On Application of Gaussian Functions for Numerical Solution of Optimal Control Problems

It is proved that the linear combinations of shifts and contractions of the Gaussian function can be used for an arbitrarily accurate approximation in the space of continuous functions of one variable on any fixed intervals. On the example of the soft lunar landing problem, a method for the numerica...

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Bibliographic Details
Published in:Automation and remote control 2019-06, Vol.80 (6), p.1026-1040
Main Author: Chernov, A. V.
Format: Article
Language:English
Subjects:
Approximation
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Continuity (mathematics)
Control
Error analysis
Error detection
Lunar landing
Mathematics
Mathematics and Statistics
Maximum principle
Mechanical Engineering
Mechatronics
Nonlinear Systems
Optimal control
Parameter sensitivity
Parameterization
Production planning
Robotics
Systems Theory
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Summary:It is proved that the linear combinations of shifts and contractions of the Gaussian function can be used for an arbitrarily accurate approximation in the space of continuous functions of one variable on any fixed intervals. On the example of the soft lunar landing problem, a method for the numerical solution of optimal control problems based on this approximation procedure of the control function is described. Within the framework of the same example, the sensitivity of constraint functionals to the specification error of optimal parameters is investigated using three approaches as follows: 1) Pontryagin’s maximum principle (both numerically and theoretically); 2) the control parametrization technique in combination with the method of sliding nodes; 3) the newly proposed method. A comparative analysis is performed that confirms the effectiveness of the third method.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117919060031