scholarly journals Adaptive Partial Train Speed Trajectory Optimization

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3302 ◽  
Author(s):  
Zhaoxiang Tan ◽  
Shaofeng Lu ◽  
Kai Bao ◽  
Shaoning Zhang ◽  
Chaoxian Wu ◽  
...  
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Pseudospectral Method ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Computation Efficiency ◽  
Full Speed ◽  
Train Operation ◽  
Train Speed ◽  
Future Work

Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.

Notch-based speed trajectory optimisation for high-speed railway automatic train operation

2021 ◽  
pp. 095440972110421
Author(s):  
Minling Feng ◽  
Chaoxian Wu ◽  
Shaofeng Lu ◽  
Yihui Wang
Keyword(s):  
High Speed ◽  
Applied Force ◽  
Mixed Integer ◽  
High Speed Railway ◽  
Train Operation ◽  
Train Speed ◽  
Automatic Train Operation ◽  
The Impact ◽  
Trajectory Optimisation

Automatic train operation (ATO) systems are fast becoming one of the key components of the intelligent high-speed railway (HSR). Designing an effective optimal speed trajectory for ATO is critical to guide the high-speed train (HST) to operate with high service quality in a more energy-efficient way. In many advanced HSR systems, the traction/braking systems would provide multiple notches to satisfy the traction/braking demands. This paper modelled the applied force as a controlled variable based on the selection of notch to realise a notch-based train speed trajectory optimisation model to be solved by mixed integer linear programming (MILP). A notch selection model with flexible vertical relaxation was proposed to allow the traction/braking efforts to change dynamically along with the selected notch by introducing a series of binary variables. Two case studies were proposed in this paper where Case study 1 was conducted to investigate the impact of the dynamic notch selection on train operations, and the optimal result indicates that the applied force can be flexibly adjusted corresponding to different notches following a similar operation sequence determined by optimal train control theory. Moreover, in addition to the maximum traction/braking notches and coasting, medium notches with appropriate vertical relaxation would be applied in accordance with the specific traction/braking demands to make the model feasible. In Case study 2, a comprehensive numerical example with the parameters of CRH380AL HST demonstrates the robustness of the model to deal with the varying speed limit and gradient in a real-world scenario. The notch-based model is able to obtain a more realistic optimal strategy containing dynamic notch selection and speed trajectory with an increase (1.622%) in energy consumption by comparing the results of the proposed model and the non-notch model.

scholarly journals Trajectory optimization of UAV based on Hp-adaptive Radau pseudospectral method

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yi Cui ◽  
Xintong Fang ◽  
Gaoqi Liu ◽  
Bin Li
Keyword(s):  
Trajectory Planning ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Tracking Error ◽  
Pseudospectral Method ◽  
Planning Problem ◽  
A Algorithm ◽  
Planning Scheme ◽  
Path Search ◽  
Simulation Results

<p style='text-indent:20px;'>Unmanned Aerial Vehicles (UAVs) have been extensively studied to complete the missions in recent years. The UAV trajectory planning is an important area. Different from the commonly used methods based on path search, which are difficult to consider the UAV state and dynamics constraints, so that the planned trajectory cannot be tracked completely. The UAV trajectory planning problem is considered as an optimization problem for research, considering the dynamics constraints of the UAV and the terrain obstacle constraints during flight. An hp-adaptive Radau pseudospectral method based UAV trajectory planning scheme is proposed by taking the UAV dynamics into account. Numerical experiments are carried out to show the effectiveness and superior of the proposed method. Simulation results show that the proposed method outperform the well-known RRT* and A* algorithm in terms of tracking error.</p>

Rapid trajectory optimization for hypersonic entry using a pseudospectral-convex algorithm

2019 ◽  
Vol 233 (14) ◽  
pp. 5227-5238 ◽  
Author(s):  
Jinbo Wang ◽  
Naigang Cui ◽  
Changzhu Wei
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Trajectory Optimization ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Interior Point Methods ◽  
Pseudospectral Method ◽  
Trust Region ◽  
Convergence Properties ◽  
Dynamic Trust

Aiming at improving the autonomy of hypersonic entry vehicles, a rapid trajectory optimization algorithm, which has the potential to be implemented online and onboard, is proposed in this paper. The nonlinear and nonconvex hypersonic entry trajectory optimization problem is transformed into a series of convex subproblems through a proper combination of the pseudospectral method and an improved successive convexification method; thus, the high discretization accuracy of the pseudospectral method and the fast and deterministic convergence properties of the convex-optimization-based algorithm can be simultaneously exploited. The resulting subproblems can be solved efficiently by matured interior-point methods, and the solution converges rapidly by adopting a novel dynamic trust-region updating approach. The optimality of the solution is verified by the optimal control theory. The effectiveness of the algorithm is demonstrated by numerical experiments.

scholarly journals The Multiobjective Trajectory Optimization for Hypersonic Glide Vehicle Based on Normal Boundary Intersection Method

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengnan Li ◽  
Tao Yang ◽  
Zhiwei Feng
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Pseudospectral Method ◽  
Optimization Method ◽  
Initial Guess ◽  
Programming Algorithm ◽  
Trajectory Design ◽  
Normal Boundary ◽  
Vehicle Trajectory ◽  
Intersection Method

To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP) is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by using the boundary intersection method and pseudospectral method. The subproblems are solved by nonlinear programming algorithm. In this method, the solution that has been solved is employed as the initial guess for the next subproblem so that the time consumption of the entire multiobjective trajectory optimization problem shortens. The maximal range and minimal peak heat problem is solved by the proposed method. The numerical results demonstrate that the proposed method can obtain the Pareto front of the optimal trajectory, which can provide the reference for the trajectory design of hypersonic glider vehicle.

Reentry Trajectory Optimization and Simulation of Hypersonic Vehicle with Maximum Cross Range Based on GPM

2014 ◽  
Vol 635-637 ◽  
pp. 1431-1437
Author(s):  
Wu Jun Huo ◽  
Xu Liu ◽  
Li Wang ◽  
Chao Song
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Control Variable ◽  
Pseudospectral Method ◽  
Hypersonic Vehicle ◽  
State Variables ◽  
Hypersonic Aircraft ◽  
Gauss Pseudospectral Method ◽  
Reentry Trajectory ◽  
Reentry Trajectory Optimization

Abstract：The application of Gauss pseudospectral method (GPM) to hypersonic aircraft reentry trajectory optimization problem with maximum cross range was introduced. The Gauss pseudospectral method was used to solve the reentry trajectory of the hypersonic vehicle with the maximum cross range. Firstly, the model of hypersonic aircraft reentry trajectory optimization control problem was established. Taking no account of course constraint, the maximum cross range was chosen as optimal performance index, and angle of attack and bank was chosen as control variable. Terminal state was constrained by position and velocity. Then GPM was applied to change trajectory optimization problem into nonlinear programming problem (NLP), and the state variables and control variables were selected as optimal parameters at all Gauss nodes. At last, optimal reentry trajectory was solved by solving the NLP with the help of SNOPT. The simulation results indicate that GPM does not need to estimate the initial cost variable, and it is not sensitive to the initial states and effective to solve trajectory optimization problem.

scholarly journals The Earth-Mars Transfer Trajectory Optimization of Solar Sail Based on hp-Adaptive Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Yufei Guo ◽  
Dongzhu Feng ◽  
Xin Wang ◽  
Cong Li ◽  
Yunzhao Liu
Keyword(s):  
Trajectory Optimization ◽  
Optimization Problem ◽  
Computational Cost ◽  
Pseudospectral Method ◽  
Solar Sail ◽  
Polar Coordinate System ◽  
Optimization Strategy ◽  
Solar Sails ◽  
Kinematic Equation ◽  
Transfer Trajectory

Solar sails have many advantages over traditional chemical propulsion spacecraft, such as needlessness of fuel, high payload ratio, long service life, and great application potential in deep space exploration, interstellar voyage, and other aerospace application fields. However, the period of solar sail transfer from the initial orbit to the desired orbit is relatively long. Thus, it is necessary to optimize the transfer trajectory of solar sail according to specific tasks. The hp-adaptive pseudospectral method combines the global pseudospectral method with the finite element method, which adopts double layer optimization strategy to solve the optimal control problem and has higher computational efficiency and accuracy than the traditional global pseudospectral method. In this paper, the pressure of solar light acting on the solar sail is analyzed, and the kinematic equation of the solar sail is established in polar coordinate system first; then the basic principle of the hp-adaptive pseudospectral method is introduced, and the steps of solving the transfer trajectory optimization problem by hp-adaptive pseudospectral method are proposed; finally, the trajectory optimization of the solar sail from Earth orbit to Sun-centered Mars orbit is simulated as an example to demonstrate the effectiveness of hp-adaptive pseudospectral method in the orbit transfer optimization problem of solar sail. The simulation results show that the adopted method is not sensitive to the initial values and has more reasonable distribution and less computational cost than the Gauss pseudospectral method.

scholarly journals Receding Horizon Trajectory Optimization with Terminal Impact Specifications

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Limin Zhang ◽  
Mingwei Sun ◽  
Zengqiang Chen ◽  
Zenghui Wang ◽  
Yongkun Wang
Keyword(s):  
Programming Language ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Pseudospectral Method ◽  
Optimization Strategy ◽  
Receding Horizon ◽  
C Programming Language ◽  
Gauss Pseudospectral Method ◽  
C Programming ◽  
The Cost

The trajectory optimization problem subject to terminal impact time and angle specifications can be reformulated as a nonlinear programming problem using the Gauss pseudospectral method. The cost function of the trajectory optimization problem is modified to reduce the terminal control energy. A receding horizon optimization strategy is implemented to reject the errors caused by the motion of a surface target. Several simulations were performed to validate the proposed method via the C programming language. The simulation results demonstrate the effectiveness of the proposed algorithm and that the real-time requirement can be easily achieved if the C programming language is used to realize it.

scholarly journals Path Planning for Rapid Large-Angle Maneuver of Satellites Based on the Gauss Pseudospectral Method

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wan Zhang ◽  
Yao Zhang ◽  
Wenbo Li ◽  
Youyi Wang
Keyword(s):  
Attitude Control ◽  
Trajectory Optimization ◽  
Optimal Trajectory ◽  
Optimization Problem ◽  
Large Angle ◽  
Pseudospectral Method ◽  
Performance Criteria ◽  
Planning Problem ◽  
Singularity Problem ◽  
Gauss Pseudospectral Method

A Gauss pseudospectral method is proposed in this study to solve the optimal trajectory-planning problem for satellite rapid large-angle maneuvers. In order to meet the requirement of rapid maneuver capability of agile small satellites, Single Gimbal Control Moment Gyros (SGCMGs) are adopted as the actuators for the attitude control systems (ACS). Because the singularity problem always exists for SGCMGs during the large-angle maneuvering of the satellites, a trajectory optimization method for the gimbal rates is developed based on the Gauss pseudospectral method. This method satisfies the control requirement of satellite rapid maneuvers and evades the singularity problem of SGCMGs. The method treats the large-angle maneuver problem as an optimization problem, which meets the boundary condition and a series of the physical constraints including the gimbal angle constraint, the gimbal rates constraint, the singularity index constraint, and some other performance criteria. This optimization problem is discretized as a nonlinear programming problem by the Gauss pseudospectral method. The optimal nonsingularity gimbal angle trajectory is obtained by the sequence of quadratic programming (SQP). This approach avoids the difficulties in solving the boundary value problem. The simulations reveal that the Gauss pseudospectral method effectively plans an optimal trajectory and satisfies all the constraints within a short time.

Identifying Physico-Chemical Laws from the Robotically Collected Data

2019 ◽  
Author(s):  
Liwei Cao ◽  
Danilo Russo ◽  
Vassilios S. Vassiliadis ◽  
Alexei Lapkin
Keyword(s):  
Experimental Data ◽  
Numerical Models ◽  
Predictor Variable ◽  
Physical Models ◽  
Training Data ◽  
Mixed Integer ◽  
Physico Chemical ◽  
Data Points ◽  
Future Work ◽  
The Relationship

<p>A mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed to identify physical models from noisy experimental data. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the number of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was coupled with the collection of experimental data in an automated fashion, and was proven to be successful in identifying the correct physical models describing the relationship between the shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of reactions. Future work will focus on addressing the limitations of the formulation presented in this work, by extending it to be able to address larger complex physical models.</p><p><br></p>

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