Periodic existence theorems in optimal control

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.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

1999

Authors dc:creator

• Livingston, Colleen, author
• Gaines, Robert E., advisor

• mathematics

Statement dc:rights

• 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.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.026689

OAI identifier oai:identifier

oai:mountainscholar.org:10217/244023