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Access Type
WSU Access
Date of Award
January 2021
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Boris Mordukhovich
Abstract
The dissertation is devoted to the study of a new class of optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which addresses unbounded discontinuous differential inclusions with intrinsic state constraints, is truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems with constrained measurable controls, we develop a refined method of discrete approximations with establishing its well-posedness and strong convergence. This approach, married to advanced tools of first-order and second-order variational analysis and generalized differentiation, allows us to derive adequate collections of necessary optimality conditions for local minimizers, first in discrete-time problems and then in the original continuous-time controlled sweeping process by passing to the limit. The new results include an appropriate maximum condition and significantly extend the previous ones obtained under essentially more restrictive assumptions. We compare them with other versions of the maximum principle for controlled sweeping processes that have been recently established for global minimizers in problems with smooth sweeping sets by using different techniques. Besides illustrative examples, we apply the obtained results to optimal control problems associated with the mobile robot model and traffic flow model through a doorway, which are formulated in this thesis. The derived optimality conditions allow us to develop an effective procedure to solve these problems in a general setting and completely calculate optimal solutions in particular situations.
Recommended Citation
Nguyen, Nguyen-Truc-Dao, "Optimization Of Controlled Sweeping Processes With Applications" (2021). Wayne State University Dissertations. 3448.
https://digitalcommons.wayne.edu/oa_dissertations/3448