The mathematical concept of multiplier robust control is applied to a dam operation problem, which is an urgent issue on river water environment, as a new industrial application of stochastic optimal control. The goal of the problem is to find a fit-for-purpose and environmentally sound operation policy of the flow discharge from a dam so that overgrowth of the harmful algae Cladophora glomerata Kützing in its downstream river is effectively suppressed. A minimal stochastic differential equation for the algae growth dynamics with uncertain growth rate is first presented. The performance index to be maximized by the operator of the dam while minimized by nature is formulated within the framework of differential games. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs equation whose solution determines the worst-case optimal operation policy of the dam, ie, the policy that the operator wants to find. Application of the model to overgrowth suppression of Cladophora glomerata Kützing just downstream of a dam in a Japanese river is then carried out. Values of the model parameters are identified with which the model successfully reproduces the observed population dynamics. A series of numerical experiments are performed to find the most effective operation policy of the dam based on a relaxation of the current policy.

A simplified stochastic control model for optimization of logistic dynamics with the control-dependent carrying capacity, which is motivated by a recent algae population management problem in the river environment, is presented. Solving the optimization problem reduces to finding a solution to a non-local first-order differential equation called tt-Jacobi-Bellman (HJB) equation. It is shown that the HJB equation has a unique viscosity solution and that the solution can be approximated with a finite difference scheme. Asymptotic estimates of the solution and the optimal control are derived and compared with numerical solutions. Finally, parameter dependence of the optimal control is examined numerically with implications to river environmental management.

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Excessive predation pressure from the waterfowl Phalacrocorax carbo (Great Cormorant) on Plecoglossus altivelis (Ayu) has recently been a severe problem of river environment in Japan. Local fishery cooperatives are currently suffering from economic difficulties due to decrease of the fish catch of P. altivelis. Local fishery cooperatives and municipalities have been enthusiastically trying to develop countermeasures that can effectively reduce the predation pressure; however, their effectiveness and efficiency have not been systematically quantified well. This aim can be achieved with the help of an appropriate mathematical model. In this paper, based on a pure death process, a practical stochastic control model for population dynamics of released P. altivelis in river environment under predation pressure from P. carbo, harvesting by human, and environmental fluctuations is proposed. Finding an optimal management strategy ultimately reduces to solving a 2D Hamilton–Jacobi–Bellman equation, which is performed with a finite element scheme. Its application to a Japanese river environment successfully computes the optimal management strategy that is consistent with the reality. Numerical sensitivity analysis of the presented mathematical model is also performed for comprehension of dependence of the optimal strategy on the model parameters.

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An increasing population and limited arable land area endanger sufficient and variegated food supplies worldwide. Greenhouse cultivation enables highly intensive plant production and thereby enables the production of abundant fresh vegetables and fruits. The salient benefits of greenhouse cultivation are supported by ingenious management of crop environments, assisted by fossil fuel and grid electricity supplies. To reduce dependence on traditional energy resources, various studies have investigated exploitation of renewable energies for greenhouse environment management. Among them, solar photovoltaic (PV) technologies are anticipated to feed electrical energy to greenhouse appliances for microclimate control. This study proposes a venetian-blind-type shading system consisting of semi-transparent PV modules as blind blades based on micro-spherical solar cell technology to achieve greenhouse shading and electricity production concurrently. In response to the solar irradiance level, the PV blind inclination was altered automatically using a direct current (DC) motor driven by electrical energy generated by the PV blind itself. The PV blind was operated continuously during a five-month test period without outage. Moreover, the PV blind generated surplus electrical energy of 2125 kJ for blind system operations during the test period. The annual surplus energy calculated under the present experimental condition was 7.8 kWh m −2 year −1 , suggesting that application of the PV blind to a greenhouse roof enables sunlight level control and electrical appliance operations in the greenhouse with a diminished fuel and grid electricity supply, particularly in high-insolation regions.Energies 2018, 11, 1681 2 of 23 produces carbon dioxide emissions, the amounts of which should be reduced in the agricultural sector [2]. Under these circumstances, various studies have been conducted to use renewable energy for managing greenhouse crop environments [3,4]. Among them, solar photovoltaics (PVs) are expected to feed electricity to appliances that are used for greenhouse environment management [5].Deploying PV arrays on the sunny ground beside a greenhouse is the simplest and most effective mode of electrical energy generation. For instance, fan and pad cooling systems in Saudi Arabia [6] and in Arizona [7], a fog cooling system in Malaysia [8], and heat pump systems in Italy [9,10] were operated with power from ground-mounted PV arrays. Nevertheless, installing PV arrays partially on a greenhouse roof might be preferred if the PV panels are intended as shading materials. Shading is a fundamentally important practice for greenhouse cultivation in high-insolation regions, such as Spain [11] or Saudi Arabia [12]. Previous studies conducted in Japan [13] and in the Mediterranean region [14,15] demonstrated that an adequate level of shading mitigates excessive temperature rises in greenhouses in summer, improving crop growth and quality [16,17]. Conventionally, nets [14,15,18] and reflective coatings [18,19] have been used as practical ...

A minimal stochastic generalization of a deterministic open-ended logistic growth model is proposed for efficiently describing the biological growth of individual organisms under natural environment. The model is a system of stochastic differential equations. Its unique solvability in a strong sense is proven, and the behaviour of the solution is analysed. The presented model is then applied to the migratory fish Plecoglossus altivelis altivelis (P. altivelis, Ayu) having a one-year life history based on the data sets collected in 2017 and 2018.