Record link: 
http://hdl.handle.net/20.500.12708/147055
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Title: 
On the Convergence of the Gradient Projection Method for Optimal Control Problems with Bang-Bang Solutions
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Citation: 
Preininger, J., & Phan, V. (2017). On the Convergence of the Gradient Projection Method for Optimal Control Problems with Bang-Bang Solutions (No. 2017–10). Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems. http://hdl.handle.net/20.500.12708/147055
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Publication Type: 
Report - Research Report
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Language: 
English
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Authors: 
Preininger, Jakob 
Phan, Vuong 
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Organisational Unit: 
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research 
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Series: 
ORCOS (Operations Research and Control Systems Theory) 
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Report No.: 
2017-10
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Date (published): 
2017
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Number of Pages: 
18
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Publisher: 
Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems, Vienna, Austria
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Keywords: 
Applied Mathematics; Computational Mathematics; Optimal control; Control and Optimization; Gradient projection method; Strong convergence; Convergence rate; Bang-bang contro
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Abstract: 
We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang-bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.
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Research Areas: 
Fundamental Mathematics Research: 50%
Mathematical and Algorithmic Foundations: 50%
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Science Branch: 
Mathematik
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