Search Results - "Mortari, Daniele"

The Theory of Connections: Connecting Points by Mortari, Daniele

“…This study introduces a procedure to obtain all interpolating functions, y=f(x)y=f(x) , subject to linear constraints on the function and its derivatives…”
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Least-Squares Solution of Linear Differential Equations by Mortari, Daniele

“…This study shows how to obtain least-squares solutions to initial value problems (IVPs), boundary value problems (BVPs), and multi-value problems (MVPs) for…”
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Using the Theory of Functional Connections to Solve Boundary Value Geodesic Problems by Mortari, Daniele

“…This study provides a least-squares-based numerical approach to estimate the boundary value geodesic trajectory and associated parametric velocity on curved…”
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Representation of Fractional Operators Using the Theory of Functional Connections by Mortari, Daniele

“…This work considers fractional operators (derivatives and integrals) as surfaces f(x,α) subject to the function constraints defined by integer operators, which…”
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Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives by Mortari, Daniele

“…This study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives,…”
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Deep Theory of Functional Connections: A New Method for Estimating the Solutions of Partial Differential Equations by Leake, Carl, Mortari, Daniele

“…This article presents a new methodology called Deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations…”
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High Accurate Mathematical Tools to Estimate the Gravity Direction Using Two Non-Orthogonal Inclinometers by Mortari, Daniele, Gardner, Anthony

“…This study provides two mathematical tools to best estimate the gravity direction when using a pair of non-orthogonal inclinometers whose measurements are…”
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Impulsive orbit correction using second-order Gauss’s variational equations by Zhang, Gang, Mortari, Daniele

“…Based on Gauss’s variational equations (GVEs), the impulsive orbital-element corrections are investigated in orbit transfer problems. Both single impulse and…”
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The Multivariate Theory of Connections by Mortari, Daniele, Leake, Carl

“…This paper extends the univariate Theory of Connections, introduced in (Mortari, 2017), to the multivariate case on rectangular domains with detailed attention…”
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Derivation of All Attitude Error Governing Equations for Attitude Filtering and Control by Bani Younes, Ahmad, Mortari, Daniele

“…This article presents the full analytical derivations of the attitude error kinematics equations. This is done for several attitude error representations,…”
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Non-Dimensional Star-Identification by Leake, Carl, Arnas, David, Mortari, Daniele

“…This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when…”
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A Return to the Sextant-Maritime Navigation Using Celestial Bodies and the Horizon by Critchley-Marrows, Joshua J R, Mortari, Daniele

“…Satellite navigation over recent decades has become the default and, in some cases, sole source of positioning for maritime vessels. The classic sextant has…”
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Univariate Theory of Functional Connections Applied to Component Constraints by Mortari, Daniele, Furfaro, Roberto

“…This work presents a methodology to derive analytical functionals, with embedded linear constraints among the components of a vector (e.g., coordinates) that…”
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The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations by Leake, Carl, Johnston, Hunter, Mortari, Daniele

“…This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of…”
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Angular Velocity and Covariance Estimates for Rigid Bodies in Near Pure-Spin Using Orientation Measurements by Kaki, Siddarth, Akella, Maruthi R., Mortari, Daniele

“…The problem of estimating relative pose and angular velocity for uncooperative space objects has garnered great interest, especially within applications such…”
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Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains by Mortari, Daniele, Arnas, David

“…This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains…”
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Theory of Functional Connections Extended to Fractional Operators by Mortari, Daniele, Garrappa, Roberto, Nicolò, Luigi

“…The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context of fractional-order operators…”
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Orbit transfer using Theory of Functional Connections via change of variables by de Almeida, Allan K., Prado, Antonio F. B. A., Mortari, Daniele

“…This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional Connections…”
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Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models by Schiassi, Enrico, De Florio, Mario, D’Ambrosio, Andrea, Mortari, Daniele, Furfaro, Roberto

“…In this work, we apply a novel and accurate Physics-Informed Neural Network Theory of Functional Connections (PINN-TFC) based framework, called Extreme Theory…”
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A Survey on Star Identification Algorithms by Spratling, Benjamin B., Mortari, Daniele

“…The author surveys algorithms used in star identification, commonly used in star trackers to determine the attitude of a spacecraft. Star trackers are a staple…”
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