Finite-Difference Approximations And Optimal Control Of Differential Inclusions

<p>This dissertation concerns the study of the generalized Bolza type problem for dynamic systems governed by constrained differential inclusions. We develop finite-discrete approximations of differential inclusions by using the implicit Euler scheme and the Runge-Kutta scheme for approximating time derivatives, while an appropriate well-posedness of such approximations is justified. Our principal result establishes the uniform approximation of strong local minimizers for the continuous-time Bolza problem by optimal solutions to the corresponding discretized finite-difference systems by the strengthen W^1,2-norm approximation of this type in the case ``intermediate" (between strong and weak minimizers) local minimizers under additional assumptions. Especially the implicitly discrete approximation is under the general ROSL setting. Finally, we derive necessary optimality conditions for each scheme for the discretized Bolza problems via suitable generalized differential constructions of variational analysis.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Tian, Yuan

Contributors dc:contributor

• Boris Mordukhovich

• Mathematics

Repository record dc:identifier

https://digitalcommons.wayne.edu/oa_dissertations/1352

OAI identifier oai:identifier

oai:digitalcommons.wayne.edu:oa_dissertations-2351