Daniele Mortari

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Theory of Functional Connections

Thesis and dissertations
  1. Mario de Florio Accurate Solutions of the Radiative Transfer Problem via Theory of Functional Connections, Scuola di Ingegneria e Architettura, Universita’ di Bologna (Italy), 2018/19
Journals
  1. Johnston, H. and Mortari, D. “Least-squares Solutions of Boundary-Value Problems in Hybrid Systems,” Journal of Computational and Applied Mathematics, Under review.
  2. Mai, T. and Mortari, D. “Theory of Functional Connections Applied to Nonlinear Programming under Equality Constraints,” Journal of Computational and Applied Mathematics, Under review.
  3. Johnston, H., Schiassi, E., Furfaro, R., and Mortari, D. “Fuel-Efficient Powered Descent Guidance on Planetary Bodies via the Theory of Functional Connections,” The Journal of Astronautical Sciences, In print.
  4. Leake, C.,  Johnston, H., and Mortari, D. “The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations,” Mathematics, 2020, 8(8), 1303.
  5. Johnston, H., Leake, C., and Mortari, D. “Least-squares Solutions of Eighth-order Boundary Value Problems using the Theory of Functional Connections“, Mathematics, 2020, Vol. 8(3), No. 397.
  6. Leake, C. and Mortari, D. “Deep Theory of Functional Connections: A New Method for Estimating the Solutions of Partial Differential Equations“, Machine Learning and Knowledge Extraction, 2020, Vol. 2, No. 1, pp. 37-55.
  7. Furfaro, R. and Mortari, D. “Least-squares Solution of a Class of Optimal Guidance Problems via Theory of Connections,” ACTA Astronautica, March 2020, Vol. 168, pp.92-103.
  8. Johnston, H., Leake, C., and Mortari, D. “Least-squares Solutions of Eighth-order Boundary Value Problems using the Theory of Functional Connections“, Mathematics, 2020, Vol. 8(3), No. 397.
  9. Leake, C., Johnston, H., Smith, L., and Mortari, D. “Analytically Embedding Differential Equation Constraints into Least-Squares Support Vector Machines using the Theory of Functional Connections,” Machine Learning and Knowledge Extraction. 2019, 1(4), 1058-1083.
  10. Mortari, D. and Leake, C. “Multivariate Theory of Connections,” Mathematics, 2019, 7(3), 296.
  11. Johnston, H., Leake, C., Efendiev, Y., and Mortari, D. “Selected Applications of the Theory of Connections: A Technique for Analytical Constraint Embedding,” Mathematics, 2019, 7(6), 537.
  12. Mortari, D., Johnston, H., and Smith, L. “High Accurate Least-Squares Solutions of Nonlinear Differential Equations,” Journal of Computational and Applied Mathematics, 2019, Vol. 352, May 15, pp. 293-307.
  13. Mortari, D. “The Theory of Connections: Connecting Points,” Mathematics, 2017, 5(4), 57.
  14. Mortari, D. “Least-Squares Solutions of Linear Differential Equations,” Mathematics, 2017, 5(4), 48. [2017 Best Paper Award, 2nd place]
Conferences
  1. Mortari, D. “The Theory of Connections. Part 1: Connecting Points,” AAS 17-255, 2017 AAS/AIAA Space Flight Mechanics Meeting Conference, San Antonio, TX, February 5-9, 2017.
  2. Mortari, D. “Least-squares Solutions of Linear Differential Equations,” AAS 17-256, 2017 AAS/AIAA Space Flight Mechanics Meeting Conference, San Antonio, TX, February 5-9, 2017.
  3. Mortari, D. “The Theory of Connections with Application,” XVI Jornadas de Trabajo en Mecánica Celeste, Soria (Spain), June 19-21, 2017.
  4. Mortari, D., Johnston, H., and Smith, L. “Least-squares Solutions of Nonlinear Differential Equations,” Paper of the 2018 AAS/AIAA Space Flight Mechanics Meeting Conference, Kissimmee, FL, January 8-12, 2018.
  5. Mortari, D. and Furfaro, R. “Theory of Connections Applied to First-Order System of Ordinary Differential Equations Subject to Component Constraints,” AAS 18-230, 2018 AAS/AIAA Astrodynamics Specialist Conference, Snowbird, UT, August 19-23, 2018.
  6. Johnston, H. and Mortari, D. “Linear Differential Equations Subject to Relative, Integral, and Infinite Constraints,” AAS 18-273, 2018 AAS/AIAA Astrodynamics Specialist Conference, Snowbird, UT, August 19-23, 2018.
  7. Johnston, H. and Mortari, D. “Theory of Connections Solution to Perturbed Lambert’s Problem,” AAS 18-282, 2018 AAS/AIAA Astrodynamics Specialist Conference, Snowbird, UT, August 19-23, 2018.
  8. Furfaro, R. and Mortari, D. “Least-squares Solution of a Class of Optimal Guidance Problems,” AAS 18-362, 2018 AAS/AIAA Astrodynamics Specialist Conference, Snowbird, UT, August 19-23, 2018.
  9. Mortari, D. “The Theory of Functional Connections: Connecting Functions,” IAA-AAS-SciTech-072, Forum 2018, Peoples’ Friendship University of Russia, Moscow (Russia), November 13-15, 2018.
  10. Johnston, H. and Mortari, D. “Weighted Least-Squares Solutions of Over-Constrained Differential Equations,” IAA-AAS-SciTech-081, Forum 2018, Peoples’ Friendship University of Russia, Moscow (Russia), November 13-15, 2018.
  11. Mortari, D. “The Theory of Functional Connections: Current Status,” XIX Colóquio Brasileiro de Dinâmica Orbital, CBDO-2018. Instituto Nacional de Pesquisas Espaciais, São José dos Campos (Brasil), Dec. 3-7, 2018
  12. Drozd, K., Furfaro, R., and Mortari, D. “Constrained Energy-Optimal Guidance in Relative Motion via Theory of Functional Connections and Rapidly-Explored Random Trees,” AAS 19-662, 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019.
  13. Mortari, D., Mai, T., and Efendiev, Y. “Theory of Functional Connections Applied to Nonlinear Programming under Equality Constraints,” AAS 19-675, of the 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019.
  14. Schiassi, E., Furfaro, R., Johnston, H., and Mortari, D. “Fuel-efficient Powered Descent Guidance on Planetary Bodies via Theory of Functional Connection,” AAS 19-718, of the 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019.
  15. Johnston, H., Leake, C., and Mortari, D. “An Analysis of the Theory of Functional Connections Subject to Inequality Constraints,” AAS 19-732, of the 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019.
  16. Mortari, D. and Leake, C. “An Explanation and Implementation of the Multivariate Theory of Functional Connections via Examples,” AAS 19-734, 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019.
  17. Johnston, H. and Mortari, D. “Orbit Propagation via the Theory of Functional Connections,” AAS 19-736, 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019.
  18. Mortari, D. “The Theory of Functional Connections: Current Status,” XXV International Congress of the Italian Association of Aeronautics and Astronautics, Rome (Italy), September 9-12, 2019.
  19. Furfaro, R., Drozd, K., and Mortari, D. “Energy-Optimal Rendezvous Spacecraft Guidance via Theory of Functional Connections,” 70th International Astronautical Congress 2019, IAF Astrodynamics Symposium, Washington, D.C., October 21-25, 2019.
  20. Schiassi, E., D’Ambrosio, A., Johnston, H., De Florio, M., Furfaro, R., Curti, F., and Mortari, D. “Physics-Informed Solution of Optimal Control Problems via Extreme Theory of Functional Connections”, AAS 20-524, Astrodynamics Specialist Conference, August 9-12, Lake Tahoe, CA.
  21. Schiassi, E., D’Ambrosio, A., Johnston, H., Furfaro, R., Curti, F., and Mortari, D. “Complete Energy Optimal Landing on Small and Large Planetary Bodies via Theory of Functional Connections”, AAS 20-557, Astrodynamics Specialist Conference, August 9-12, Lake Tahoe, CA.
  22. Furfaro, R., Schiassi, E., Drozd, K., and Mortari, D. “Physics-Informed Neural Networks and Theory of Functional Connections for Optimal Space Guidance Applications,” IAC 2020, 71-st International Astronautical Congress, 12-16 October 2020, Dubai, United Arab Emirates.

Publications on Sling-Sat

  1. Missel, J. and Mortari, D. “Sling Satellite for Debris Removal with Aggie Sweeper,” AAS 10-256, AAS/AIAA Space Flight Mechanics Meeting Conference, New Orleans, LO, Feb. 13-17, 2011.
  2. Missel, J. and Mortari, D. “Optimization of Debris Removal Path for TAMU Sweeper,” AAS 12-167, AAS/AIAA Space Flight Mechanics Meeting Conference, Charleston, SC, Jan. 29 – Feb. 2, 2012.
  3. Missel, J. and Mortari, D. “Removing Space Debris through Sequential Captures and Ejections,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 36, No. 3, 2013, pp. 743-752.
  4. Missel, J. and Mortari, D. “Path Optimization for Space Sweeper with Sling-Sat: A Method of Active Space Debris Removal,” COSPAR Advances in Space Research, Vol. 52, No. 7, 2013, pp. 1339-1348.

Videos on Sling-Sat

  1. TAMU-Sweeper Sling-Sat explained for large audience [Link to Youtube video]. [Download video in mp4 format] [video]
  2. KAGS-TV Interview (August 2, 2012) [Link #1], [Link #2].
  3. Poster [Link]
  4. LASR video [Link].