Convergence for the optimal control problems using collocation at Legendre-Gauss points

2021 ◽  
pp. 014233122110433
Author(s):  
Heng Mai
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Shooting Method ◽  
Pseudospectral Method ◽  
Single Step ◽  
The Novel ◽  
Step Method ◽  
Gauss Method ◽  
Gauss Points

The convergence of the novel Legendre-Gauss method is established for solving a continuous optimal control problem using collocation at Legendre-Gauss points. The method allows for changes in the number of Legendre-Gauss points to meet the error tolerance. The continuous optimal control problem is first discretized into a nonlinear programming problem at Gauss collocations by the Legendre-Gauss method. Subsequently, we prove the convergence of the Legendre-Gauss algorithm under the assumption that the continuous optimal control problem has a smooth solution. Compared with those of the shooting method, the single step method, and the general pseudospectral method, the numerical example shows that the Legendre-Gauss method has higher computational efficiency and accuracy in solving the optimal control problem.

A pseudospectral method for solving optimal control problem of a hybrid tracked vehicle

2017 ◽  
Vol 194 ◽  
pp. 588-595 ◽  
Author(s):  
Shouyang Wei ◽  
Yuan Zou ◽  
Fengchun Sun ◽  
Onder Christopher
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pseudospectral Method ◽  
Tracked Vehicle

Study on the optimal lane changing steering input under different road adhesion coefficients

2019 ◽  
Vol 234 (3) ◽  
pp. 384-395
Author(s):  
Xinglong Zhang ◽  
Youqun Zhao ◽  
Wenxin Zhang ◽  
Fen Lin ◽  
Liguo Zang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Inverse Dynamics ◽  
Pseudospectral Method ◽  
Reference Value ◽  
Unmanned Vehicles ◽  
Control Input ◽  
Computational Accuracy ◽  
Lane Changing

To study the influence of road adhesion coefficient on lane changing steering input, vehicle handling inverse dynamics based on hp-adaptive Radau pseudospectral method is proposed in this article. First, a steering inverse dynamics model is established and then the inverse dynamics problem is converted into an optimal control problem. Second, by applying the hp-adaptive Radau pseudospectral method, the optimal control problem is converted into a nonlinear programming problem, which is then solved through sequential quadratic programming. Besides, two contrast verifications are carried out to validate the correctness and advantages of the proposed method. The simulation results show that the obtained control input satisfies the vehicle dynamic constraints. And comparing with Gauss Pseudospectral Method (GPM), hp-adaptive Radau pseudospectral method has higher computational accuracy and computational efficiency when solving non-smooth problem. The study of optimal steering input can provide guidance for driver’s lane changing behavior, so that the accident rate caused by human factors can be decreased. The proposed method can provide a reference value into the active safety of manned and unmanned vehicles.

Trajectory planning with mid-air collision avoidance for quadrotor unmanned aerial vehicles

2021 ◽  
pp. 095441002110440
Author(s):  
Yuhang Jiang ◽  
Shiqiang Hu ◽  
Christopher J Damaren
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Unmanned Aerial Vehicles ◽  
Collision Avoidance ◽  
Trajectory Planning ◽  
Pseudospectral Method ◽  
Planning Problem ◽  
Aerial Vehicles ◽  
Optimal Control Algorithms

Flight collision between unmanned aerial vehicles (UAVs) in mid-air poses a potential risk to flight safety in low-altitude airspace. This article transforms the problem of collision avoidance between quadrotor UAVs into a trajectory-planning problem using optimal control algorithms, therefore achieving both robustness and efficiency. Specifically, the pseudospectral method is introduced to solve the raised optimal control problem, while the generated optimal trajectory is precisely followed by a feedback controller. It is worth noting that the contributions of this article also include the introduction of the normalized relative coordinate, so that UAVs can obtain collision-free trajectories more conveniently in real time. The collision-free trajectories for a classical scenario of collision avoidance between two UAVs are given in the simulation part by both solving the optimal control problem and querying the prior results. The scalability of the proposed method is also verified in the simulation part by solving a collision avoidance problem among multiple UAVs.

A NEW COMBINATION OF BROYDEN-FLETCHER-GOLDFARB-SHANNO AND BRENT TECHNIQUES IN SHOOTING METHOD FOR SOLVING NON-CLASSICAL OPTIMAL CONTROL PROBLEM

2017 ◽  
Vol 102 (11) ◽  
pp. 2785-2796
Author(s):  
Wan N. A. W. Ahmad ◽  
Mohd Saifullah Rusiman ◽  
Suliadi F. Sufahani ◽  
Alan Zinober ◽  
Mahathir Mohammad ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Shooting Method ◽  
New Combination

scholarly journals Multiphase Return Trajectory Optimization Based on Hybrid Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Yi Yang ◽  
Ying Nan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Optimization ◽  
Pseudospectral Method ◽  
Optimization Method ◽  
Natural Computation ◽  
Improve Calculation ◽  
Computation Algorithm ◽  
The Right

A hybrid trajectory optimization method consisting of Gauss pseudospectral method (GPM) and natural computation algorithm has been developed and utilized to solve multiphase return trajectory optimization problem, where a phase is defined as a subinterval in which the right-hand side of the differential equation is continuous. GPM converts the optimal control problem to a nonlinear programming problem (NLP), which helps to improve calculation accuracy and speed of natural computation algorithm. Through numerical simulations, it is found that the multiphase optimal control problem could be solved perfectly.

scholarly journals Optimization of cereal output in presence of locusts

2016 ◽  
Vol 6 (1) ◽  
pp. 53-61 ◽  
Author(s):  
Nacima Moussouni ◽  
Mohamed Aidene
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pontryagin Maximum Principle ◽  
Shooting Method ◽  
The Pontryagin Maximum Principle

In this paper, we study a modelization of the evolution of cereal output production, controlled by adding fertilizers and in presence of locusts, then by adding insecticides. The aim is to maximize the cereal output and meanwhile minimize pollution caused by adding fertilizers and insecticides.The optimal control problem obtained is solved theoretically by using the Pontryagin Maximum Principle, and then numerically with shooting method.

USING PSEUDOSPECTRAL METHOD TO SEARCH FOR PROPELLANT-OPTIMAL TRAJECTORIES OF THE INTERNATIONAL SPACE STATION ATTITUDE CONTROL MANEUVERS

2019 ◽  
pp. 121-133
Author(s):  
A.A. Prutko ◽  
S.N. Atroshenkov ◽  
A.V. Bogachev ◽  
A.E. Starchenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
International Space Station ◽  
Motion Control ◽  
Attitude Control ◽  
Space Station ◽  
Pseudospectral Method ◽  
Optimal Trajectories ◽  
International Space

The paper discusses the problem of searching for propellant-optimal trajectories of the International Space Station attitude control maneuvers involving spatial turns through large angles using attitude control jet thrusters. Development of such algorithms for controlling the ISS angular motion is currently a crucial task for Russian developers of the onboard software. In order to generate the optimal trajectory for the attitude control maneuver, the paper proposes to use the Lobatto pseudospectral method. This method allows stating the optimal control problem as a nonlinear mathematical programming problem which can be solved using the method of sequential quadratic programming. Simulation results demonstrated significant savings of attitude control thrusters propellant and life during station attitude control maneuvers in comparison with the algorithms that are currently used in the motion control system of the ISS Russian Segment. Key words: International Space Station, optimal control problem, angular motion control, pseudospectral method, nonlinear programming

scholarly journals A Trajectory Planning Method for Autonomous Valet Parking via Solving an Optimal Control Problem

Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6435
Author(s):  
Chen Chen ◽  
Bing Wu ◽  
Liang Xuan ◽  
Jian Chen ◽  
Tianxiang Wang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Pseudospectral Method ◽  
Initial Guess ◽  
Planning Method ◽  
Planning Problem ◽  
Starting Position ◽  
Dynamic Obstacle Avoidance

In the last decade, research studies on parking planning mainly focused on path planning rather than trajectory planning. The results of trajectory planning are more instructive for a practical parking process. Therefore, this paper proposes a trajectory planning method in which the optimal autonomous valet parking (AVP) trajectory is obtained by solving an optimal control problem. Additionally, a vehicle kinematics model is established with the consideration of dynamic obstacle avoidance and terminal constraints. Then the parking trajectory planning problem is modeled as an optimal control problem, while the parking time and driving distance are set as the cost function. The homotopic method is used for the expansion of obstacle boundaries, and the Gauss pseudospectral method (GPM) is utilized to discretize this optimal control problem into a nonlinear programming (NLP) problem. In order to solve this NLP problem, sequential quadratic programming is applied. Considering that the GPM is insensitive to the initial guess, an online calculation method of vertical parking trajectory is proposed. In this approach, the offline vertical parking trajectory, which is calculated and stored in advance, is taken as the initial guess of the online calculation. The selection of an appropriate initial guess is based on the actual starting position of parking. A small parking lot is selected as the verification scenario of the AVP. In the validation of the algorithm, the parking trajectory planning is divided into two phases, which are simulated and analyzed. Simulation results show that the proposed algorithm is efficient in solving a parking trajectory planning problem. The online calculation time of the vertical parking trajectory is less than 2 s, which meets the real-time requirement.

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