2021/05/17 by Hunter Johnston, Johnston, Hunter
Engineering · #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Spacecraft Dynamics and Control #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2105.08034
openalex publication_date 2021/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Theory of Functional Connections (TFC) is a general methodology for\nfunctional interpolation that can embed a set of user-specified linear\nconstraints. The functionals derived from this method, called \constrained\nexpressions, analytically satisfy the imposed constraints and can be leveraged\nto transform constrained optimization problems to unconstrained ones. By\nsimplifying the optimization problem, this technique has been shown to produce\na numerical scheme that is faster, more accurate, and robust to poor\ninitialization. The content of this dissertation details the complete\ndevelopment of the Theory of Functional Connections. First, the seminal paper\non the Theory of Functional Connections is discussed and motivates the\ndiscovery of a more general formulation of the constrained expressions.\nLeveraging this formulation, a rigorous structure of the constrained expression\nis produced with associated mathematical definitions, claims, and proofs.\nFurthermore, the second part of this dissertation explains how this technique\ncan be used to solve ordinary differential equations providing a wide variety\nof examples compared to the state-of-the-art. The final part of this work\nfocuses on unitizing the techniques and algorithms produced in the prior\nsections to explore the feasibility of using the Theory of Functional\nConnections to solve real-time optimal control problems, namely optimal landing\nproblems.\n