Abstract
In this paper we present high-order generalizations of the Maximum Principle for an optimal control problem with terminal data when the linearization around the reference trajectory is not completely controllable. They apply to both singular and abnormal cases and give nontrivial conditions in these cases. The proofs rely on high-order approximations. Specifically, a high-order generalization of the Lyusternik theorem is used to describe high-order tangent directions for non-regular equality constraints.
This research was supported in part by NSF Grant DMS-9622967 and SIUE Research Scholar Award and 1996 Summer Fellowship and also supported in part by NSF Grant DMS-9503356.
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Ledzewicz, U., Schättler, H. (1998). High-Order Extended Maximum Principles for Optimal Control Problems with Non-Regular Constraints. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_14
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DOI: https://doi.org/10.1007/978-1-4757-6095-8_14
Publisher Name: Springer, Boston, MA
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