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Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2020年第16期42卷 3168-3182页

作者： Demir, Okan Ozbay, Hitay Bilkent Univ Elect & Elect Engn Ankara Cankaya Turkey

This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

关键词： Static output feedback optimal sensor placement approximate dynamic programming

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Cross-docking based factory logistics unitisation process: An approximate dynamic programming approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期311卷 112-124页

作者： Lyu, Zhongyuan Huang, George Q. Univ Hong Kong Dept Ind & Mfg Syst Engn Hong Kong Peoples R China Hong Kong Polytech Univ Dept Ind & Syst Engn Hong Kong Peoples R China

The factory logistics increases in importance as more processes and types of components are needed to produce a product. Due to the limited industrial space and stressful competitive environment, manufacturers increasingly outsource logistics-related activities to Third-Party Logistics (3PLs) and Supply hubs. However, the challenges, including unsynchronised decisions with other partners, non-value-added warehousing operations, and excessive space occupation, still burden manufacturers. This research proposes a cross-docking-based factory logistics unitisation process (CD-FLUP) that integrates the cross-docking technique into the assembly line feeding process and uses mobile shelves for component holding and delivery. We formulate the CD-FLUP with an integer program to minimise the total number of shelf units put into storage and the number of deliveries to assembly lines. Based on time decomposition, we propose an approximate dynamic programming (ADP) approach to solve the model efficiently. The time-varying value function approximation (VFA) developed in the proposed ADP approach reduces the approximation parameters and speeds up convergence significantly. The numerical experiment shows that the proposed ADP can generate high-quality solutions far more efficiently than a commercial solver. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： Logistics Unitisation Zero warehousing intelligent manufacturing (ZWIM) approximate dynamic programming Cross-docking

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Optimal Hour-Ahead Bidding in the Real-Time Electricity Market with Battery Storage Using approximate dynamic programming

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INFORMS JOURNAL ON COMPUTING 2015年第3期27卷 525-543页

作者： Jiang, Daniel R. Powell, Warren B. Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08540 USA

There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with an increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to exploit variations in electricity spot prices, is becoming an important way of paying for expensive investments into grid-level storage. Independent system operators such as the New York Independent System Operator (NYISO) require that battery storage operators place bids into an hour-ahead market (although settlements may occur in increments as small as five minutes, which is considered near "real-time"). The operator has to place these bids without knowing the energy level in the battery at the beginning of the hour and simultaneously accounting for the value of leftover energy at the end of the hour. The problem is formulated as a dynamic program. We describe and employ a convergent approximate dynamic programming (ADP) algorithm that exploits monotonicity of the value function to find a revenue-generating bidding policy;using optimal benchmarks, we empirically show the computational benefits of the algorithm. Furthermore, we propose a distribution-free variant of the ADP algorithm that does not require any knowledge of the distribution of the price process (and makes no assumptions regarding a specific real-time price model). We demonstrate that a policy trained on historical real-time price data from the NYISO using this distribution-free approach is indeed effective.

关键词： approximate dynamic programming bidding hour-ahead energy storage real-time market

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Efficient approximate dynamic programming based on design and analysis of computer experiments for infinite-horizon optimization

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COMPUTERS & OPERATIONS RESEARCH 2020年 124卷

作者： Chen, Ying Liu, Feng Rosenberger, Jay M. Chen, Victoria C. P. Kulvanitchaiyanunt, Asama Zhou, Yuan Harbin Inst Technol Dept Management Sci & Engn Harbin 150000 Heilongjiang Peoples R China Stevens Inst Technol Sch Syst & Enterprises Hoboken NJ 07030 USA Harvard Med Sch Massachusetts Gen Hosp Boston MA 02114 USA MIT Picower Inst Learning & Memory Cambridge MA 02139 USA Univ Texas Arlington Dept Ind Mfg & Syst Engn Arlington TX 76019 USA Coraline Co Ltd Bangkok Thailand

The approximate dynamic programming (ADP) method based on the design and analysis of computer experiments (DACE) approach has been demonstrated as an effective method to solve multistage decision-making problems in the literature. However, this method is still not efficient for infinite-horizon optimization considering the required large volume of sampling in the state space and high-quality value function identification. Therefore, we propose a sequential sampling algorithm and embed it into a DACE-based ADP method to obtain a high-quality value function approximation. Considering the limitations of the traditional stopping criterion (Bellman error bound), we further propose a 45-degree line stopping criterion to terminate value iteration early by identifying an optimally equivalent value function. A comparison of the computational results with those of other three existing policies indicates that the proposed sampling algorithm and stopping criterion can determine a high-quality ADP policy. Finally, we discuss the extrapolation issue of the value function approximated by multivariate adaptive regression splines, the results of which further demonstrate the quality of the ADP policy generated in this study. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： approximate dynamic programming State space sampling Stopping criterion Extrapolation

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An aggregation-based approximate dynamic programming approach for the periodic review model with random yield

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期281卷 286-298页

作者： Voelkel, Michael A. Sachs, Anna-Lena Thonemann, Ulrich W. Univ Cologne Dept Supply Chain Management & Management Sci D-50923 Cologne Germany Univ Lancaster Dept Management Sci Lancaster England

A manufacturer places orders periodically for products that are shipped from a supplier. During transit, orders get damaged with some probability, that is, the order is subject to random yield. The manufacturer has the option to track orders to receive information on damages and to potentially place additional orders. Without tracking, the manufacturer identifies potential damages after the order has arrived. With tracking, the manufacturer is informed about the damage when it occurs and can respond to this information. We model the problem as a dynamic program with stochastic demand, tracking cost, and random yield. For small problem sizes, we provide an adjusted value iteration algorithm that finds the optimal solution. For moderate problem sizes, we propose a novel aggregation-based approximate dynamic programming (ADP) algorithm and provide solutions for instances for which it is not possible to obtain optimal solutions. For large problem sizes, we develop a heuristic that takes tracking costs into account. In a computational study, we analyze the performance of our approaches. We observe that our ADP algorithm achieves savings of up to 16% compared to existing heuristics. Our heuristic outperforms existing ones by up to 8.1%. We show that dynamic tracking reduces costs compared to tracking always or never and identify savings of up to 3.2%. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Inventory approximate dynamic programming Random yield Tracking Value of information

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Demand side energy management of EV charging stations by approximate dynamic programming

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ENERGY CONVERSION AND MANAGEMENT 2019年 196卷 878-890页

作者： Wu, Yu Ravey, Alexandre Chrenko, Daniela Miraoui, Abdellatif Univ Bourgogne Franche Comte UTBM CNRS FEMTO ST Inst Belfort France Univ Bourgogne Franche Comte UTBM CNRS FCLAB Belfort France

The high operation cost of the EV charging station (EVCS) is a severe challenge for the development of electric vehicles, which lead to the general shortage of the EVCS. In order to reduce the operation costs of the EVCS, an approximate dynamic programming (ADP) based energy management system (EMS) is proposed for the EVCS equipped with multiple types of chargers (EVCS-MTC). A fuzzy logic guiding system has been designed to allocate each vehicle an appropriate charging spot based on its charging urgency. Multiple EVs can acquire the charging service through a common charger in the EVCS-MTC. In the proposed EMS, the approximate dynamic programming (ADP) and the evolution algorithm (EA) are combined to determine the optimal charging start time for each EV. This characteristic provides the charging device with the maximum autonomy to select the preferred flexible charging pattern, which can prolong the battery lifetime and reduce the communication requirements of the control system. With taking the dynamic electricity price and uncertain future charging demand into account, the proposed EMS can achieve a total cost reduction of over 50% compared with the conventional charging scheme in the numerical studies.

关键词： EV charging station Demand side energy management approximate dynamic programming Flexible charging pattern Multiple types of EV charger

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An approximate dynamic programming method for the optimal control of Alkai-Surfactant-Polymer flooding

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JOURNAL OF PROCESS CONTROL 2018年 64卷 15-26页

作者： Ge, Yulei Li, Shurong Chan, Peng China Univ Petr East China Coll Informat & Control Engn Qingdao 266580 Peoples R China Beijing Univ Posts & Telecommun Automat Sch Beijing 100876 Peoples R China Jiangsu Automat Res Inst Lianyungang 222006 Peoples R China

Since the complexity, coupling, distributed parameter, etc. of alkali-surfactant-polymer (ASP) flooding, common optimization methods cannot acquire the optimal solutions well. This paper brings an optimal control method for ASP flooding based on approximate dynamic programming (ADP). At first, take the net present value (NPV) as the performance index. Then the Actor-Critic algorithm based on gradient descent method is adopted to get the optimal injection strategy, in which Actor and Critic are used to approximate the control and value function, respectively. To improve the approximation performance, the linear approximation basis function based on system characteristic is constructed. Furthermore, to train and predict the control and value function in next step, a temporal difference (TD) learning algorithm is introduced to update the weight coefficients. Then, the control in ADP is generated according to the Gauss function and its weight is updated according to the sigmoid function of TD error, so that the optimal control can be searched. At last, the enhanced oil recovery problem of ASP flooding with four injection wells and nine production wells is solved by the proposed method to test the effect of proposed method. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： ASP flooding approximate dynamic programming Actor-Critic algorithm Temporal difference learning algorithm TD error Linear basis function

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Optimal Management for Parking-Lot Electric Vehicle Charging by Two-Stage approximate dynamic programming

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IEEE TRANSACTIONS ON SMART GRID 2017年第4期8卷 1722-1730页

作者： Zhang, Lei Li, Yaoyu Univ Texas Dallas Dept Elect Engn Richardson TX 75080 USA Walmart Labs Sunnyvale CA 94085 USA Univ Texas Dallas Dept Mech Engn Richardson TX 75080 USA

This paper targets the day-time charging scenario for plug-in electric vehicles at parking-lots near commercial places, where most vehicles have extended parking time. Compared with night-time charge scenarios for residential buildings, commercial building parking-lot charging during day-time feature significant stochastic vehicle arrival and departure, as well as highly dynamic electricity price. A two-stage approximate dynamic programming framework is proposed to determine the optimal charging strategy, utilizing the predicted short-term future information and long-term estimation from historical data. All the vehicles are desired to be charged to full prior to the departure time specified under constrained total charging capacity. The uncharged amount is subject to a significant penalty cost. Simulation scenarios are created by modeling the vehicle arrival behavior as Poisson process, including arrival time, departure time, and arrival state of charge. The simulation results show that the proposed method can significantly decrease the energy cost.

关键词： Charging management demand response electric vehicle approximate dynamic programming smart grid

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Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

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JOURNAL OF SCHEDULING 2010年第6期13卷 597-607页

作者： Ronconi, Debora P. Powell, Warren B. Univ Sao Paulo Escola Politecn Dept Prod Engn BR-05508900 Sao Paulo Brazil Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

关键词： Tardiness approximate dynamic programming Single machine Scheduling

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An approximate dynamic programming approach to convex quadratic knapsack problems

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COMPUTERS & OPERATIONS RESEARCH 2006年第3期33卷 660-673页

作者： Hua, ZS Zhang, B Liang, L Univ Sci & Technol China Sch Business Hefei 230026 Anhui Peoples R China

Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic programming relaxation (CQPR), and (b) the integral parts of the solutions to CQPR. We propose a new heuristic which adaptively fixes the variables according to the solution of CQPR. We report computational results for QKPs with up to 200 integer variables. Our numerical results illustrate that the new heuristic produces high-quality solutions to large-scale QKPs fast and robustly. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： approximate dynamic programming quadratic knapsack problem heuristics

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