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oai:mountainscholar.org:10217/2440232026-04-07T11:04:47Zcom_10217_100532com_10217_100000com_10217_100468com_10217_100303col_10217_100536col_10217_100469

Livingston, Colleen, author Gaines, Robert E., advisor 2026-04-06T18:25:14Z 1999 https://hdl.handle.net/10217/244023 https://doi.org/10.25675/3.026689 This paper considers existence theorems for the optimal control problem min (x,u) lo(x(0),x(T))+ ʃT0 fo(t,x(t),x(t),u(t)) subject to: x(t) = f(t ,x(t),u(t)) (x(0), x(T)) ∈ B (x(t),u(t)) ∈ F x ∈ An[0, T] u ∈ Lm[0, T] Using the results of R.T. Rockafellar this problem is reformulated into a problem in which the control and the constraints are absorbed into the objective function. Rockafellar has established a general existence theorem for such control problems. This existence theorem requires finding bounds on a Hamiltonian function. In his work Rockafellar specialized his results to certain initial value problems. The central new theorems in this paper specialize Rockafellar's general theorem to periodic problems in optimal control. These theorems are then coupled with results of R.E. Gaines and J. Peterson which give necessary conditions for a finite minimum. doctoral dissertations English eng Colorado State University. Libraries 1980-1999 Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. Per the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users. mathematics Periodic existence theorems in optimal control Text Doctor of Philosophy (Ph.D.) Doctoral Mathematics Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access