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Convergence of the gradient projection method in optimal control problems

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Abstract

The article examines the convergence of the popular gradient projection method for optimal control problems with fixed time and a free right-hand end point. General conditions are derived that substantiate weak convergence of the sequence of control iterations to the set of extremum controls satisfying Pontryagin’s maximum principle. Under stronger assumptions we prove strong convergence of the sequence in the Banach L 1-norm.

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Authors
  1. M. S. Nikol’skii
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Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 139–148, 2003.

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Nikol’skii, M.S. Convergence of the gradient projection method in optimal control problems. Comput Math Model 18, 148–156 (2007). https://doi.org/10.1007/s10598-007-0015-y

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  • DOI: https://doi.org/10.1007/s10598-007-0015-y

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