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
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
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Publisher:
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%
