Optimal Stochastic Control of Energy Storage System Based on Pontryagin Minimum Principle for Flattening PEV Fast Charging in a Service Area

This letter discusses stochastic optimal control of an energy storage system (ESS) for reducing the impact on the grid of fast charging of electric vehicles in a charging area. A trade off is achieved between the objectives of limiting the charging power exchanged with the grid, and the one of limiting the fluctuation, around a given reference, of the ESS energy. We show that the solution of the problem can be derived from the one of a related deterministic problem, requiring the realistic assumption that the charging area operator knows an estimate of the aggregated charging power demand over the day. In addition, two alternative configurations of the charging area are discussed, and it is shown that, while they share the same solution, one better mitigates the demand uncertainty. Numeric simulations are provided to validate the proposed approach

An Optimal Extraction Problem with Price Impact

A price-maker company extracts an exhaustible commodity from a reservoir, and sells it instantaneously in the spot market. In absence of any actions of the company, the commodity's spot price evolves either as a drifted Brownian motion or as an Ornstein-Uhlenbeck process. While extracting, the company affects the market price of the commodity, and its actions have an impact on the dynamics of the commodity's spot price. The company aims at maximizing the total expected profits from selling the commodity, net of the total expected proportional costs of extraction. We model this problem as a two-dimensional degenerate singular stochastic control problem with finite fuel. To determine its solution, we construct an explicit solution to the associated Hamilton-Jacobi-Bellman equation, and then verify its actual optimality through a verification theorem. On the one hand, when the (uncontrolled) price is a drifted Brownian motion, it is optimal to extract whenever the current price level is larger or equal than an endogenously determined constant threshold. On the other hand, when the (uncontrolled) price evolves as an Ornstein-Uhlenbeck process, we show that the optimal extraction rule is triggered by a curve depending on the current level of the reservoir. Such a curve is a strictly decreasing $C^{\infty}$-function for which we are able to provide an explicit expression. Finally, our study is complemented by a theoretical and numerical analysis of the dependency of the optimal extraction strategy and value function on the model's parameters.Comment: 36 pages; 5 figure

Sum-rules and bath-parametrization for quantum cluster theories

We analyze cellular dynamical mean-field theory (CDMFT) and the dynamical cluster approximation (DCA). We derive exact sum-rules for the hybridization functions and give examples for DMFT, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum-rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath-parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. In two dimensions we find, that we need so many bath-sites to obtain a reliable parametrization that Lanczos calculations are hardly feasible with current computers. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization.Comment: 11 pages, 14 figure

An optimal extraction problem with price impact

Ferrari G, Koch T. An optimal extraction problem with price impact. Center for Mathematical Economics Working Papers. Vol 603. Bielefeld: Center for Mathematical Economics; 2018.A price-maker company extracts an exhaustible commodity from a reservoir, and sells it instantaneously in the spot market. In absence of any actions of the company, the commodity's spot price evolves either as a drifted Brownian motion or as an Ornstein- Uhlenbeck process. While extracting, the company affects the market price of the commodity, and its actions have an impact on the dynamics of the commodity's spot price. The company aims at maximizing the total expected profits from selling the commodity, net of the total expected proportional costs of extraction. We model this problem as a two-dimensional degenerate singular stochastic control problem with finite fuel. To determine its solution, we construct an explicit solution to the associated Hamilton-Jacobi-Bellman equation, and then verify its actual optimality through a verification theorem. On the one hand, when the (uncontrolled) price is a drifted Brownian motion, it is optimal to extract whenever the current price level is larger or equal than an endogenously determined constant threshold. On the other hand, when the (uncontrolled) price evolves as an Ornstein-Uhlenbeck process, we show that the optimal extraction rule is triggered by a curve depending on the current level of the reservoir. Such a curve is a strictly decreasing C1-function for which we are able to provide an explicit expression. Finally, our study is complemented by a theoretical and numerical analysis of the dependency of the optimal extraction strategy and value function on the model's parameters.MSC2010 subject classification: 93E20; 49L20; 91B70; 91B76; 60G40. OR/MS subject classification: Dynamic programming/optimal control: applications, Markov; Probability: stochastic models applications, diffusio

On a Strategic Model of Pollution Control

Ferrari G, Koch T. On a Strategic Model of Pollution Control . Center for Mathematical Economics Working Papers. Vol 586. Bielefeld: Center for Mathematical Economics; 2017.This paper proposes a strategic model of pollution control. A firm, representative of the productive sector of a country, aims at maximizing its profits by expanding its production. Assuming that the output of production is proportional to the level of pollutants' emissions, the firm increases the level of pollution. The government of the country aims at minimizing the social costs due to the pollution, and introduces regulatory constraints on the emissions' level, which then effectively cap the output of production. Supposing that the firm and the government face both proportional and fixed costs in order to adopt their policies, we model the previous problem as a stochastic impulse two-person nonzero-sum game. The state variable of the game is the level of the output of production which evolves as a general linearly controlled one-dimensional Itô-diffusion. Following an educated guess, we first construct a pair of candidate equilibrium policies and of corresponding equilibrium values, and we then provide a set of sufficient conditions under which they indeed realize an equilibrium. Our results are complemented by a numerical study when the (uncontrolled) output of production evolves as a geometric Brownian motion, and the firm's operating prot and the government's running cost functions are of power type. An analysis of the dependency of the equilibrium policies and values on the model parameters yields interesting new behaviors that we explain as a consequence of the strategic interaction between the firm and the government

Quality of Experience Provision in the Future Internet

This work deals with the satisfaction of the quality of experience (QoE) requirements in the perspective of the emerging future Internet framework. The evolution of the Internet is pointing out its limitations, which are likely to hinder its potential. In this respect, this paper introduces an innovative approach to cope with some key limitations of the present communication networks. In particular, the need of efficiently utilizing the available network resources and of guaranteeing the user expectations in terms of QoE requires a full cognitive approach, which is realized by the introduction of a novel architecture design, the so-called future Internet core platform. The future Internet core platform aims at bringing together the applications world with the network world, hence introducing a further cognitive level while enabling a new generation of applications: network-aware applications. This paper is concerned with an important aspect of the intelligent connectivity between applications and network: the service class association, which, if performed with a cognitive approach, can yield some important improvements and advantages in the emerging information era. The key idea presented in this paper is a real-time dynamic control procedure for the selection of the optimal service class. The approach is based on theoretical considerations validated by a proof-of-concept simulation

Coronary angiography using spectral detector dual-energy CT:is it the time to assess myocardial first-pass perfusion?

Coronary computed tomography angiography (CCTA) represents a common approach to the diagnostic workup of patients with suspected coronary artery disease. Technological development has recently allowed the integration of conventional CCTA information with spectral data. Spectral CCTA used in clinical routine may allow for improving CCTA diagnostic performance by measuring myocardial iodine distribution as a marker of first-pass perfusion, thus providing additional functional information about coronary artery disease

Statistical hadronization phenomenology in K/πK/\pi fluctuations at ultra-relativistic energies

We discuss the information that can be obtained from an analysis of fluctuations in heavy ion collisions within the context of the statistical model of particle production. We then examine the recently published experimental data on ratio fluctuations, and use it to obtain constraints on the statistical properties (physically relevant ensemble, degree of chemical equilibration, scaling across energies and system sizes) and freeze-out dynamics (amount of reinteraction between chemical and thermal freeze-out) of the system.Comment: Proceedings, SQM2009. Fig. 4, the main results figure, was wrong due to editing mistake, now correcte