On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions

J. Preininger () and P. T. Vuong ()
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J. Preininger: Vienna University of Technology
P. T. Vuong: Vienna University of Technology

Computational Optimization and Applications, 2018, vol. 70, issue 1, No 8, 238 pages

Abstract: 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.

Keywords: Gradient projection method; Strong convergence; Convergence rate; Optimal control; Bang–bang control; 47J20; 49J15; 49M05; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10589-018-9981-6

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