相关论文: Segmentation of the spacecraft transfer problem th…
This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional Connections (TFC) mathematical framework by a specific change of coordinates. In these problems,…
This study applies a new approach, the Theory of Functional Connections (TFC), to solve the two-point boundary-value problem (TPBVP) in non-Keplerian orbit transfer. The perturbations considered are drag, solar radiation pressure,…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g. the Moon or Mars) using the recently developed Theory of Functional Connections. The…
A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…
A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge,…
The growing population of man-made objects with the build up of mega-constellations not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but above all poses a serious…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory…
Differential equations (DEs) are used as numerical models to describe physical phenomena throughout the field of engineering and science, including heat and fluid flow, structural bending, and systems dynamics. While there are many other…
Satellite-terrestrial communications are severely constrained by high path loss, limited spectrum resources, and time-varying channel conditions, rendering conventional bit-level transmission schemes inefficient and fragile, particularly in…
This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for…
Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…
Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the…
A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is…
In this work, we introduce Fed-Span: \textit{\underline{fed}erated learning with \underline{span}ning aggregation over low Earth orbit (LEO) satellite constellations}. Fed-Span aims to address critical challenges inherent to distributed…
This article presents a novel and comprehensive approach for analyzing bending behavior of the tapered perforated beam under an exponential load. The governing differential equation includes important factors like filling ratio ($\alpha$),…
This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…