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Trajectory planning for autonomous aerospace vehicles amid known obstacles and conflicts

JOURNAL OF GUIDANCE CONTROL AND dynamicS 2004年第6期27卷 997-1008页

作者： Yang, HI Zhao, YJ Univ Minnesota Minneapolis MN 55455 USA

A discrete search strategy is presented for potential real-time generations of four-dimensional trajectories for a single autonomous aerospace vehicle amid known obstacles and conflicts. A model of autonomous operation is first developed. The problem of and requirements on real-time trajectory generations for autonomous aerospace vehicles are discussed. After an overview of various potential solution frameworks, a discrete search strategy is developed. In this strategy, a four-dimensional search space is defined and discretized. Potential obstacles and conflicts are represented by several basic geometric shapes and their combinations. Mathematical conditions are developed for a trajectory segment to be outside of an obstacle or conflict. Then, the A* search technique is used to obtain trajectory solutions, in which successor points are selected that avoid obstacles and conflicts and that satisfy dynamic motion constraints of the vehicle. A linear combination of flight distance and flight time is optimized in the trajectory generation process. A heuristic function that approximates this performance index is developed for the A* search procedure. Examples are provided that illustrate the application of the proposed method.

关键词： Autonomous Aerospace Vehicle Search Algorithm Real Time Trajectory Planning Flight Trajectory stochastic dynamic programming Heading Angle Computer Memory Computer Systems Flight Vehicle Helicopters

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Optimal market timing strategies under transaction costs

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2002年第2期30卷 97-108页

作者： Li, W Lam, K Hong Kong Polytech Univ Fac Business & Informat Syst Dept Business Studies Kowloon Hong Kong Peoples R China Hong Kong Baptist Univ Sch Business Dept Finance & Decis Sci Kowloon Tong Peoples R China

In this paper, we consider optimal market timing, strategies under transaction costs. We assume that the asset's return follows an auto-regressive model and use long-term investment growth as the objective of a market timing strategy which entails the shifting of funds between a risky asset and a riskless asset. We give the optimal trading strategy for a finite investment horizon, and analyze its limiting behavior. For a finite horizon, the optimal decision in each step depends on two threshold values. If the return today is between the two values, nothing needs to be done, otherwise funds will be shifted from one asset to another, depending on which threshold value is being exceeded. When investment horizon tends to infinity, the optimal strategy converges to a stationary policy, which is shown to be closely related to a well-known technical trading rule, called Momentum Index trading rule. An integral equation of them two threshold values is given. Numerical results for the limiting stationary strategy are presented. The results confirm the obvious guess that the no-transaction region increases as the transaction cost increase. Finally, the limiting stationary strategy is applied to data in the Hang Seng Index Futures market in Hong Kong. The out-of-sample performance of the limiting stationary strategy is found to be better than the simple strategy sed in literature, which is based on an 1-step ahead forecast of return. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： market timing autoregressive models growth-optimal investment strategy stochastic dynamic programming

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Modelling Water Blending-Sensitivity of Optimal Policies

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ENVIRONMENTAL MODELING & ASSESSMENT 2009年第6期14卷 749-757页

作者： Webby, R. B. Green, D. A. Metcalfe, A. V. Univ Adelaide Sch Math Sci Adelaide SA 5005 Australia

Water blending is modelled as a combination of a linear program and a stochastic dynamic program. Optimal policies are found for linear and integer-linear formulations using both an expected monetary value and conditional value-at-risk criterion. The sensitivity of these solutions to the discretisation over volume and over time is investigated.

关键词： Water resource allocation Linear programming stochastic dynamic programming Conditional value-at-risk

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On the structural properties of a discrete-time single product revenue management problem

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OPERATIONS RESEARCH LETTERS 2009年第4期37卷 273-279页

作者： Aydin, Seray Akcay, Yalcin Karaesmen, Fikri Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey Koc Univ Coll Business Adm & Econ TR-34450 Istanbul Turkey

We consider a multi-period revenue management problem in which multiple classes of demand arrive over time for the common inventory. The demand classes are differentiated by their revenues and their arrival distributions. We investigate monotonicity properties of varying problem parameters on the optimal reward and the policy. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Revenue management stochastic dynamic programming Optimal control policies

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Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2012年第1期135卷 81-93页

作者： Kenne, Jean-Pierre Dejax, Pierre Gharbi, Ali IRCCyN Ecole Mines Nantes Logist & Prod Syst Grp Dept Automat Control & Ind Engn F-44307 Nantes 3 France Univ Quebec Dept Mech Engn Lab Integrated Prod Technol Ecole Technol Super Montreal PQ H3C 1K3 Canada Univ Quebec Automated Prod Engn Dept Prod Syst Design & Control Lab Ecole Technol Super Montreal PQ H3C 1K3 Canada

This paper deals with the production planning and control of a single product involving combined manufacturing and remanufacturing operations within a closed-loop reverse logistics network with machines subject to random failures and repairs. While consumers traditionally dispose of products at the end of their life cycle, recovery of the used products may be economically more attractive than disposal, while remanufacturing of the products also pursues sustainable development goals. Three types of inventories are involved in this network. The manufactured and remanufactured items are stored in the first and second inventories. The returned products are collected in the third inventory and then remanufactured or disposed of. The objective of this research is to propose a manufacturing/remanufacturing policy that would minimize the sum of the holding and backlog costs for manufacturing and remanufacturing products. The decision variables are the production rates of the manufacturing and the remanufacturing machines. The optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. A computational algorithm, based on numerical methods, is used for solving the optimal control problem. Finally, a numerical example and a sensitivity analysis are presented to illustrate the usefulness of the proposed approach. The structure of the optimal control policy is discussed depending on the value of costs and parameters and extensions to more complex reverse logistics networks are discussed. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Reverse logistics Closed-loop supply chains Manufacturing/remanufacturing Optimal control Production planning stochastic dynamic programming Numerical methods

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Uncertainty based operation of large scale reservoir systems: Dez and Karoon experience

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 2003年第4期39卷 961-975页

作者： Karamouz, M Mousavi, SJ Amirkabir Univ Technol Sch Civil & Environm Engn Tehran Iran Iran Univ Sci & Technol Struct & Hydrostruct Res Ctr Dept Civil Engn Tehran Iran

Reservoir operation involves a complex set of human decisions depending upon hydrologic conditions in the supply network including watersheds, lakes, transfer tunnels, and rivers. Water releases from reservoirs are adjusted in an attempt to provide a balanced response to different demands. When a system involves more than one reservoir, computational burdens have been a major obstacle in incorporating uncertainties and variations in supply and demand. A new generation of stochastic dynamic programming was developed in the 1980s and 1990s to incorporate the forecast and demand uncertainties. The Bayesian stochastic dynamic programming (BSDP) model and its extension, Demand Driven stochastic dynamic programming (DDSP) model, are among those models. Recently, a Fuzzy stochastic dynamic programming model (FSDP) also was developed for a single reservoir to model the errors associated with discretizing the variables using fuzzy set theory. In this study the DDSP and the FSDP models were extended and simplified for a complex system of Dez and Karoon reservoirs in the southwestern part of Iran. The simplified models are called Condensed Demand Driven stochastic programming (CDDSP) and Condensed Fuzzy stochastic dynamic programming (CFSDP). The optimal operating policies developed by the CDDSP and the CFSDP models were simulated in a classical model and a fuzzy simulation model, respectively. The case study was used to demonstrate the advantages of implementing the proposed algorithm, and the results show the significant value of the proposed fuzzy based algorithm.

关键词： stochastic dynamic programming reservoir operation fuzzy set theory uncertainty imprecision reservoir system fuzzy rule-based modeling

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Optimal delivery of two similar products to N ordered customers with product preferences

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2019年 209卷 194-204页

作者： Kyriakidis, Epaminondas G. Dimitrakos, Theodosis D. Karamatsoukis, Constantinos C. Athens Univ Econ & Business Dept Stat Patiss 76 Athens 10434 Greece Univ Aegean Dept Math Karlovassi 83200 Samos Greece Hellen Mil Acad Dept Mil Sci Vari 16673 Attica Greece

We study a mathematical model for a specific vehicle routing problem in which a vehicle starts its route from a depot loaded with items of two similar but not identical products. The vehicle must deliver the products to N customers according to a predefined sequence. It is assumed that each customer prefers either product 1 or product 2 with known probabilities and the quantity that each customer demands is a random variable with known distribution. The actual preference and demand of each customer are revealed upon the vehicle's arrival at customer's site. The demand of each customer cannot exceed the vehicle capacity and the vehicle is allowed during its route to return to the depot to restock with quantities of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. If there is shortage for the desired product it is permitted to deliver the other product at a reduced price. The optimal routing strategy is found by implementing a suitable stochastic dynamic programming algorithm. It is possible to prove that the optimal routing strategy has a specific threshold-type structure. Furthermore, if we consider the same problem without the assumption that the customers are ordered, numerical experiments indicate that the optimal routing strategy can be computed for N <= 8.

关键词： Vehicle routing stochastic dynamic programming Similar products

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Pricing flexible electricity contracts

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IEEE TRANSACTIONS ON POWER SYSTEMS 2000年第2期15卷 477-482页

作者： Bjorgan, R Song, HL Liu, CC Dahlgren, R Univ Washington Dept Elect Engn Seattle WA 98195 USA ALSTOM ESCA Corp Bellevue WA USA

This paper is concerned with pricing of electricity contracts that allow flexible scheduling of the supply or demand of electric energy, The contracts are priced based on the principle of no-arbitrage. Variables of the contracts are used to determine arbitrage opportunities and the price of contracts. Pricing of flexible contracts involves a scheduling policy. By representing the spot price with an appropriate stochastic process, the scheduling policy can be found using stochastic dynamic programming. Simulation examples illustrate the tradeoffs between prices and scheduling flexibility.

关键词： electricity market power system economics pricing stochastic optimization stochastic dynamic programming stochastic spot price process

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The importance of functional form in optimal control solutions of problems in population dynamics

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ECOLOGY 2002年第5期83卷 1357-1371页

作者： Runge, MC Johnson, FA Univ Georgia Warnell Sch Forest Resources Athens GA 30602 USA US Fish & Wildlife Serv Patuxent Wildlife Res Ctr Off Migratory Bird Management Laurel MD 20708 USA

Optimal control theory is finding increased application in both theoretical and applied ecology, and it is a central element of adaptive resource management. One of the steps in an adaptive management process is to develop alternative models of system dynamics, models that are all reasonable in light of available data, but that differ substantially in their implications for optimal control of the resource. We explored how the form of the recruitment and survival functions in a general population model for ducks affected the patterns in the optimal harvest strategy, using a combination of analytical, numerical, and simulation techniques. We compared three relationships between recruitment and population density (linear, exponential, and hyperbolic) and three relationships between survival during the nonharvest season and population density (constant, logistic, and one related to the compensatory harvest mortality hypothesis). We found that the form of the component functions had a dramatic influence on the optimal harvest strategy and the ultimate equilibrium state of the system. For instance, while it is commonly assumed that a compensatory hypothesis leads to higher optimal harvest rates than an additive hypothesis, we found this to depend on the form of the recruitment function, in part because of differences in the optimal steady-state population density. This work has strong direct consequences for those developing alternative models to describe harvested systems, but it is relevant to a larger class of problems applying optimal control at the population level. Often, different functional forms will not be statistically distinguishable in the range of the data. Nevertheless, differences between the functions outside the range of the data can have an important impact on the optimal harvest strategy. Thus, development of alternative models by identifying a single functional form, then choosing different parameter combinations from extremes on the likelihood profil

关键词： adaptive management compensatory mortality density-dependence equilibrium analysis harvest theory optimal control theory population dynamics reproductive function stochastic dynamic programming survival function

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A gridding method for Bayesian sequential decision problems

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2003年第3期12卷 566-584页

作者： Brockwell, AE Kadane, JB Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA

This article introduces a numerical method for finding optimal or approximately optimal decision rules and corresponding expected losses in Bayesian sequential decision problems. The method, based on the classical backward induction method, constructs a grid approximation to the expected loss at each decision time, viewed as a function of certain statistics of the posterior distribution of the parameter of interest. In contrast with most existing techniques, this method has a computation time which is linear in the number of stages in the sequential problem. It can also be applied to problems with insufficient statistics for the parameters of interest. Furthermore, it is well-suited to be implemented using parallel processors.

关键词： backward induction batch sequential Bayesian sequential analysis fully sequential Monte Carlo integration parallel computing stochastic dynamic programming

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