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approximate dynamic programming via Penalty Functions

IFAC-PapersOnLine 2017年第1期50卷 11814-11821页

作者： Beuchat, Paul N. Lygeros, John Automatic Control Laboratory ETH Zürich ZH8006 Switzerland

In this paper, we propose a novel formulation for encoding state constraints into the Linear programming approach to approximate dynamic programming via the use of penalty functions. To maintain tractability of the resulting optimization problem that needs to be solved, we suggest a penalty function that is constructed as a point-wise maximum taken over a family of low-order polynomials. Once the penalty functions are designed, no additional approximations are introduced by the proposed formulation. The effectiveness and numerical stability of the formulation is demonstrated through examples. © 2017

关键词： dynamic programming Linear programming Optimal control systems Stochastic control systems Stochastic systems approximate dynamic programming Low order polynomials Optimization problems Penalty function Point wise Soft constraint State constraints Stochastic optimal control problem

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Online Optimal Operation of Microgrid using approximate dynamic programming under Uncertain Environment 37

Online Optimal Operation of Microgrid using Approximate Dyna...

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37th Chinese Control Conference (CCC)

作者： Ji, Ying Wang, Jianhui Fang, Xiaoke Zhang, Huaguang Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China

ISBN: (纸本)9789881563958

This paper focuses on economical operation of a grid-connected microgrid in real-time. An online optimization model is developed to achieve the microgrid operation in the process of dynamic optimal control, and through information feedback and online optimization to reduce the impact of uncertainty in a MG. The online optimization model has the characteristics of nonlinear and discontinuous, so an approximate dynamic programming (ADP) algorithm is used to solve this online model. Finally, the proposed online optimization model is tested in the European benchmark microgrid system. The simulation results show that the online optimization model overcomes the impacts of random fluctuations of renewable energy and loads and reduces the operating cost of the microgrid.

关键词： microgrid uncertainty online optimization approximate dynamic programming

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An approximate dynamic programming approach for wind power dispatch in wind farms 37

An approximate dynamic programming approach for wind power d...

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37th Chinese Control Conference (CCC)

作者： Zhuo, Wenhao Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

ISBN: (纸本)9789881563958

With appropriate control based on predicted data of renewable energy sources, battery energy storage systems (BESS) can increase the dispatchability of wind and solar power. In a deregulated electricity market, proper charge and discharge decisions of BESS made at different price periods are likely to increase the profit for renewable power plants. In this paper, we propose an energy trading strategy for wind farms with BESS to control the actual power sold to the electric grid. To maximize the income and minimize the battery lifetime consumption, an approximate dynamic programming algorithm is produced to solve the optimal charge and discharge actions of the BESS within a future period. The rolling horizon approach is utilized, and the algorithm works with both short-term and long-term predicted data that are updated in every control step. The use of an approximate technique is to avoid the long computation time resulted from a large-scale BESS, and to meet time constraints in the rolling horizon approach. The algorithm is tested with practical wind power and electricity price data.

关键词： power control battery energy storage system battery lifetime estimation approximate dynamic programming

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Control of a networked microgrid system with an approximate dynamic programming approach

Control of a networked microgrid system with an approximate ...

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第三十八届中国控制会议

作者： Wenhao Zhuo School of Electrical Engineering and Telecommunications the University of New South Wales

Constructing microgrids with renewable energy systems and storage units can be a feasible solution to smooth the fluctuation of renewable power and increase its penetration. In recent years, research on microgrids has proven that the overall electricity and operational costs in microgrids can be further reduced with a networked microgrid system. One major issue in controlling microgrids with renewable power systems is the uncertainties due to forecasting errors, and optimization problems in a microgrid network can be could be challenging to implement due to a large number of uncertainties. In this paper, we propose an approximate dynamic programming-based power management strategy in a microgrid network system, and the objective is to minimize the overall cost over a control horizon with predicted renewable power, electricity price and load demand. The network consists of several microgrids and a centralized energy management system. The use of the approximate dynamic programming algorithm is to address the ‘curse of dimensionality' due to high dimensional state and control spaces in the network.

关键词： Control of power systems control of microgrids optimal control battery energy storage system approximate dynamic programming

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Microgrid energy management strategy with battery energy storage system and approximate dynamic programming 37

Microgrid energy management strategy with battery energy sto...

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37th Chinese Control Conference (CCC)

作者： Zhuo, Wenhao Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

ISBN: (纸本)9789881563958

The growth in distributed renewable power systems provides opportunities to construct more microgrids. With the help of battery energy storage systems (BESS) in the microgrids, the variable and intermittent renewable energy can be smoothed and utilized locally without risking the main electrical grid. Furthermore, the energy costs in microgrids can be reduced significantly with proper control of BESS based on predicted data of renewable power and electricity price. In this paper, we propose an energy management strategy for microgrids with renewable power systems integrated with BESS. A deregulated energy market environment is considered, which allows energy trading from private participates to the main electrical grids. The objective is to maximize the profit gained by selling the excessive renewable energy generated and minimize the cost to meet the load demand in the microgrid, and an approximate dynamic programming algorithm is proposed to solve the issue. The operational cost from battery lifetime consumption is considered, and the rolling horizon approach is utilized for long-term simulation. Both short-term and long-term forecasting are used in the algorithm and updated in every control stage. The algorithm is tested with practical wind power, load demand, and electricity price data.

关键词： microgrid battery energy storage system battery lifetime estimation approximate dynamic programming

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approximate dynamic programming via Penalty Functions

Approximate Dynamic Programming via Penalty Functions

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Beuchat, Paul N. Lygeros, John ETH Automat Control Lab CH-8006 Zh Switzerland

关键词： Stochastic optimal control problems approximate dynamic programming Soft constraints

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approximate dynamic programming for the United States Air Force Officer Manpower Planning Problem

Approximate Dynamic Programming for the United States Air Fo...

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作者： Kimberly S. West Air Force Institute of Technology

学位级别：硕士

The United States Air Force (USAF) makes officer accession and promotion decisions annually. Optimal manpower planning of the commissioned officer corps is vital to ensuring a well-balanced manpower system. A manpower system that is neither over-manned nor under-manned is desirable as it is most cost effective. The Air Force Officer Manpower Planning Problem (AFO-MPP) is introduced, which models officer accessions, promotions, and the uncertainty in retention rates. The objective for the AFO-MPP is to identify the policy for accession and promotion decisions that minimizes expected total discounted cost of maintaining the required number of officers in the system over an infinite time horizon. The AFO-MPP is formulated as an infinite-horizon Markov decision problem, and a policy is found using approximate dynamic programming. A least-squares temporal differencing (LSTD) algorithm is employed to determine the best approximate policies. Six computational experiments are conducted with varying retention rates and officer manning starting conditions. The policies determined by the LSTD algorithm are compared to the benchmark policy, which is the policy currently practiced by the USAF. Results indicate that when the manpower system is in a starting state with on-target numbers of officers per rank, the ADP policy outperforms the benchmark policy. When the starting state is unbalanced, with more officers in junior ranking positions, the benchmark policy outperforms the ADP policy. When the starting state is unbalanced, with more officers in senior ranking positions, there is not statistical difference between the ADP and benchmark policy. In this starting state, ADP policy has smaller variance, indicating the ADP policy is more dependable than the benchmark policy.

关键词： manpower planning officer sustainment workforce planning Markov decision processes MDP approximate dynamic programming ADP approximate policy iteration least squares temporal differences LSTD

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Three bounded proofs for nonlinear multi-input multi-output approximate dynamic programming based on the Lyapunov stability theory

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OPTIMAL CONTROL APPLICATIONS & METHODS 2018年第1期39卷 35-50页

作者： Huang, Zhijian Xiong, Xuemei Chen, Wentao Zhang, Qin Liu, Yihua Chen, Yuli Shanghai Maritime Univ Merchant Marine Coll Shanghai 201306 Peoples R China Shanghai Jiao Thng Univ Inst Power Plant & Automat Shanghai 200030 Peoples R China

The approximate dynamic programming needs 2 prerequisites to be an effective optimal control method. Firstly, it must be assured to be stable and convergent before application. Secondly, the control system should mainly he a nonlinear multi-input multi-output form. Thus, this paper introduces a nonlinear multi-input multi-output approximate dynamic programming and proves that it is stable in Lyapunov sense, therefore it is convergent. Besides, the Lyapunov function design is also analyzed. These proofs are based on the Lyapunov stability theory in the form of the utility function of quadratic, square-weighted sum, and absolute value. Thereafter, 3 typical control examples of nonlinear multi-input multi-output approximate dynamic programming arc offered to show their applications and verify the proofs. The proof overcomes the complex derivation, and the results contain 3 practical and systematic bounded proofs. It is for the first time that the proof focuses on nonlinear multi-input multi-output approximate dynamic programming from the view of utility function. What is more, the results can also serve as an effective analysis and guide for the utility function design and the stability criterion of nonlinear multi-input multi-output approximate dynamic programming as well.

关键词： approximate dynamic programming bounded proof convergent emission glider idling Lyapunov stability theory multi-input multi-output nonlinear utility function

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Risk-Averse approximate dynamic programming with Quantile-Based Risk Measures

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MATHEMATICS OF OPERATIONS RESEARCH 2018年第2期43卷 554-579页

作者： Jiang, Daniel R. Powell, Warren B. Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08540 USA

In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs;we call the overall objective a dynamic quantile-based risk measure (DQBRM). In particular, we consider optimizing dynamic risk measures where the one-step risk measures are QBRMs, a class of risk measures that includes the popular value at risk (VaR) and the conditional value at risk (CVaR). Although there is considerable theoretical development of risk-averse MDPs in the literature, the computational challenges have not been explored as thoroughly. We propose data-driven and simulation-based approximate dynamic programming (ADP) algorithms to solve the risk-averse sequential decision problem. We address the issue of inefficient sampling for risk applications in simulated settings and present a procedure, based on importance sampling, to direct samples toward the "risky region" as the ADP algorithm progresses. Finally, we show numerical results of our algorithms in the context of an application involving risk-averse bidding for energy storage.

关键词： approximate dynamic programming dynamic risk measures energy trading reinforcement learning Q-learning

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Time-dependent green vehicle routing problem with stochastic vehicle speeds: An approximate dynamic programming algorithm

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TRANSPORTATION RESEARCH PART D-TRANSPORT AND ENVIRONMENT 2017年 54卷 82-98页

作者： Cimen, Mustafa Soysal, Mehmet Hacettepe Univ Management Sci Ankara Turkey Hacettepe Univ Operat Management Ankara Turkey

This paper addresses a Time Dependent Capacitated Vehicle Routing Problem with stochastic vehicle speeds and environmental concerns. The problem has been formulated as a Markovian Decision Process. As distinct from the traditional attempts on the problem, while estimating the amount of fuel consumption and emissions, the model takes time dependency and stochasticity of the vehicle speeds into account. The Time Dependent Capacitated Vehicle Routing Problem is known to be NP-Hard for even deterministic settings. Incorporating uncertainty to the problem increases complexity, which renders classical optimization methods infeasible. Therefore, we propose an approximate dynamic programming based heuristic as a decision aid tool for the problem. The proposed Markovian Decision Model and approximate dynamic programming based heuristic are flexible in terms that more environmentally friendly solutions can be obtained by changing the objective function from cost minimization to emissions minimization. The added values of the proposed decision support tools have been shown through computational analyses on several instances. The computational analyses show that incorporating vehicle speed stochasticity into decision support models has potential to improve the performance of resulting routes in terms of travel duration, emissions and travel cost. In addition, the proposed heuristic provides promising results within relatively short computation times. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Green vehicle routing Stochastic time dependent capacitated vehicle routing problem approximate dynamic programming Markovian Decision Process

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