The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	Coherent control of dispersive waves
Author:	Adriazola, Jimmie
View Online:	njit-etd2021-061 (xx, 165 pages ~ 13.7 MB pdf)
Department:	Department of Mathematical Sciences
Degree:	Doctor of Philosophy
Program:	Mathematical Sciences
Document Type:	Dissertation
Advisory Committee:	Goodman, Roy (Committee chair) Shirokoff, David (Committee member) Frederick, Cristina (Committee member) Moore, Richard O. (Committee member) Aceves, Alejandro (Committee member)
Date:	2021-12
Keywords:	Hamiltonian dynamical systems Nonlinear waves Optimal control theory PDS constrained optimization Solitons
Availability:	Unrestricted
Abstract:	This dissertation addresses some of the various issues which can arise when posing and solving optimization problems constrained by dispersive physics. Considered here are four technologically relevant experiments, each having their own unique challenges and physical settings including ultra-cold quantum fluids trapped by an external field, paraxial light propagation through a gradient index of refraction, light propagation in periodic photonic crystals, and surface gravity water waves over shallow and variable seabeds. In each of these settings, the physics can be modeled by dispersive wave equations, and the technological objective is to design the external trapping fields or propagation media such that a high fidelity or degree of coherence of the wave phenomena is achieved. Optimal control theory is used as the analytical and computational framework in addressing these design problems. Optimal control problems are, generally speaking, challenging searches over infinite-dimensional spaces. Methods from Hamiltonian dynamical systems, asymptotic analysis, the integrability structure of the uncontrolled constraints, and simple physical intuition are employed to better guide these searches. By introducing the dimensional reductions afforded by these methods, our computational searches are significantly more efficient, over naively attempting to search the entire space of admissible controls, both in terms of the desired outcomes and in terms of expended computational resources. The optimal control problems posed throughout this dissertation also have the additional challenge of being nonconvex optimization problems. In order to efficiently address the nonconvex nature of these problems, the program used is a global, nonconvex search which is then accelerated by fast local methods. This methodology is specifically tailored toward maintaining feasibility of implementing the computationally constructed control policies in technologically relevant settings.