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Existence of optimal controls for nonlinear systems in Banach spaces

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Abstract

Using a recent result of Castaing and Clauzure on the lower semicontinuity of integral functionals, we prove the existence of an optimal control for a broad class of nonlinear infinite-dimensional control systems. An example of a distributed parameter system is worked in detail.

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Additional information

This research was supported by NSF Grant No. DMS-84-03135.

Communicated by L. Cesari

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Papageorgiou, N.S. Existence of optimal controls for nonlinear systems in Banach spaces. J Optim Theory Appl 53, 451–459 (1987). https://doi.org/10.1007/BF00938949

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Key Words

  • Evolution operators
  • optimal control
  • weak compactness
  • measurable functions
  • Gronwall's inequality