Abstract
This paper deals with optimal control problems subject to differentiable perturbations in the objective function and constraints. The results of [9] are applied to obtain upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of the directional derivative. In particular, the results show the close connection between the multipliers of the Minimum Principle and the sensitivity of the optimal value with respect to perturbations.
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Communicated by J. Stoer
Partially supported by the Deutsche Forschungsgemeinschaft under No. Ma 691/2
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Maurer, H. Differential stability in optimal control problems. Appl Math Optim 5, 283–295 (1979). https://doi.org/10.1007/BF01442559
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DOI: https://doi.org/10.1007/BF01442559