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Order reduction and control of hyperbolic, countercurrent distributed parameter systems using method of characteristics

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CHEMICAL ENGINEERING SCIENCE 2014年 110卷 153-163页

作者： Munusamy, Sudhakar Narasimhan, Sridharakumar Kaisare, Niket S. Indian Inst Technol Dept Chem Engn Madras 600036 Tamil Nadu India ABB Corp Res Ctr Bangalore 560048 Karnataka India

The aim of this paper is to develop a model reduction technique based on method of characteristics (MOC) for control of counter-current distributed parameter systems that are modeled by semi-linear hyperbolic partial differential equations (ROES). In our previous work, MOC was shown to be a suitable model reduction technique tot a class of hyperbolic PDEs. This concept is extended to counter-current systems, wherein the so-called characteristic lines have slopes with opposite signs. Two different approximations are proposed that allow the use of MOC as a model reduction technique. The open-loop results from MOC are compared with a large dimensional model, based on the method of lines. The MOC-based models are used for closed loop simulations within the approximate dynamic programming (ADP) framework. Two case studies are considered: a non-adiabatic plug flow reactor (having characteristics with two different slopes) and a non-adiabatic fixed bed reactor (having characteristics with three different slopes). We demonstrate that using the MOC-based model in an ADP controller results in a significant improvement in computational time, along with a slight improvement in controller performance. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Distributed parameter system Method of characteristics Hyperbolic PDE Counter current systems approximate dynamic programming Model order reduction

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Fixed-final-time optimal tracking control of input-affine nonlinear systems

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NEUROCOMPUTING 2014年第0期129卷 528-539页

作者： Heydari, Ali Balakrishnan, S. N. South Dakota Sch Mines & Technol Dept Mech Engn Rapid City SD 57701 USA Missouri Univ Sci & Technol Mech & Aerosp Engn Dept Rolla MO 65409 USA

In this study, approximate dynamics programming framework is utilized for solving the Bellman equation related to the fixed-final-time optimal tracking problem of input-affine nonlinear systems. Convergence of the weights of the neurocontroller in the proposed successive approximation based algorithms is provided and the network is trained to provide the optimal solution to the problems with (a) unspecified initial conditions (b) different time horizons, and (c) different reference trajectories under certain general conditions. Numerical simulations illustrate the versatility of the proposed neurocontroller. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Fixed-final-time optimal control Optimal tracking approximate dynamic programming Adaptive critics

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Reducing the computational effort of optimal process controllers for continuous state spaces by using incremental learning and post-decision state formulations

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JOURNAL OF PROCESS CONTROL 2014年第3期24卷 133-143页

作者： Senn, Melanie Link, Norbert Pollak, Jurgen Lee, Jay H. Karlsruhe Univ Appl Sci Inst Appl Res D-76133 Karlsruhe Germany Karlsruhe Inst Technol Inst Appl Mat Reliabil Components & Syst D-76131 Karlsruhe Germany Korea Adv Inst Sci & Technol Dept Chem & Biomol Engn Taejon 305701 South Korea

Multistage optimization problems that are represented by Markov Decision Processes (MDPs) can be solved by the approach of dynamic programming (DP). However, in process control problems involving continuous state spaces, the classical DP formulation leads to computational intractability known as the 'curse of dimensionality'. This issue can be overcome by the approach of approximate dynamic programming (ADP) using simulation-based sampling in combination with value function approximators replacing the traditional value tables. In this paper, we investigate different approaches of ADP in the context of a deep cup drawing process, which is simulated by a finite element model. In applying ADP to the problem, Artificial Neural Networks (ANNs) are created as global parametric function approximators to represent the value functions as well as the state transitions. For each time step of the finite time horizon, time-indexed function approximations are built. We compare a classical DP approach to a backward ADP approach with batch learning of the ANNs and a forward ADP approach with incremental learning of the ANNs. In the batch learning mode, the ANNs are trained from temporary value tables constructed by exhaustive search backwards in time. In the incremental learning mode, on the other hand, the ANNs are initialized and then improved continually using data obtained by stochastic sampling of the simulation moving forward in time. For both learning modes, we obtain value function approximations with good performance. The cup deep drawing process under consideration is of medium model complexity and therefore allows us to apply all three methods and to perform a comparison with respect to the achieved efficiency and the associated computational effort as well as the decision behavior of the controllers. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Optimal control Continuous state space dynamic programming approximate dynamic programming Artificial Neural Network

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Sampled fictitious play for multi-action stochastic dynamic programs

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IIE TRANSACTIONS 2014年第7期46卷 742-756页

作者： Ghate, Archis Cheng, Shih-Fen Baumert, Stephen Reaume, Daniel Sharma, Dushyant Smith, Robert L. Univ Washington Seattle WA 98195 USA Singapore Management Univ Sch Informat Syst Singapore 178902 Singapore US Postal Serv Arlington VA USA Gen Motors R&D & Strateg Planning Operat Res Act Warren MI USA Univ Michigan Ind & Operat Engn Dept Ann Arbor MI 48109 USA Univ Michigan Ann Arbor MI 48109 USA Univ Michigan Natl Sci Fdn Ann Arbor MI 48109 USA Univ Michigan Dynam Syst Optimizat Lab Ann Arbor MI 48109 USA

This article introduces a class of finite-horizon dynamic optimization problems that are called multi-action stochastic dynamic Programs (DPs). Their distinguishing feature is that the decision in each state is a multi-dimensional vector. These problems can in principle be solved using Bellman's backward recursion. However, the complexity of this procedure grows exponentially in the dimension of the decision vectors. This is called the curse of action space dimensionality. To overcome this computational challenge, an approximation algorithm is proposed that is rooted in the game-theoretic paradigm of Sampled Fictitious Play (SFP). SFP solves a sequence of DPs with a one-dimensional action space that are exponentially smaller than the original multi-action stochastic DP. In particular, the computational effort in a fixed number of SFP iterations is linear in the dimension of the decision vectors. It is shown that the sequence of SFP iterates converges to a local optimum, and a numerical case study in manufacturing is presented in which SFP is able to find solutions with objective values within 1% of the optimal objective value hundreds of times faster than the time taken by backward recursion. In this case study, SFP solutions are also better by a statistically significant margin than those found by a one-step look ahead heuristic.

关键词： game theory approximate dynamic programming operations management

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OPTIMAL STOCHASTIC SWITCHING UNDER CONVEXITY ASSUMPTIONS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2014年第1期52卷 164-188页

作者： Hinz, Juri Univ Technol Sydney Sch Math Sydney NSW 2037 Australia

We address a method of approximate calculation of optimal control policy applicable to a particular class of stochastic control problems, whose stochastic dynamics exhibit a certain convexity preserving property. Problems of this type appear in many applications and encompass important examples arising in the area of optimal stopping and in the framework of control, based on partial observations. Utilizing this specific structure, we suggest a numerical method which enjoys a number of desirable properties. In particular, we work out a remarkably strong method for calculation of the value function: Within our numerically well-trackable approach, we show a convergence to the value function of the original problem uniformly on compact sets. This issue can be of great advantage, particularly for high-dimensional control problem, where the only competing methods from least-squares Monte Carlo family are able to serve merely L-p-convergence, under several restrictions. Since the presented algorithm is simple and stable, and the procedures are dimension-independent, the author hopes that it can help solving high-dimensional control problems when other methods reach their computational limits.

关键词： Markov decision approximate dynamic programming least squares Monte Carlo

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Data-Driven Neuro-Optimal Temperature Control of Water-Gas Shift Reaction Using Stable Iterative Adaptive dynamic programming

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2014年第11期61卷 6399-6408页

作者： Wei, Qinglai Liu, Derong Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China

In this paper, a novel data-driven stable iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal temperature control problems for water-gas shift (WGS) reaction systems. According to the system data, neural networks (NNs) are used to construct the dynamics of the WGS system and solve the reference control, respectively, where the mathematical model of the WGS system is unnecessary. Considering the reconstruction errors of NNs and the disturbances of the system and control input, a new stable iterative ADP algorithm is developed to obtain the optimal control law. The convergence property is developed to guarantee that the iterative performance index function converges to a finite neighborhood of the optimal performance index function. The stability property is developed to guarantee that each of the iterative control laws can make the tracking error uniformly ultimately bounded (UUB). NNs are developed to implement the stable iterative ADP algorithm. Finally, numerical results are given to illustrate the effectiveness of the developed method.

关键词： Adaptive critic designs adaptive dynamic programming (ADP) approximate dynamic programming approximation errors data-driven control neural networks (NNs) optimal control reinforcement learning water-gas shift (WGS)

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Optimal and robust strategies for freeway traffic management under demand and supply uncertainties: an overview and general theory

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2014年第10期10卷 849-877页

作者： Zhong, R. X. Sumalee, A. Pan, T. L. Lam, William H. K. Sun Yat Sen Univ Sch Engn Res Ctr Intelligent Transportat Guangzhou 510275 Guangdong Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hong Kong Hong Kong Peoples R China King Mongkuts Inst Technol Ladkrabang Dept Civil Engn Bangkok Thailand Beijing Jiaotong Univ Sch Traff & Transportat Beijing Peoples R China

This paper investigates optimal decision-making for traffic management under demand and supply uncertainties by stochastic dynamic programming. Traffic flow dynamics under demand and supply uncertainties is described by a simplified version of the stochastic cell transmission model. Based on this model, the optimal traffic management problem is analysed wherein the existence of solution is guaranteed by verifying the well-posed condition. An analytical optimal control law is derived in terms of a set of coupled generalised recursive Riccati equations. As optimal control laws may be fragile with respect to model misspecification, a robust (optimal) decision-making law that aims to act robust with respect to the parameter misspecification in the traffic flow model (which can be originated from model calibration), and to attenuate the effect of disturbances in freeway networks (wherein demand uncertainty is usually regarded as a kind of disturbance) is proposed. Conventionally, network uncertainties have been considered to induce negative effects on traffic management in transportation literature. In contrast, the proposed methodology outlines an interesting issue that is to make benefit (or trade-off) from the inherent network uncertainties. Finally, some practical issues in traffic management that can be addressed by extending the current framework are briefly discussed.

关键词： optimal traffic management stochastic dynamic programming robustness approximate dynamic programming ramp metering dynamic pricing

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Energy-Efficient Link Selection and Transmission Scheduling in Mobile Cloud Computing

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IEEE WIRELESS COMMUNICATIONS LETTERS 2014年第2期3卷 153-156页

作者： Xiang, Xudong Lin, Chuang Chen, Xin Univ Sci & Technol Beijing Dept Comp Sci & Technol Beijing 100083 Peoples R China Tsinghua Univ Tsinghua Natl Lab Informat Sci & Technol Beijing 100084 Peoples R China Beijing Informat Sci & Technol Univ Comp Sch Beijing 100101 Peoples R China

Mobile cloud computing (MCC) converges mobile computing and Cloud computing for augmenting resource-poor mobile devices to run heavier applications. With the increasing ubiquity of mobile devices, MCC exhibits vast application potential in various areas. Energy-efficient data transmission is a key issue in MCC due to energy-poverty of mobile devices. In this letter, we address the issue of energy-efficient link selection and data transmission scheduling for delay-tolerant and data-intensive applications in MCC. We first formulate the problem as a discrete-time stochastic dynamic program (SDP) that aims to optimize both system throughput and energy consumption. To solve the formulated SDP, we then propose a scalable approximate dynamic programming (ADP) algorithm that does not require the statistics of exogenous stochastic information (e.g., data arrival). Simulation studies show that the proposed ADP algorithm can reduce the average energy consumed for delivering a packet by a maximum of over 40 percent compared to alternative minimum-delay and SALSA policies.

关键词： Energy consumption transmission scheduling link selection approximate dynamic programming mobile cloud computing

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On the approximate Linear programming Approach for Network Revenue Management Problems

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INFORMS JOURNAL ON COMPUTING 2014年第1期26卷 121-134页

作者： Tong, Chaoxu Topaloglu, Huseyin Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14853 USA

One method to obtain high-quality bid prices for network revenue management problems involves using the approximate linear programming approach on the dynamic programming formulation of the problem. This approach ends up with a linear program whose number of constraints increases exponentially with the number of flight legs in the airline network. The linear program is solved using constraint generation, where each constraint can be generated by solving a separate integer program. The necessity to solve integer programs and the slow convergence behavior of constraint generation are generally recognized as drawbacks of this approach. In this paper, we show how to effectively eliminate these drawbacks. In particular, we establish that constraint generation can actually be carried out by solving minimum-cost network flow problems with natural integer solutions. Furthermore, using the structure of minimum-cost network flow problems, we a priori reduce the number of constraints in the linear program from exponential to linear in the number of flight legs. It turns out that the reduced linear program can be solved without using separate problems to generate constraints. The reduced linear program also provides a practically appealing interpretation. Computational experiments indicate that our results can speed up the computation time for the approximate linear programming approach by a factor ranging between 13 and 135.

关键词： dynamic programming optimal control applications transportation air revenue management approximate dynamic programming

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dynamic Pricing of Perishable Assets Under Competition

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MANAGEMENT SCIENCE 2014年第5期60卷 1241-1259页

作者： Gallego, Guillermo Hu, Ming Columbia Univ Dept Ind Engn & Operat Res New York NY 10027 USA Univ Toronto Rotman Sch Management Toronto ON M5S 3E6 Canada

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice, and then leave immediately with some likelihood of no purchase. The purchase likelihood depends on the time of purchase, product attributes, and current prices. The demand structure includes time-variant linear and multinomial logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be solved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment, and the latter captures the aggregate supply constraints over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large.

关键词： revenue management oligopoly dynamic pricing open-loop feedback strategy differential game stochastic game approximate dynamic programming

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