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作者： Hatzell, Kelsey Bridget PennState University Libraries

学位级别：Master of Science

This thesis developed a single state equivalent circuit model of a Lithium Iron Nanophosphate battery and applied the model with optimal control strategies to explore an optimal charging problem. Charging and discharging open-circuit potentials, resistances, and an overall battery capacity was estimated experimentally. The model was verified against experimental data and at low charge rates the model matches experimental data <1% error. The model was used to develop optimal charging schedules in order to optimize energy throughput in a battery. The results were compared to a simple single charge rate, and two experimental trajectories. The results indicate that optimizing for energy throughput may be a trivial objective function for the given constraints. Nevertheless, the results suggest three primary trends (1.) Charging trajectories begin at low charge rates, (2.) Optimized trajectories indicate that pulses of current should be added at 30% and 70% SoC, (3.) Optimal charging protocols magnitudes differ based on initial state of charge. Future work intends to use this framework to explore a physics based model with more rigorous constraints.

关键词： Lithium Ion Batteries Optimal Charging deterministic dynamic programming

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COMPARISON OF STOCHASTIC AND deterministic dynamic programming FOR RESERVOIR OPERATING RULE GENERATION

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JAWRA Journal of the American Water Resources Association 1987年第1期23卷 1-9页

作者： Karamouz, Mohammad Houck, Mark H. Department of Civil and Enviromnental Engineering Polytechnic University Brooklyn New York 11201 333 Jay St United States School of Civil Engineering Purdue University West Lafayette Indiana 47907 United States

ABSTRACT: Two dynamic programming models — one deterministic and one stochastic — that may be used to generate reservoir operating rules are compared. The deterministic model (DPR) consists of an algorithm that cycles through three components: a dynamic program, a regression analysis, and a simulation. In this model, the correlation between the general operating rules, defined by the regression analysis and evaluated in the simulation, and the optimal deterministic operation defined by the dynamic program is increased through an iterative process. The stochastic dynamic program (SDP) describes streamflows with a discrete lag‐one Markov process. To test the usefulness of both models in generating reservoir operating rules, real‐time reservoir operation simulation models are constructed for three hydrologically different sites. The rules generated by DPR and SDP are then applied in the operation simulation model and their performance is evaluated. For the test cases, the DPR generated rules are more effective in the operation of medium to very large reservoirs and the SDP generated rules are more effective for the operation of small reservoirs. Copyright © 1987, Wiley Blackwell. All rights reserved

关键词： deterministic dynamic programming optimization reservoir operation stochastic dynamic programming water resources management

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Time reduction of the dynamic programming computation in the case of hybrid vehicle

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INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS 2017年第Sup2期53卷 S213-S227页

作者： Vinot, Emmanuel IFSTTAR 25 Ave Francois Mitterrand F-69500 Bron France

deterministic dynamic programming is frequently used to solve the management problem of hybrid vehicles (choice of mode and power sharing between thermal and electric sources). However, it is time consuming and thus difficult to use in global sizing optimization or in parametric studies. This paper presents a comparison between three methods to compute the DDP problems. These methods are applied on the well known case of the Toyota PRIUS. It proves that a dense matrix method can reduce the computation time by up to 10 compared to more intuitive solving methods.

关键词： deterministic dynamic programming solving algorithms hybrid vehicle

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Time periodic optimal policy for operation of a water storage tank using the dynamic programming approach

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APPLIED MATHEMATICS AND COMPUTATION 2019年 353卷 418-431页

作者： Unami, Koichi Mohawesh, Osama Fadhil, Rasha M. Kyoto Univ Grad Sch Agr Kyoto 6068502 Japan Mutah Univ Fac Agr Al Karak 61710 Jordan Univ Mosul Coll Engn Mosul Iraq

Operation of a water storage tank in a specific environment motivates mathematical studies on a discrete-time deterministic dynamic programming problem. The operator decides whether or not to open the valve releasing the water in the tank to a drip irrigation system, based on the information on the storage volume of the tank. Two cases of functional regularity, which are Lipschitz continuous and of bounded variations, are considered for the reward defining the performance index to be maximized. Firstly, it is shown that the value function inherits the Lipschitz continuity of the reward in the infinite time horizon problem with discounting. Then, time periodic value functions are discussed in terms of the fixed-point theorem. Discrete approximation of value functions is discussed as well, to conduct numerical experiments with a-posteriori error estimation applied to the real-world problem where the discount rate approaches to unity. It is found that a Skiba point appears as a threshold of valve opening for each day in an optimal policy for operation. Practically, setting a constant threshold throughout the period is quite reasonable and acceptable for the operator of the water storage tank to irrigate the farmland. (C) 2019 Elsevier Inc. All rights reserved.

关键词： deterministic dynamic programming Bellman equation Water storage tank Time periodic optimal policy Skiba point

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Optimal design of a power-split hybrid hydraulic bus

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2016年第12期230卷 1699-1718页

作者： Ramdan, Muhammad Iftishah Stelson, Kim A. Univ Sains Malaysia Sch Mech Engn Nibong Tebal 14300 Penang Malaysia Univ Minnesota Dept Mech Engn 111 Church St SE Minneapolis MN 55455 USA

The hydraulic power-split architecture, or the hydromechanical transmission, can exist in over 1000 configurations. Since a specific hydromechanical transmission configuration has a unique kinematic characteristic, the optimal hydromechanical transmission configuration for one application is different from the optimal hydromechanical transmission configurations for other applications. This study finds the optimal hydromechanical transmission configuration for a hybrid hydraulic city bus. Since a hydromechanical transmission uses at least one planetary gear set, the process of finding a suitable hydromechanical transmission configuration for a hybrid hydraulic city bus is very time consuming, but this study simplifies the procedure by utilizing the critical speed ratio (crit), where (crit) is the missing link between the planetary gear set configuration, its gear ratio and its kinematic characteristic. This simplification also allows complex dual-stage hydromechanical transmission architecture configurations to be considered as candidates for the optimal drivetrain of the hybrid hydraulic city bus. The hydromechanical transmission configuration candidates are simulated over three city bus driving cycles and, to ensure that they operate at the optimal conditions for each driving cycle, dynamic programming is used. This study also establishes two power recirculation modes, one of which is useful because of its high efficiency. A single-stage power-split architecture configuration candidate is found to be the optimal drivetrain for a hydromechanical transmission bus.

关键词： Hybrid hydraulic heavy-duty vehicle bus hybrid hydraulic city bus hydromechanical transmission single-stage power-split dual-stage power-split power recirculation power-split architecture optimization deterministic dynamic programming

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Period three implies heavy discounting

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Mathematics of Operations Research 1994年第4期19卷 1007-1007页

作者： Sorger, Gerhard

A condition is derived that must be satisfied by a continuous function h : X → X in order to be the optimal policy function of a strictly concave deterministic dynamic programming problem which is defined on the state space X and which has a given discount factor ρ. We use this condition to show that there is no such dynamic programming problem on a one-dimensional state space that generates optimal solutions which are periodic with minimal period three unless the discount rate exceeds 82%. This bound holds uniformly for all strictly concave problems and all period-three-cycles.

关键词： deterministic dynamic programming discounting period-three-cycles chaos stochastic dominance

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Optimal greedy policies for stochastic control models

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Mathematical Methods of Operations Research 1996年第1期44.0卷 115-133页

作者： Liebig, Thilo Rieder, Ulrich Department of Mathematics VII University of Ulm 89069 Ulm Germany

We introduce the notion of a greedy policy for general stochastic control models. Sufficient conditions for the optimality of the greedy policy for finite and infinite horizon are given. Moreover, we derive error bounds if the greedy policy is not optimal. The main results are illustrated by Bayesian information models, discounted Bayesian search problems, stochastic scheduling problems, single-server queueing networks and deterministic dynamic programs.

关键词： deterministic dynamic programming Error bounds Greedy policies MDP with an absorbing set Stochastic control models

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HIERARCHICAL APPROACH TO MULTICRITERIA dynamic-programming

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INFOR 1992年第2期30卷 138-147页

作者： TRZASKALIK, T

Multi-criteria, multi-period discrete decision problems are considered. It is assumed that the decision maker has fixed single hierarchy in the set of multi-period criteria. The paper aims at discribing hierarchical approach to multi-criteria discrete dynamic programming. Then, a new interactive hierarchical dynamic programming technique based on the concept of period structure of considered solution is introduced. In the following stages we consider next criteria, one by one, using single objective dynamic programming method and we reduce sets of states and decisions according to the decision maker's period requirments. After the last stage the decision maker is asked to point to one solution which suits him best. This solution is tested and, if it is not efficient, the set of efficient solutions better than the chosen one is constructed and presented. The decision maker can choose the final solution among the indicated solutions. If he is not satisfied, he can: - point to another solution and repeat the last part of the procedure, - repeat all the procedure with changed period parameters, - break it. Finally, an example illustrating the introduced method is shown.

关键词： MULTICRITERIA programming deterministic dynamic programming LEXICOGRAFIC AND QUASI-LEXICOGRAFIC PROBLEMS

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The costate variable in a stochastic renewable resource model

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Natural Resource Modeling 2006年第1期19卷 45-66页

作者： Lyon, Kenneth S. Pande, Saket Economics Department Utah State University Logan UT 84322-3530 3530 Old Main Hill United States Center for World Food Studies (SOW-VU) Vrije Universiteit Amsterdam Netherlands

In this paper we discuss the costate variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the costate variable in deterministic control models has been discussed extensively in the literature. See for example Lyon [1999], Clark [1990, pp. 102 107] and Arrow and Kurz [1970, pp. 35 37];however, there is little discussion of this variable for stochastic models, even though thecostate variable has similar roles in the two models. In both models the costate variableis a shadow value of the associated state variable, and as such has the role of rationingthe use of the state variable. In addition, as has been shown in Lyon [1999], in natural resource problems the costate variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example to help solidify the results. © 2006 Rocky Mountain Mathematics Consortium.

关键词： Costate variable deterministic dynamic programming Renewable resource model Simulation Stochastic dynamic programming

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