Access Type
Open Access Dissertation
Date of Award
January 2015
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Boris Mordukhovich
Abstract
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.
Recommended Citation
Tian, Yuan, "Finite-Difference Approximations And Optimal Control Of Differential Inclusions" (2015). Wayne State University Dissertations. 1352.
https://digitalcommons.wayne.edu/oa_dissertations/1352