenbeck processes (supOU process), generating a sub-exponential autocorrelation function observed in actual data. The integral operator Riccati equation is heuristically derived to determine the optimal control of the infinite-dimensional system. In addition, its finite-dimensional version is derived with a discretized distribution of the reversion speed and computed by a finite difference scheme. The optimality of the Riccati equation is analyzed by a verification argument. The supOU process is parameterized based on the actual data of a perennial river. The convergence of the numerical scheme is analyzed through computational experiments. Finally, we demonstrate the application of the proposed model to realistic problems along with the Kolmogorov backward equation for the performance evaluation of controls.

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arXiv2021

Hamilton-Jacobi-Bellman-Isaacs equation for rational inattention in the long-run management of river environments under uncertainty

A new stochastic control model for the long-run environmental management of rivers is mathematically and numerically analyzed, focusing on a modern sediment replenishment problem with unique nonsmooth and nonlinear properties. Rational inattention as a novel adaptive strategy to collect information and intervene against the target system is modeled using Erlangization. The system dynamics containing the river discharge following a continuous-state branching with an immigration-type process and the controlled sediment storage dynamics lead to a nonsmooth and nonlocal infinitesimal generator. Modeling uncertainty, which is ubiquitous in certain applications, is considered in a robust control framework in which deviations between the benchmark and distorted models are penalized through relative entropy. The partial integro-differential Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation as an optimality equation is derived, and its uniqueness, existence, and optimality are discussed. A monotone finite difference scheme guaranteeing the boundedness and uniqueness of numerical solutions is proposed to discretize the HJBI equation and is verified based on manufactured solutions. Model applications are also conducted with the parameter values identified from the available data and physical formulae. The computational results suggest that environmental management should be rationally inattentive in a state-dependent and adaptive manner.

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arXiv2021

Analytical and numerical solutions to ergodic control problems arising in environmental management

Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on sediment storage management as a modern engineering problem, we formulate, analyze, and compute a new ergodic control problem under discrete observations: a simple but non-trivial mathematical problem. We give optimality and comparison results of the corresponding HJB equation having unique non-smoothness and discontinuity. To numerically compute HJB equations, we propose a new fast-sweep method resorting to neither pseudo-time integration nor vanishing discount. The optimal policy and the effective Hamiltonian are then computed simultaneously. Convergence rate of numerical solutions is computationally analyzed. An advanced robust control counterpart where the dynamics involve uncertainties is also numerically considered.

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arXiv2021

Towards Control of Dam and Reservoir Systems with Forward-Backward Stochastic Differential Equations Driven by Clustered Jumps

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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arXiv2021

Impulsive fishery resource transporting strategies based on an open-ended stochastic growth model having a latent variable

In inland fisheries, transporting fishery resource individuals from a habitat to spatially apart habitat(s) has recently been considered for fisheries stock management in the natural environment. However, its mathematical optimization, especially finding when and how much of the population should be transported, is still a fundamental unresolved issue. We propose a new impulse control framework to tackle this issue based on a simple but new stochastic growth model of individual fishes. The novel growth model governing individuals' body weights uses a Wright-Fisher model as a latent driver to reproduce plausible growth dynamics. The optimization problem is formulated as an impulse control problem of a cost-benefit functional constrained by a degenerate parabolic Fokker-Planck equation of the stochastic growth dynamics. Because the growth dynamics have an observable variable and an unobservable variable (a variable difficult or impossible to observe), we consider both full-information and partial-information cases. The latter is more involved but more realistic because of not explicitly using the unobservable variable in designing the controls. In both cases, resolving an optimization problem reduces to solving the associated Fokker-Planck and its adjoint equations, the latter being non-trivial. We present a derivation procedure of the adjoint equation and its internal boundary conditions in time to efficiently derive the optimal transporting strategy. We finally provide a demonstrative computational example of a transporting problem of Ayu sweetfish (Plecoglossus altivelis altivelis) based on the latest real data set.

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arXiv2021

Stochastic impulse control of non-smooth dynamics with partial observation and execution delay: application to an environmental restoration problem

Non-smooth dynamics driven by stochastic disturbance arise in a wide variety of engineering problems. Impulsive interventions are often employed to control stochastic systems; however, the modeling and analysis subject to execution delay have been less explored. In addition, continuously receiving information of the dynamics is not always possible. In this paper, with an application to an environmental restoration problem, a continuous-time stochastic impulse control problem subject to execution delay under discrete and random observations is newly formulated and analyzed. The dynamics have a non-smooth coefficient modulated by a Markov chain, and eventually attain an undesirable state like a depletion due to the non-smoothness. The goal of the control problem is to find the most cost-efficient policy that can prevent the dynamics from attaining the undesirable state. We demonstrate that finding the optimal policy reduces to solving a non-standard system of degenerate elliptic equations, the optimality equation, which is rigorously and analytically verified in a simplified case. The associated Fokker-Planck equation for the controlled dynamics is derived and solved explicitly as well. The model is finally applied to numerical computation of a recent river environmental restoration problem. The optimality and Fokker-Planck equations are successfully computed, and the optimal policy and the probability density functions are numerically obtained. The impacts of execution delay are discussed to deeper analyze the model.

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arXiv2020

Mathematical and computational approaches for stochastic control of river environment and ecology: from fisheries viewpoint

We present a modern stochastic control framework for dynamic optimization of river environment and ecology. We focus on a fisheries problem in Japan, and show several examples of simplified optimal control problems of stochastic differential equations modeling fishery resource dynamics, reservoir water balance dynamics, benthic algae dynamics, and sediment storage dynamics. These problems concern different phenomena with each other, but they all reduce to solving degenerate parabolic or elliptic equations. Optimal controls and value functions of these problems are computed using finite difference schemes. Finally, we present a higher-dimensional problem of controlling a dam-reservoir system using a semi-Lagrangian discretization on sparse grids. Our contribution shows the state-of-art of modeling, analysis, and computation of stochastic control in environmental engineering and science, and related research areas.

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arXiv2020

A simple model on streamflow management with a dynamic risk measure

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 Levy 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.

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arXiv2020

River environmental restoration based on random observations of a non-smooth stochastic dynamical system

Earth and soils are indispensable elements of river environment. Dam-downstream environment and ecosystems have been severely affected by reduced or even stopped sediment supply from the upstream. Replenishing earth and soils from outside the river has been considered as an effective way to mitigate this issue. However, its cost-effective implementation has not been considered from a theoretical side. This paper presents a tractable new stochastic control model to deal with this issue. The sediment dynamics in the river environment follow non-smooth and continuous-time piecewise deterministic dynamics. The model assumes that the observation of the sediment dynamics is carried out only randomly and discretely, and that the sediment can be replenished at each observation time with cost. This partial observation assumption is consistent with the fact that continuously obtaining the environmental information is difficult in applications. The performance index to penalize the sediment depletion has a non-smooth term as well. We demonstrate that these non-smoothness factors harmonize with a dynamic programming principle, and derive the optimality equation in a degenerate elliptic form governing the most cost-efficient sediment replenishment policy. We analytically derive and verify an exact solution under a simplified condition for a discounted case, an Ergodic case, and a complete information case. A more realistic case is handled using a high-resolution finite difference scheme. We then provide the optimal sediment replenishment policy numerically.

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arXiv2020

A random observation-based management model of population dynamics and its ecological application

A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only randomly and time-discretely observe and impulsively intervene the population dynamics governed by a regime-switching stochastic differential equation. The hybrid nature of the problem leads to an optimality equation containing an integro-differential equation and a static optimization problem. It is therefore different from the conventional Hamilton-Jacobi-Bellman equations. Existence and solvability issues of this optimality equation are analyzed in a viscosity sense. Its exact solution to a reduced but still nontrivial model is derived as well. The model is finally applied to a realistic environmental management problem in a river using a finite difference scheme.

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arXiv2015

On Dual-Finite Volume Methods for Extended Porous Medium Equations

This article shows that the unconditional stability of the Dual-Finite Volume Method, which is at least valid for linear problems, is not true for generic nonlinear differential equations including the PMEs unless the coefficient appearing in the numerical fluxes are appropriately evaluated. This article provides a theoretically truly isotone numerical fluxes specialized for solving the PMEs presented, which is still as simple as the conventional fully-upwind counterpart.

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