Optimal Mechanisms for Heterogeneous Multi-cell Aquifers

Standard economic models of groundwater management impose restrictive assumptions regarding perfect transmissivity (i.e., the aquifer behaves as a bathtub), no external effects of groundwater stocks, observability of individual extraction rates, and/or homogenous agents. In this article, we derive regulatory mechanisms for inducing the socially optimal extraction path in Markov perfect equilibrium for aquifers in which these assumptions do not hold. In spite of the complexity of the underlying system, we identify an interesting case in which a simple linear mechanism achieves the social optimum. To illustrate potential problems that can arise by erroneously imposing simplifying assumptions, we conduct a simulation based on data from the Indian state of Andhra Pradesh.Common Property Resource, Differential Games, Groundwater Extraction, Imperfect Monitoring, Markov Perfect Equilibrium

About modeling and control strategies for scheduling crop irrigation

International audienceWe propose a new simplified crop irrigation model and study the optimal control which consists in maximizing the biomass production at harvesting time, under a constraint on the total amount of water used. Under water scarcity, we show that a strategy with a singular arc can be better than a simple bang-bang control as commonly used. The gain is illustrated on numerical simulations. This result is a promising first step towards the application of control theory to the problem of optimal irrigation scheduling

International Conference on Dynamic Control and Optimization - DCO 2021: book of abstracts

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Recent Advances in Path Integral Control for Trajectory Optimization: An Overview in Theoretical and Algorithmic Perspectives

This paper presents a tutorial overview of path integral (PI) control approaches for stochastic optimal control and trajectory optimization. We concisely summarize the theoretical development of path integral control to compute a solution for stochastic optimal control and provide algorithmic descriptions of the cross-entropy (CE) method, an open-loop controller using the receding horizon scheme known as the model predictive path integral (MPPI), and a parameterized state feedback controller based on the path integral control theory. We discuss policy search methods based on path integral control, efficient and stable sampling strategies, extensions to multi-agent decision-making, and MPPI for the trajectory optimization on manifolds. For tutorial demonstrations, some PI-based controllers are implemented in MATLAB and ROS2/Gazebo simulations for trajectory optimization. The simulation frameworks and source codes are publicly available at https://github.com/INHA-Autonomous-Systems-Laboratory-ASL/An-Overview-on-Recent-Advances-in-Path-Integral-Control.Comment: 16 pages, 9 figure

Investment rigidity and policy measures

Postprint (published version

The factor bias of technical change and technology adoption under uncertainty

This dissertation examines the impact of uncertainty on the factor bias of technical change and technological adoption behavior. An Ito stochastic control model, which is characterized by endogenous factor-augmenting technical change, is developed to investigate the relationship between uncertainty and the bias of technical change;The results show that, if a risk-averse firm faces input price uncertainty, technical change will be biased toward the input that has the more certain price. Output price uncertainty does not affect the direction of technical change bias but does affect the degree of bias. Under output price uncertainty and an input price uncertainty, technical change may be biased toward the input that has a certain price if the contemporaneous correlation coefficient between the two processes is negative or insignificantly positive. On the contrary, if the coefficient is significantly positive, technical change may be biased toward the input that has an uncertain price;It is also shown that, under production uncertainty, technical progress will be biased toward risk-reducing inputs and against risk-increasing inputs. The degree of technical change bias would be increased as the riskiness increases or as the firm becomes more risk averse;The model is integrated to incorporate hedging or forward contracts. Under output price uncertainty, the existence of forward markets has no effect on the direction of technical change bias but has an effect on the degree of bias. Under output price uncertainty and an input price uncertainty, if the forward market is unbiased, technical change will be biased toward the input that has a certain price;This dissertation also examines the effect of price uncertainty on technology adoption patterns and technological change. The results indicate that a reduction in the variance of output price will increase the rate of technology adoption and the intrafirm diffusion speed of yield-increasing technologies. The opposite is true for cost-reducing technologies

Optimal Management of Beaver Population using a Reduced-Order Distributed Parameter Model and Single Network Adaptive Critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a single network adaptive critic (SNAC) neural-network architecture

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

An Analysis of Optimal Agricultural Fertilizer Application Decisions in the Presence of Market and Weather Uncertainties and Nutrient Pollution

This thesis addresses the questions of how uncertain corn market and weather factors affect optimal fertilizer application decisions of the farmer and the social planner, and what factors drive the divergence between the two. Nutrient runoff from agricultural activities has become a primary source of surface water quality deterioration worldwide. Over-application of fertilizer in agricultural production represents a non-point source pollution which is causing extensive nutrient loading in water bodies and has a severe impact on the global environment. There is evidence that farmers apply more fertilizer than is socially optimal and more than is recommended by government agencies. This thesis first investigates the farmer’s optimal fertilizer application under crop price uncertainty by constructing an inter-temporal farmer’s decision model under two alternative stochastic price processes. Closed form results are derived, which indicate that an increase in price uncertainty implies a reduction in the quantity of fertilizer applied in the farmer’s optimal decision problem. Numerous factors that could impact the optimal fertilization decision are examined as well. The farmer’s decision model is then enhanced by allowing for two possible fertilizer application times in the growing season and the inclusion of additional stochastic state variables such as rainfall and temperature, in the corn yield model. The model is parameterized for average conditions in Iowa corn growing regions. Employing a Monte Carlo approach, numerical results conclude that for a wide range of parameter assumptions the farmer’s optimal strategy is to apply fertilizer at planting rather than later as a side dressing. This thesis analyzes the impacts of price uncertainty, fertilizer cost and other economic parameters on the farmer’s optimal fertilizer application strategy. The thesis also analyzes the optimal decisions of a social planner whose objective function includes an estimate of the damages caused by nitrogen leakage and denitrification. Numerical results show that including the damages from pollution affect both the quantity and timing of fertilizer application. Assumptions about the frequency and quantity of rainfall have an important impact on the optimal decision. This is an important consideration for public policy as climate change affects weather patterns over the next decade and beyond