Tube Stochastic Differential Dynamic Programming for Robust Low-Thrust Trajectory Optimization Problems

2018 ◽  
Author(s):  
Naoya Ozaki ◽  
Ryu Funase
Keyword(s):  
Dynamic Programming ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Low Thrust ◽  
Differential Dynamic Programming

scholarly journals A Survey on Low-Thrust Trajectory Optimization Approaches

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 88
Author(s):  
David Morante ◽  
Manuel Sanjurjo Rivo ◽  
Manuel Soler
Keyword(s):  
Optimal Control ◽  
Objective Function ◽  
Trajectory Optimization ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Mathematical Framework ◽  
Low Thrust ◽  
Discrete State ◽  
Hybrid Optimal Control

In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers.

scholarly journals A Modified Dynamic Programming Approach for 4D Minimum Fuel and Emissions Trajectory Optimization

Aerospace ◽  
2021 ◽  
Vol 8 (5) ◽  
pp. 135
Author(s):  
Kawser Ahmed ◽  
Kouamana Bousson ◽  
Milca de Freitas Coelho
Keyword(s):  
Dynamic Programming ◽  
Fuel Consumption ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Computational Effort ◽  
Programming Approach ◽  
Optimal Trajectories ◽  
Flight Trajectory ◽  
Aircraft Fuel ◽  
Fuel Consumption And Emissions

4D flight trajectory optimization is an essential component to improve flight efficiency and to enhance air traffic capacity. this technique not only helps to reduce the operational costs, but also helps to reduce the environmental impact caused by the airliners. This study considers Dynamic Programming (DP), a well-established numerical method ideally suited to solve 4D flight Trajectory Optimization Problems (TOPs). However, it bears some shortcomings that prevent the use of DP in many practical real-time implementations. This paper proposes a Modified Dynamic Programming (MDP) approach that reduces the computational effort and overcomes the drawbacks of the traditional DP. In this paper, two numerical examples with fixed arrival times are presented, where the proposed MDP approach is successfully implemented to generate optimal trajectories that minimize aircraft fuel consumption and emissions. Then the obtained optimal trajectories are compared with the corresponding reference commercial flight trajectory for the same route in order to quantify the potential benefit of reduction of aircraft fuel consumption and emissions.

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