Application of Dynamic Programming Algorithm Based on Model Predictive Control in Hybrid Electric Vehicle Control Strategy

A good hybrid vehicle control strategy cannot only meet the power requirements of the vehicle,but also effectively save fuel and reduce emissions.In this paper,the construction of model predictive control in hybrid electric vehicle is proposed.The solving process and the use of reference trajectory are discussed for the application of MPC based on dynamic programming algorithm.The simulation of hybrid electric vehicle is carried out under a specific working condition.The simulation results show that the control strategy can effectively reduce fuel consumption when the torque of engine and motor is reasonably distributed,and the effectiveness of the control strategy is verified.

Powertrain Fuel Consumption Modeling and Benchmark Analysis of a Parallel P4 Hybrid Electric Vehicle Using Dynamic Programming

The goal of this work is to develop a hybrid electric vehicle model that is suitable for use in a dynamic programming algorithm that provides the benchmark for optimal control of the hybrid powertrain. The benchmark analysis employs dynamic programming by backward induction to determine the globally optimal solution by solving the energy management problem starting at the final timestep and proceeding backwards in time. This method requires the development of a backwards facing model that propagates the wheel speed of the vehicle for the given drive cycle through the driveline components to determine the operating points of the powertrain. Although dynamic programming only searches the solution space within the feasible regions of operation, the benchmarking model must be solved for every admissible state at every timestep leading to strict requirements for runtime and memory. The backward facing model employs the quasi-static assumption of powertrain operation to reduce the fidelity of the model to accommodate these requirements. Verification and validation testing of the dynamic programming algorithm is conducted to ensure successful operation of the algorithm and to assess the validity of the determined control policy against a high-fidelity forward-facing vehicle model with a percent difference of fuel consumption of 1.2%. The benchmark analysis is conducted over multiple drive cycles to determine the optimal control policy that provides a benchmark for real-time algorithm development and determines control trends that can be used to improve existing algorithms. The optimal combined charge sustaining fuel economy of the vehicle is determined by the dynamic programming algorithm to be 32.99 MPG, a 52.6% increase over the stock 3.6 L 2019 Chevrolet Blazer.

Comparison between dynamic programming and genetic algorithm for hydro unit economic load dispatch

The hydro unit economic load dispatch （ELD） is of great importance in energy conservation and emission reduction. Dynamic programming （DP） and genetic algorithm （GA） are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA＇s performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.

A Dynamic Programming Algorithm on Project- Gang Investment Decision Making

The investment decision making of Project Gang, the projects that are associated with one another on economy and technique, is studied. In order to find out the best Scheme that can make the maximum profit, a dynamic programming algorithm on the investment decision making of Project Gang is brought forward, and this algorithm can find out the best Scheme of distributing the m resources to the n Items in the time of O(m 2 n).

A Dynamic Programming Algorithm for the Ridersharing Problem Restricted with Unique Destination and Zero Detour on Trees

We deal with the problem of sharing vehicles by individuals with similar itineraries which is to find the minimum number of drivers, each of which has a vehicle capacity and a detour to realize all trips. Recently, Gu et al. showed that the problem is NP-hard even for star graphs restricted with unique destination, and gave a polynomial-time algorithm to solve the problem for paths restricted with unique destination and zero detour. In this paper we will give a dynamic programming algorithm to solve the problem in polynomial time for trees restricted with unique destination and zero detour. In our best knowledge it is a first polynomial-time algorithm for trees.

Closed-form solution to the dynamic programming for a heavy-duty parallel hybrid vehicle energy management

Dynamic programming(DP)is frequently used to obtain the optimal solution to the hybrid electric vehicle(HEV)energy management.The trade-off between the accuracy and the computational effort is the biggest problem for the DP method.The closed-form solution to the DP is proposed to solve this problem.Firstly,the affine linear model of the engine fuel rate is obtained based on engine test data.The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery.Then,the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split.The results show that this method can greatly reduce the computing burden by 93%while ensuring near-optimal fuel economy compared with the conventional DP method.

A new hybrid algorithm for global optimization and slope stability evaluation

A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm(GSA)with the sequential quadratic programming(SQP),namely GSA-SQP,for solving global optimization problems and minimization of factor of safety in slope stability analysis.The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution.In addition,it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution.A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA.In addition,the effectiveness of the proposed method for slope stability analysis was investigated using three case studies of slope stability problems from the literature.The factor of safety of earth slopes was evaluated using the Morgenstern–Price method.The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.

Implementable Strategy Research of Brake Energy Recovery Based on Dynamic Programming Algorithm for a Parallel Hydraulic Hybrid Bus

The purpose of this paper is to develop an implementable strategy of brake energy recovery for a parallel hydraulic hybrid bus. Based on brake process analysis, a dynamic programming algorithm of brake energy recovery is established. And then an implementable strategy of brake energy recovery is proposed by the constraint variable trajectories analysis of the dynamic programming algorithm in the typical urban bus cycle. The simulation results indicate the brake energy recovery efficiency of the accumulator can reach 60% in the dynamic programming algorithm. And the hydraulic hybrid system can output braking torque as much as possible.Moreover, the accumulator has almost equal efficiency of brake energy recovery between the implementable strategy and the dynamic programming algorithm. Therefore, the implementable strategy is very effective in improving the efficiency of brake energy recovery.The road tests show the fuel economy of the hydraulic hybrid bus improves by 22.6% compared with the conventional bus.

A hybrid dynamic programming-rule based algorithm for real-time energy optimization of plug-in hybrid electric bus

The optimization of the control strategy of a plug-in hybrid electric bus(PHEB) for the repeatedly driven bus route is a key technique to improve the fuel economy. The widely used rule-based(RB) control strategy is lacking in the global optimization property, while the global optimization algorithms have an unacceptable computation complexity for real-time application. Therefore, a novel hybrid dynamic programming-rule based(DPRB) algorithm is brought forward to solve the global energy optimization problem in a real-time controller of PHEB. Firstly, a control grid is built up for a given typical city bus route, according to the station locations and discrete levels of battery state of charge(SOC). Moreover, the decision variables for the energy optimization at each point of the control grid might be deduced from an off-line dynamic programming(DP) with the historical running information of the driving cycle. Meanwhile, the genetic algorithm(GA) is adopted to replace the quantization process of DP permissible control set to reduce the computation burden. Secondly, with the optimized decision variables as control parameters according to the position and battery SOC of a PHEB, a RB control is used as an implementable controller for the energy management. Simulation results demonstrate that the proposed DPRB might distribute electric energy more reasonably throughout the bus route, compared with the optimized RB. The proposed hybrid algorithm might give a practicable solution, which is a tradeoff between the applicability of RB and the global optimization property of DP.

User preference-based intelligent road route recommendation using SARSA and dynamic programming

Traffic congestion is one of the main challenges in transportation engineering. It directly impactsthe economy by increasing travel time and affecting the environment by excessive fuel consumptionand emission. Road route recommendation to overcome the congestion by alternativeroute suggestions has gained high importance. The existing route recommendation systems areproposed using the reinforcement learning algorithm (Q-learning). The techniques suggestedin this paper are state-action-reward-state-action (SARSA) algorithm and dynamic programming(DP) to guide the commuters to reach the destination with an optimal solution. The algorithmconsiders travel time, cost, flexibility, and traffic intensity as the user preference attributes torecommend an optimal route. The recommended system is implemented by building a roadnetwork graph. We assign values to each user preference attribute along the edges, which cantake high(1) or low(0) values. By considering these values, the system recommends the route.The proposed system performance is evaluated based on computation time, cumulative reward,and accuracy. The results show that DP outperforms the SARSA algorithm.

A HYBRID GRANULARITY PARALLEL ALGORITHM FOR PRECISE INTEGRATION OF STRUCTURAL DYNAMIC RESPONSES

Precise integration methods to solve structural dynamic responses and the corresponding time integration formula are composed of two parts： the multiplication of an exponential matrix with a vector and the integration term. The second term can be solved by the series solution. Two hybrid granularity parallel algorithms are designed, that is, the exponential matrix and the first term are computed by the fine-grained parallel algorithra and the second term is computed by the coarse-grained parallel algorithm. Numerical examples show that these two hybrid granularity parallel algorithms obtain higher speedup and parallel efficiency than two existing parallel algorithms.

A Hybrid Particle Swarm Optimization and Genetic Algorithm for Model Updating of A Pier-Type Structure Using Experimental Modal Analysis

Conventional design of pier structures is based on the assumption of fully rigid joints. In practice, the real connections are semi-rigid that cause changes in dynamic characteristics. In this study, quality of the joints is investigated by considering changes in natural frequencies. For this purpose, numerical and experimental modal analyses are carried out on related physical model of a pier type structure. When numerical results are evaluated,natural frequencies generally do not match the expected experimental results. Uncertainties in different aspects of engineering problems are always a challenge for researchers. The numerical models which are constructed on the basis of highly idealized scheme may not be able to represent all of the physical aspects of the physical one. For this study, determination of percentage of semi-rigid joints is considered as an optimization problem based on the numerical and experimental frequencies. Probabilistic sensitivity analysis is also used to determine the search space.A new technique of optimization problem is solved by a combination of smart particle swarm optimization(PSO)and genetic algorithms, and a complicated and efficient system for model updating process is introduced. It is observed that the hybrid PSO-Genetic algorithm is applicable and appropriate in model updating process. It performs better than PSO algorithm, considering the good agreement between theoretical frequencies and experimental ones,before and after model updating.

Dynamic airspace sectorization via improved genetic algorithm

This paper deals with dynamic airspace sectorization （DAS） problem by an improved genetic algorithm （iGA）. A graph model is first constructed that represents the airspace static structure. Then the DAS problem is formulated as a graph-partitioning problem to balance the sector workload under the premise of ensuring safety. In the iGA, multiple populations and hybrid coding are applied to determine the optimal sector number and airspace sectorization. The sector constraints are well satisfied by the improved genetic operators and protect zones. This method is validated by being applied to the airspace of North China in terms of three indexes, which are sector balancing index, coordination workload index and sector average flight time index. The improvement is obvious, as the sector balancing index is reduced by 16.5 %, the coordination workload index is reduced by 11.2 %, and the sector average flight time index is increased by 11.4 % during the peak-hour traffic.

Solving open vehicle problem with time window by hybrid column generation algorithm

This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.

A Hybrid GA-SQP Algorithm for Analog Circuits Sizing

This study presents a hybrid algorithm obtained by combining a genetic algorithm (GA) with successive quadratic sequential programming (SQP), namely GA-SQP. GA is the main optimizer, whereas SQP is used to refine the results of GA, further improving the solution quality. The problem formulation is done in the framework named RUNE (fRamework for aUtomated aNalog dEsign), which targets solving nonlinear mono-objective and multi-objective optimization problems for analog circuits design. Two circuits are presented: a transimpedance amplifier (TIA) and an optical driver (Driver), which are both part of an Optical Network-on-Chip (ONoC). Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results obtained with SQP algorithm. The outcome is very encouraging and suggests that the hybrid proposed method is very efficient in solving analog design problems.

Dynamic Optimization Algorithm for Flying Trajectory of a Free flying Space Robot

A new method of dynamic optimization for the flying trajectory of a free flying space robot based on its flying motion characteristics is presented. The continuous flying trajectory is broken into a number of segment and the control efforts and the duration of the segment are chosen as the optimization parameters. The objective function is made by using the weighted sum of the fuel used and the time spent, and the constraint equations are selected. Finally, the internal point punishment function method is adopted in the optimization program, and the results of computer simulation are given.

A NEW DETERMINISTIC FORMULATION FOR DYNAMIC STOCHASTIC PROGRAMMING PROBLEMS AND ITS NUMERICAL COMPARISON WITH OTHERS

A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.

MLD-MPC Approach for Three-Tank Hybrid Benchmark Problem

The present paper aims at validating a Model Predictive Control(MPC),based on the Mixed Logical Dynamical(MLD)model,for Hybrid Dynamic Systems(HDSs)that explicitly involve continuous dynamics and discrete events.The proposed benchmark system is a three-tank process,which is a typical case study of HDSs.The MLD-MPC controller is applied to the level control of the considered tank system.The study is initially focused on the MLD approach that allows consideration of the interacting continuous dynamics with discrete events and includes the operating constraints.This feature of MLD modeling is very advantageous when an MPC controller synthesis for the HDSs is designed.Once the MLD model of the system is well-posed,then the MPC law synthesis can be developed based on the Mixed Integer Programming(MIP)optimization problem.For solving this MIP problem,a Branch and Bound(B&B)algorithm is proposed to determine the optimal control inputs.Then,a comparative study is carried out to illustrate the effectiveness of the proposed hybrid controller for the HDSs compared to the standard MPC approach.Performances results show that the MLD-MPC approach outperforms the standardMPCone that doesn’t consider the hybrid aspect of the system.The paper also shows a behavioral test of the MLDMPC controller against disturbances deemed as liquid leaks from the system.The results are very satisfactory and show that the tracking error is minimal less than 0.1%in nominal conditions and less than 0.6%in the presence of disturbances.Such results confirm the success of the MLD-MPC approach for the control of the HDSs.

基于改进HybridA^(*)的非完整约束机器人路径规划算法研究

为了实现单舵轮AGV在物流场景下的精准自主导航,针对基于HybridA*算法搜索的路径容易贴近障碍物的缺陷和算法在路径平滑后可能与障碍物冲突的问题,本文提出一种基于改进HybridA*的非完整约束轮式移动机器人路径规划方法。对于路径搜索部分,将距离场地图引入启发式函数,以提高搜索效率,并保持搜索路径远离障碍物;对于路径平滑部分,将优化问题转化为二次规划问题,通过边界约束保证避障效果。在ROS平台上仿真实验的结果表明,该路径规划方法可有效用于非完整约束系统,为单舵轮AGV自主导航的准确运动奠定了路径智能规划的基础。

Bus frequency optimization in a large-scale multi-modal transportation system:integrating 3D-MFD and dynamic traffic assignment

A properly designed public transport system is expected to improve traffic efficiency.A high-frequency bus service would decrease the waiting time for passengers,but the interaction between buses and cars might result in more serious congestion.On the other hand,a low-frequency bus service would increase the waiting time for passengers and would not reduce the use of private cars.It is important to strike a balance between high and low frequencies in order to minimize the total delays for all road users.It is critical to formulate the impacts of bus frequency on congestion dynamics and mode choices.However,as far as the authors know,most proposed bus frequency optimization formulations are based on static demand and the Bureau of Public Roads function,and do not properly consider the congestion dynamics and their impacts on mode choices.To fill this gap,this paper proposes a bi-level optimization model.A three-dimensional Macroscopic Fundamental Diagram based modeling approach is developed to capture the bi-modal congestion dynamics.A variational inequality model for the user equilibrium in mode choices is presented and solved using a double projection algorithm.A surrogate model-based algorithm is used to solve the bi-level programming problem.