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Optimal Control Problems with Switching PointsThe main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
Document ID
19910022841
Acquisition Source
Langley Research Center
Document Type
Thesis/Dissertation
Authors
Seywald, Hans
(Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
Date Acquired
September 6, 2013
Publication Date
September 1, 1991
Publication Information
Publisher: NASA
Subject Category
Launch Vehicles And Launch Operations
Report/Patent Number
NASA-CR-4393
NAS 1.26:4393
Accession Number
91N32155
Funding Number(s)
CONTRACT_GRANT: NAG1-946
PROJECT: RTOP 946-01-00-78
CONTRACT_GRANT: F49620-87-C-0116
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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