Access Type
Open Access Dissertation
Date of Award
January 2025
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Boris Mordukhovich
Abstract
Optimization and optimal control have a wide range of applications across fields like engineering, biology, data science, and economics. This dissertation is devoted to advanced optimal control problems discontinuous constrained differential inclusions of the sweeping type involving the duration of the dynamic process into optimization, which are truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems, we use the method of discrete approximation while establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. This approach, married to advanced tools of variational analysis, enables this research to derive necessary optimality conditions for the original problem with a wide range of applications, including nanoparticle dynamics, marine surface vehicles, and robotics models. Key contributions also include the development of numerical algorithms to solve these optimization problems, using the Python Dynamic Optimization library GEKKO to simulate solutions to the posed robotics problems in the case of any fixed number of robots.
Recommended Citation
Nguyen, Thi Dai Trang, "Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications" (2025). Wayne State University Dissertations. 4263.
https://digitalcommons.wayne.edu/oa_dissertations/4263