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Generalized Differentiation of a Class of Normal Cone Operators and Sensitivity of Optimal Control problems

SET-VALUED AND VARIATIONAL ANALYSIS 2022年第4期30卷 1333-1361页

作者： Toan, N. T. Thuy, L. Q. Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

This paper studies generalized differentiation for a class of normal cone operators and sensitivity of solution to a class of parametric discrete optimal control problems. We first establish the Fr ' echet and Mordukhovich coderivatives of a class of normal cone operators in Asplund spaces. We then use the obtained results to compute and estimate the Fr ' echet coderivative of the solution map to parametric discrete optimal control problems with nonlinear state equations.

关键词： Fr ' echet coderivative Normal cone operator Parametric discrete optimal control problem dynamic programming problem Solution map Nonlinear state equation

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Approximate dynamic programming-based decentralised robust optimisation approach for multi-area economic dispatch considering wind power uncertainty

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IET RENEWABLE POWER GENERATION 2020年第13期14卷 2376-2385页

作者： Zhu, Jianquan Wang, Chenxi Guo, Ye Luo, Tianyun Mo, Xiemin Xia, Yunrui South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Peoples R China

This study presents a fully decentralised robust optimisation (RO) approach for multi-area economic dispatch (MA-ED) in the presence of wind power uncertainty. Unlike traditional algorithms, the authors formulate this MA-ED problem as dynamic programming problem, and decompose the centralised robust MA-ED problem into a series of sub-problems based on approximate dynamic programming algorithm. The value functions are proposed for each area to iteratively estimate the impacts of its dispatches on the dispatches of other areas which make decisions subsequently. The proposed algorithm does not require a central operator but only needs to exchange a small amount of information among neighbouring areas to achieve fully decentralised decision-making. It is practical in cases where the centralised operator cannot be implemented considering the dispatch independence and the detailed data of one area is unavailable considering the privacy. Additionally, the accuracy, adaptability and computational efficiency of the proposed algorithm are illustrated using numerical simulations on two test systems and an actual power system.

关键词： decision making power generation dispatch power generation economics decentralised control optimisation dynamic programming fully decentralised decision-making dispatch independence approximate dynamic programming-based robust optimisation approach multiarea economic dispatch wind power uncertainty fully decentralised robust optimisation dynamic programming problem centralised robust MA-ED problem approximate dynamic programming algorithm dispatches neighbouring areas

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The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control problem

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ACTA MATHEMATICA VIETNAMICA 2020年第2期45卷 365-382页

作者： Nguyen Thi Toan Le Quang Thuy Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

Motivated by the works of Toan and Kien (J. Nonlinear Convex Anal.12:635-650,2011) and Thuy and Toan (Acta Math. Vietnam.43:175-199,2018) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz property of the value function and the Aubin property of the solution map to a parametric dynamic programming problem with linear constraints. By establishing abstract results on the Lipschitz property of the value function to a parametric programming and the Aubin property of the solution map to a parametric variational inequality, we obtain the Lipschitz property of the value function and the Aubin property of the solution map to a parametric discrete optimal control problem.

关键词： Parametric discrete optimal control problem dynamic programming problem Solution map Value function Lipschitz property Aubin property

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THE USING OF dynamic programming IN PURCHASING BECO ALLOYS 28

THE USING OF DYNAMIC PROGRAMMING IN PURCHASING BECO ALLOYS

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28th International Conference on Metallurgy and Materials (METAL)

作者： Lampa, Martin Sikorova, Andrea Samolejova, Andrea VSB Tech Univ Ostrava Ostrava Czech Republic

ISBN: (纸本)9788087294925

In his work, a manager will come across situations, which will require him to make easy or complicated decisions. The company management often has to take into account the sequence of decisions, of which every decision affects the following one. The tool used to find solutions to the consequential types of decision problems is called dynamic programming. A key part of the logistics process is purchasing the necessary raw materials for production for the best possible price. This article deals deals with the subject of optimalization of purchasing BECO alloys (an alloy of copper and beryllium) in order to achieve the highest possible conservation of financial resources, that's why the timing of purchase is a deciding factor in terms of the manager`s responsibilities.

关键词： Optimization management dynamic programming problem

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The Mordukhovich Coderivative and the Local Metric Regularity of the Solution Map to a Parametric Discrete Optimal Control problem

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ACTA MATHEMATICA VIETNAMICA 2018年第1期43卷 175-199页

作者： Le Quang Thuy Nguyen Thi Toan Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

In this paper, we study the Mordukhovich coderivative and the local metric regularity in Robinson's sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost functions. By establishing abstract results on the coderivative and the local metric regularity of the solution map to a parametric variational inequality, we obtain the Mordukhovich coderivative and the local metric regularity in Robinson's sense of the solution map to a parametric discrete optimal control problem.

关键词： Parametric discrete optimal control problem dynamic programming problem Solution map Local metric regularity Mordukhovich coderivative

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Global optimal energy management control strategies for connected four-wheel-drive hybrid electric vehicles

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IET INTELLIGENT TRANSPORT SYSTEMS 2017年第5期11卷 264-272页

作者： Qiu, Lihong Qian, Lijun Zomorodi, Hesam Pisu, Pierluigi Hefei Univ Technol Dept Vehicle Engn Hefei 230009 Peoples R China Clemson Univ Int Ctr Automot Res Greenville SC 29607 USA

This study presents a novel decentralised hierarchical global energy management control strategy for a group of connected four-wheel-drive hybrid electric vehicles (HEVs) in urban road conditions. In the higher level controller, signal phase and timing information and the optimal cruising velocity are combined to generate the target velocities for the HEVs. A model predictive control framework that focuses on the tracking of the target velocity and the associated desired control variable for every individual vehicle is proposed for the prediction of the optimal velocity that compromises fuel economy, mobility and safety. In the lower level controller, a dynamic programming problem is formulated that utilises the predicted velocity for the global energy management optimisation of every individual HEV. Simulation results validate the advantages of the proposed higher and lower level controllers.

关键词： energy management systems hybrid electric vehicles wheels predictive control fuel economy dynamic programming level control optimal control global optimal energy management control strategy connected four-wheel-drive hybrid electric vehicles decentralised hierarchical global energy management control strategy urban road conditions level controller timing information optimal cruising velocity target velocity generation HEVs model predictive control framework fuel economy dynamic programming problem global energy management optimisation

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Swing options in commodity markets: a multidimensional Levy diffusion model

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2014年第1期79卷 31-67页

作者： Eriksson, Marcus Lempa, Jukka Nilssen, Trygve Kastberg Univ Oslo Dept Math N-0316 Oslo Norway Oslo & Akershus Univ Coll Inst Econ N-0130 Oslo Norway Univ Agder Dept Econ & Business Adm N-4604 Kristiansand Norway

We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional L,vy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermore, we discuss the issues caused by the multi-dimensionality of the commodity price model. The results are illustrated numerically with three explicit examples.

关键词： Swing option Flexible load contract dynamic programming problem Multi-factor model Levy diffusion HJB-equation Finite difference method

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Demand-side technology standards under inefficient pricing regimes - Are they effective water conservation tools in the long-run?

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ENVIRONMENTAL & RESOURCE ECONOMICS 2003年第1期26卷 107-124页

作者： Timmins, C Yale Univ Dept Econ New Haven CT 06520 USA

When price-setting regulators have objectives other than maximizing social surplus, the conservation potential of demand-side technology standards can be significantly diminished. This paper demonstrates this by empirically recovering the socially sub-optimal preferences of a group of water managers in a groundwater-dependent region of California and simulating their inefficient price response to the mandated adoption of low-flow appliances by homeowners. The resulting reduction in the conservation potential of these appliances is quantified, and a modest tax is shown to be a relatively cost-effective policy tool for conservation. If non-price conservation policies are preferred according to equity criteria, the paper suggests that, in order to preserve their conservation potential, policy-makers should be required to continue to set prices as if no technology standards had been introduced.

关键词： demand-side technology standard dynamic programming problem efficient pricing groundwater

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