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Variable Step-Size discrete dynamic programming for Vehicle Speed Trajectory Optimization

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2019年第2期20卷 476-484页

作者： Ye, Ziqi Li, Kailai Stapelbroek, Michael Savelsberg, Rene Guenther, Marco Pischinger, Stefan Rhein Westfal TH Aachen Inst Combust Engines VKA D-52074 Aachen Germany Karlsruhe Inst Technol Inst Anthropornat & Robot Intelligent Sensor Actuator Syst Lab D-76131 Karlsruhe Germany FEV Europe GmbH D-52078 Aachen Germany

Predictive energy management has become a new focus of the automobile industry for its high potential of further reducing energy consumption. Based on previous works on predictive speed optimization using discrete dynamic programming (DDP), this paper introduces a novel approach of applying DDP with variable step size in stage variable discretization, which can realize a better tradeoff between precision and computational cost. In this approach, a "meshing" algorithm searches the points of interest (POI), such as speed limit change, traffic lights, and road curvatures, where changes in vehicle speed are expected. The algorithm increases the step-size resolution close to these points and reduces the resolutions in positions further away from POI, where the optimized vehicle speed is insensitive to the step size. With this approach, the position of POI can be precisely located to solve the DDP problem. In a test case with a relatively high density of POI, the computational cost is reduced by more than 53% by only sacrificing less than 1% of precision compared to a fixed step-size discretization with high resolutions. It can be expected that, with a lower density of POI, the computational cost will be reduced even further.

关键词： discrete dynamic programming intelligent vehicles intelligent transportation systems V2X predictive driving

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Research and application of the flatness target curve discrete dynamic programming based on two-dimensional decision making

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 256卷

作者： Jin, Shuren Li, Xu Wang, Pengfei Li, Xiaohua Zhang, Dianhua Northeastern Univ State Key Lab Rolling & Automat 83 LaneWenhua Rd Shenyang 110819 Liaoning Peoples R China Yanshan Univ Natl Engn Res Ctr Equipment & Technol Cold Strip R Qinhuangdao 066004 Heibei Peoples R China

The flatness target curve (FTC) is a fundamental process model in cold rolling flatness control, which directly affects the quality control effect of the strip. The accurate and efficient setting of the flatness target curve is the key to ensuring continuous rolling and is a common problem faced by various production companies. This paper establishes a discrete dynamic planning (DDP) setting method for FTC with two-dimensional decision-making. To quantitatively analyze the roles of the coefficients in the FTC, the preprocessing process is established using standardized processing methods and statistical analysis methods. The flatness target curve discrete dynamic programming (FTC-DDP) is based on Bellman optimization theory with a dual structure of local and system decision-making. The decision-making functions are established based on the effect of each coefficient on FTC geometric characteristics. The concepts of "curvature factor" and "wedge factor" are innovatively proposed to obtain the decision-making value functions. The regression analysis establishes the solution equations of even number coefficients, odd number coefficients, and gain coefficients, respectively. Roll bending and tilting roll analyze the FTC's ability to correct flatness defects. Meanwhile, utilizing a 1450 mm five-stand six-roll cold rolling mill, it is verified that FTC-DDP can quickly and accurately set the FTC, which provides an effective solution for obtaining high-precision and high-quality cold-rolled strips. Application results show that FTC-DDP can reduce the difficulty of setting up FTC by more than 70 %, reduce the setup time to milliseconds, and improve the setup accuracy by more than 50 %.

关键词： Cold-rolled strip Flatness control Flatness target turve discrete dynamic programming Decision-making

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Fuel Economy Optimal Control of E_REB Based on discrete dynamic programming

Fuel Economy Optimal Control of E_REB Based on Discrete Dyna...

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3rd Global Congress on Intelligent Systems (GCIS)

作者： Cao Dong-jiang Lin Cheng Sun Feng-chun Beijing Inst Technol Natl Engn Lab Elect Vehicle Beijing 100081 Peoples R China

ISBN: (纸本)9781467330725

For a certain type of Extended-Range Electric Bus(E_REB), by using discrete dynamic programming(DP) algorithm setting the battery state of charge(SOC) as state variable, seting the baterry power and the engine power as control variables, and taking the fuel economy in complete driving cycle of E_REB as the objective of optimization, then a mathematical model of equivalent fuel economy optimal control and its corresponding DP recursive equation were established. By reasonable and balanced using of the battery power and the engine power, the optimal E_REB 'mixed depletion mode' control strategies were constructed and obtained. In the process of solving DP algorithm, an algorithm of state variable SOC restricting the exploring region was applied which largely reduces the amount of computation, and effectively alleviates the curse of dimensionality in the calculation of the DP. Finally a Matlab / Simulink model is established to verify the obtained strategy and compare its results with those of instantaneous optimal control strategy. The results show that better fuel economy is obtained using globally optimal control on the premise of meeting the the principle of E_REB battery energy depletion.

关键词： component E_REB equivalent fuel economy discrete dynamic programming globally optimal control

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OPTIMALITY IN TRANSIENT MARKOV-CHAINS AND LINEAR-programming

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MATHEMATICAL programming 1980年第1期18卷 1-6页

作者： SUTHERLAND, WRS Mathematics Department Dalhousie University Halifax B3H 4H8 Nova Scotia Canada

It is shown how a discrete Markov programming problem can be transformed, using a linear program, into an equivalent problem from which the optimal decision rule can be trivially deduced. This transformation is applie... 详细信息

关键词： discrete dynamic programming Optimal Markov Chains Linear programming

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SEQUENCE ALIGNMENTS IN THE NEIGHBORHOOD OF THE OPTIMUM WITH GENERAL APPLICATION TO dynamic-programming

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES 1983年第10期80卷 3123-3124页

作者： WATERMAN, MS UNIV SO CALIF LOS ANGELES DEPT BIOL SCILOS ANGELESCA 90089

When applying dynamic programming techniques to obtain optimal sequence alignments, a set of weights must be assigned to mismatches, insertion/deletions, etc. These weights are not predetermined, although efforts are being made to deduce biologically meaningful values from data. In addition, there are sometimes unknown constraints on the sequences that cause the "true" alignment to disagree with the optimum (computer) solution. To assist in overcoming these difficulties, an algorithm has been developed to produce all alignments within a specified distance of the optimum. The distance can be chosen after the optimum is computed, and the algorithm can be repeated at will. Earlier algorithms to solve this problem were very complex and not practical for any case involving sequences with significant time or storage requirements. The algorithm presented here overcomes these difficulties and has application to general, discrete dynamic programming problems.

关键词： algorithms discrete dynamic programming K th shortest paths sequence distance sequence homology

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IDENTIFICATION AND OPTIMAL OUTPUT CONTROL OF A LABORATORY POWER-SYSTEM

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1980年第6期127卷 237-244页

作者： ABDALLA, OH WALKER, PAW Department of Electrical Engineering and Electronics University of Liverpool Liverpool UK

The paper describes the design of an optimal controller, based on output feedback, to provide integrated control of the exciter and prime mover of micro-synchronous-generator. Modelling of the control input-output measurement dynamics of the power system by an output prediction equation using least-squares analysis, is followed by multivariable control-system design based on discrete dynamic programmiing to minimise a quadratic performance index. This approach avoids any reference to the system state vector, which may contain states which are difficult to measure, and thus any need for state estimation techniques or the omission of unmeasurable states from the state feedback control law. The paper evaluates the effectiveness of this controller over a wide range of operating conditions, including dynamic and transient stability boundaries and 3-phase faults, with and without permanent line outage.

关键词： Simulation, modelling and identification exciter 3-phase faults multivariable control systems Multivariable control systems output prediction equation permanent line outage feedback Synchronous machines micro synchronous generator quadratic performance index identification dynamic programming prime mover Control of electric power systems Optimal control integrated control synchronous generators control system synthesis least squares analysis discrete dynamic programming output feedback design stability power system control optimal control laboratory power system dynamics optimal controller Control system analysis and synthesis methods Stability in control theory

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AN APPROXIMATION SCHEME FOR THE MINIMUM TIME FUNCTION

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1990年第4期28卷 950-965页

作者： BARDI, M FALCONE, M CTR RECH MATH DECIS PARISFRANCE UNIV ROME LA SAPIENZA DEPARTIMENTO MATEMATI-00185 ROMEITALY

This paper presents an approximation scheme for the nonlinear minimum time problem with compact target. The scheme is derived from a discrete dynamic programming principle and the main convergence result is obtained by applying techniques related to discontinuous viscosity solutions for Hamilton–Jacobi equations. The convergence is proved under general controllability assumptions on both the continuous-time and the discrete-time systems. An explicit sufficient condition on the system and the target ensuring the desired controllability is given. This condition is shown to be necessary and sufficient for the Lipschitz continuity of the minimum time function if the target is smooth. An extension to the case of a point-shaped target is given.

关键词： 49C20 93C55 discrete dynamic programming viscosity solution weak limits Hamilton–Jacobi equation time-optimal control

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Upshift optimization control of dedicated hybrid transmission with P2 configuration

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VEHICLE SYSTEM dynamicS 2022年第4期60卷 1416-1439页

作者： Zhao, Zhiguo Zhou, Peidong Li, Jingwei Huang, Qiqi Liang, Kaichong Tongji Univ Sch Automot Studies Shanghai Peoples R China

Based on the traditional automatic transmission, Dedicated Hybrid Transmission (DHT) with P2 configuration is developed by replacing hydraulic torque converter with a wet electronically controlled clutch and a driving motor. The paper proposed a coordinated control strategy of the upshift process for the P2 configuration parallel hybrid vehicle equipped with DHT to ensure the shift quality. Firstly, considering the meshing transmission loss, the dynamics modelling of DHT shifting process was built by Lagrange method, and the model parameters were identified by bench test;Secondly, taking no jerk as the constraint and minimum slipping work as the optimisation goal, the forward discrete dynamic programming was used to solve the optimal control law of the transmission torque of the shifting clutch and the input shaft torque of transmission. Besides, for the hybrid operation mode, further considering the influence of the motor, engine and main clutch, two coordinated control strategies of the main clutch engagement and slipping were proposed. The simulation results show that the two coordinated control strategies can achieve small jerk and slipping work, ensure smoothness in the course of gear shift. And by the method of slipping control of the main clutch, the shifting time can be shortened.

关键词： Dedicated hybrid transmission with p2 configuration coordinated control strategy discrete dynamic programming slip control of the main clutch

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dynamic pricing using flexible heterogeneous sales response models

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OR SPECTRUM 2024年第1期46卷 29-72页

作者： Aschersleben, Philipp Steiner, Winfried J. Tech Univ Clausthal Dept Mkt Julius Albert Str 2 D-38678 Clausthal Zellerfeld Germany

We combine nonparametric price response modeling and dynamic pricing. In particular, we model sales response for fast-moving consumer goods sold by a physical retailer using a Bayesian semiparametric approach and incorporate the price of the previous period as well as further time-dependent covariates. All nonlinear effects including the one-period lagged price dynamics are modeled via P-splines, and embedding the semiparametric model into a Hierarchical Bayesian framework enables the estimation of nonlinear heterogeneous (i.e., store-specific) immediate and lagged price effects. The nonlinear heterogeneous model specification is used for price optimization and allows the derivation of optimal price paths of brands for individual stores of retailers. In an empirical study, we demonstrate that our proposed model can provide higher expected profits compared to competing benchmark models, while at the same time not seriously suffering from boundary problems for optimized prices and sales quantities. Optimal price policies for brands are determined by a discrete dynamic programming algorithm.

关键词： Sales response models Functional flexibility Store heterogeneity Price dynamics Price optimization discrete dynamic programming

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Application of artificial neural network for optimal operation of a multi-purpose multi-reservoir system, I: initial solution and selection of input variables

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SUSTAINABLE WATER RESOURCES MANAGEMENT 2020年第4期6卷 1-13页

作者： Shaikh, Safayat Ali Aliah Univ Dept Civil Engn Kolkata India

In this two-part series research paper, the effect of different input variables for optimal operation of a multipurpose multi-reservoir system using artificial neural network (ANN) models has been thoroughly investigated. As an alternative to multi-reservoir stochastic model, dynamic programming-based ANN models are developed. Due to nonavailability of any specific criterion to select the number and type of input variables for such ANN model, an exhaustive study with various combinations of input variables for single-reservoir ANN models is done. Damodar Valley, a multi-purpose multi-reservoir system in India, is used for this study. Results obtained from discrete dynamic programming, an optimization technique, are used as training data for ANN models. With different combinations of input data, five types of ANN models are developed. ANN models are simulated with generated inflow sequence as well as different types of observed historical inflow sequences. For each simulation, 240 monthly networks are trained and stored. Four different stochastic dynamic programming (SDP) models of the system are developed considering one reservoir at a time approach. Linear regression analysis is performed between the results obtained from ANN models with results of the best SDP model. Objective function values as well as different regression parameters are compared to select preferred ANN model and its input variables.

关键词： Artificial neural network discrete dynamic programming Stochastic dynamic programming Reservoir operation

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