Luis Duffaut

Luis A. Duffaut Espinosa

Luis A. Duffaut Espinosa

Assistant Professor

Department of Electrical and Biomedical Engineering

Electrical and Computer Engineering Program

College of Engineering and Mathematical Sciences

University of Vermont


Affiliated with:


Research Interests


My primary research interests lie in dynamic modeling, control, and estimation of nonlinear dynamical systems in the fields of autonomy and robotics. The complexities and uncertainties inherent in modern ground, aerial, maritime, and space systems have shifted research towards data-driven models and learning technologies. As a result, data-driven control and estimation have emerged as key paradigms aiming to enhance adaptability and responsiveness of systems addresssing modern societal challenges. I am dedicated to developing robust frameworks for safe data-driven methodologies via the characterization of state-of-the-art systems as combinatorial operators that unveil the fundamental behaviors and components of these mechanisms. Additionally, recognizing the vulnerability of data-driven systems to hacking and sensor failures, my research also emphasizes augmenting the resilience and robustness of controllers designed with these methods.


Autonomy and Robotics Program


Autonomy and robotics are transformative technologies driving innovation across many sectors, including manufacturing, transportation, healthcare, agriculture, defense, and energy. The Autonomy and Robotics program at UVM sits at the intersection of Electrical and Computer Engineering, Mechanical Engineering, and Computer Science. The program advances human knowledge and equips undergraduate and graduate students with the skills they need to lead in this dynamic field.



Biographical Sketch


I received the B.S. degree in physics from the Universidad Nacional de Ingeniería, Lima, Perú, in 2003, the M.S. degree in mathematics with mention in stochastic processes from the Pontificia Universidad Católica del Perú, Lima, Perú, in 2005, and the Ph.D. degree in electrical and computer engineering from Old Dominion University, Norfolk, VA, USA, in 2009. I held postdoctoral positions at Old Dominion University (2010), Johs Hopkins University (2010-2011), and the University of New South Wales in Australia (2011-203). Then I was a consultant for the Consultative Group on International Agricultural Research (2013-2016) while holding an adjunct position at George Mason university (2014-2016). In 2016, I joined the University of Vermont as research professor and in 2019 as an assistant profesor. In 2024, I was honored on receiving the CAREER Award from the National Science Foundation.



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Research


Research Laboratory


Autonomous and Intelligent Systems Research Laboratory (AIRLab)

Role: Co-Director (with H. Ossareh)

The AIRLab is driving the future of intelligent systems. Our research on data-driven and model-free estimation and control algorithms enable engineered systems to adapt to complex, real-world environments, pushing beyond traditional boundaries. With a dynamic mix of ground robots, aerial drones, robotic arms, and power grid simulators in the lab as our validation platforms, we tackle some of the most exciting challenges in autonomy.


Research Projects


CAREER: A Universal Framework for Safety-Aware Data-Driven Control and Estimation

Role: Principal Investigator

Duration: 2024-2029

Brief Description: This research enables safe data-driven control and estimation methods for autonomy applications. Here we develop a universal framework for the simultaneous design of control policies and safety measures based on recent advances in the mathematical modeling of dynamical systems. The objective is the automatic synthesis of safety-aware control laws for highly complex systems as a function of their real-time input-output information. Specifically, we leverage a novel framework for system representation that systematically encodes its input-output behavior, namely the Chen-Fliess framework, which allows the use of algebraic optimization routines on the system's information, by eliminating the need for a state-space coordinate frame that otherwise will require over-parametrizations that can lead to infeasibility. The specific goals are: (1) provide an algebraic framework for the analysis and optimization of data-driven control systems, (2) develop input-output reachability analysis in the Chen-Fliess framework, and (3) develop data-driven methods for the synthesis of safe control laws based on reachability analysis and control barrier functions in the Chen-Fliess framework.

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CREEL: Cold Weather Summit-to-Shore Environmental Observation Network

Role: Task leader - UAS Snowpack Monitoring

Duration: 2022-2025

Brief description: Snowpack measurements are crucial for cold-weather environmental observation. Developing comprehensive sampling regimes that account for the spatial variability of snow depth and area is challenging using traditional methods. This project proposes the deployment of an array of low-cost, distributed sensors for tracking snow depth and coverage together with the characterization of the spatial co-variability of different measurement methods to aid in the design of snowpack measurement networks. Through this effort, we will develop distributed sensing capabilities as well as address the research question: what environmental/terrain factors (e.g., vegetation/canopy structure, micro-topography) enable low-cost tech (imaging, GPS) to be reliable and accurate for snowpack reconstruction? From the methodological perspective, spatial generators based on the self-similar properties of the field of interest will be used to generate higher resolution data sets of snow spatial distribution. Additionally, the team will unveil the signature of LiDAR information to extract features that have the potential for detecting and differentiating snow properties of interest.

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CREEL: Army Visual and Tactical Arctic Reconnaissance (AVATAR)

Role: Task Leader - Efficient Real-Time Data Assimilation and Terrain Reconstruction in Cold Regions with Limited Information and Power

Duration: 2020-2023

Brief description: Robust navigation for Arctic missions presents a number of unique challenges, including: lack of network connectivity, limited or unreliable access to satellite positioning systems, relative sparsity of geographic landmarks, limited power, and the highly dynamic nature of the environment. This project seeks to improve robust navigation in the harsh environments by developing a holistic technology for topography and feature reconstruction using sensors implemented on static stations and on a fleet of aerial drones. Our approach explores venues to avoid, recover or overcome GPS jamming, which is a real complication faced by missions, for instance, in Arctic regions. The two key questions that we answer in this project are: how can navigation information be reliably identified in real-time using distributed, sparse, and noisy data from the sensors; and what is the optimal number and configuration of sensors to maximize navigation information. To answer the first question, we propose to integrate three key methodologies: model-free Kalman filter (MKF) for temporal data reconstruction, Kriging for spatial data reconstruction, and set-theoretic methods for uncertainty quantification and robust decision making. For the second question, an efficient optimization routine is proposed to determine the locations where the highest information value to be feed into the estimation algorithms provided by the first question.

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NASA-EPSCoR: Algorithms and Test-bed for Agile Attitude Control of Reconnaissance Drones in Atmosphere Lacking or Weightless Environments

Role: Principal Investigator

Duration: 2022-2023

Brief description: NASA’s latest mission to Mars showcased humankind’s ability to deploy exploring aerial drones in outer worlds such as Mars. This was certainly an achievement that gave light into the broader impact of drone technologies currently used on earth for reconnaissance and exploration. Further developing technologies that assist humans in these endeavours has become priority for the US through NASA. The objective of the project was to simulate, built and test drone like autonomous platforms that facilitate risk-less human exploration in places with no atmosphere and/or weightless conditions such as the moon and/or asteroids. Specifically, the proposers will design and build a test-bed for small, agile and efficient drone-like autonomous vehicles that can perform in weightless and/or atmosphere-free environments.

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NASA EPSCoR - New Unified Framework for Scalable, Risk-Aware, and Resilient Estimation and Control of Satellite Swarms

Role: Co-Principal Investigator (co-PI)

Main collaborator: H. Ossareh (PI)

Duration: 2021-2023

Brief description: Current satellite swarm missions rely heavily on communications with a ground station. The calculations and final dispatch of most maneuvers and trajectory refinements are calculated on the ground and approved by human operators, and then beamed to the satellites for execution. It is not surprising that this lack of onboard perception and autonomy has limited the type and complexity of swarm missions, especially those beyond the Earth orbit, where communication delays may be prohibitive. To overcome this lack of autonomy and unleash the full potential of satellite swarms, new theories and methods, as well as computationally-efficient and scalable algorithms, in the following key areas are required: (i) uncertainty quantification and robustification; (ii) formation and trajectory planning; (iii) real-time, collision-free navigation and control; and (iv) robust, cooperative estimation and sensor fusion. The proposed project seeks to fill these gaps by researching and developing a validated and fully-integrated computational and operational framework for formation planning, estimation, and control of a satellite swarm, with application to an SAR swarm in close formation.

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ARPA-e PlusUp: Packetized Energy Management (PEM) Coordinating Transmission and Distribution

Role: Co-Principal Investigator (co-PI)

Main Collaborator: Mads Almassalkhi (PI)

Duration: 2019-2021

Brief description: This project leverages and advances the bottom-up, demand-side management technology of packetized energy management (PEM) to coordinate Distributed Energy Resources (DERs) at scale to provide synthetic frequency-regulating reserves while simultaneously managing low-voltage grid constraints in real-time. Specifically, the work iin this project extended PEM technology from providing just 5-minute balancing reserves to also provide frequency-regulating reserves like automatic generation control (AGC) and satisfy Synthetic Frequency-Responsive Reserves capabilities.

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Collaborative: EAGER: Hybrid Control Architectures Combining Physical Models and Real-time Learning

Role: Principal Investigator

Main Collaborator: W. Steven Gray (Old Dominion University)

Duration: 2018-2020

Brief description: Artificial neural networks have traditionally been the backbone of machine learning. While these biologically inspired learning systems certainly have their strengths, they also have limitations in the context of control engineering. This project developed a new control architecture which combined the advantages of model-based design methods with those of real-time learning. The specific objectives of the project are to (1) advance the theoretical foundations that underpin real-time learning for control applications, including the cascading of these new learning units for deep learning (2) optimize and adapt the novel theoretical results for real-time control of smart grids to provide a priori performance guarantees. The main problem here lies in the uncertainty coming from the over-simplified/poorly modeled dynamics of the grid in addition to the action of renewable resources.

Website: Click here

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Publications

  1. D. Waleed, J. Friz-Trillo and L. A. Duffaut Espinosa, “Minimum Control Effort on Data-Driven Control of Quadcopter,” International Journal of Control, in preparation.
  2. I. Perez, L. A. Duffaut Espinosa, “Second-Order Optimization of Chen-Fliess Series for Input-Output Reachability Analysis,” Systems and Control Letters, in preparation.
  3. I. Perez, L. A. Duffaut Espinosa, “Input-Output Reachable Set Overestimation via Chen-Fliess Series,” IEEE Transactions on Automatic Control, in preparation.
  4. F. Boudaghi, D. Waleed, L. A. Duffaut Espinosa, "Data Reconstruction Using Smart Sensor Placement" Sensors, 24, 6008, 2024.
  5. H. Mavalizadeh, L. A. Duffaut Espinosa, M. Almassalkhi, "Improving Frequency Response With Synthetic Damping Available From Fleets of Distributed Energy Resources," in IEEE Transactions on Power Systems, vol. 39, no. 2, pp. 4498-4509, 2024.
  6. I. Perez, L. A. Duffaut Espinosa, and F. Rosales, “Feedback Dynamic Control for Exiting a Debt-Induced Spiral in a Deterministic Keen Model,” PLoS ONE 19(2): e0295859, 2024.
  7. A. Khurram, M. Amini, L. A. Duffaut Espinosa, P. Hines, M. Almassalkhi, “Real-time Grid and DER Co-simulation Platform for Testing Large-scale DER Control Schemes,” IEEE Transactions on Smart Grid, vol. 13, no 6, pp. 4367-4378, 2022.
  8. L. A. Duffaut Espinosa, M. Almassalkhi, and Adil Khurram, “Reference-Tracking Control Policies for Packetized Coordination of Heterogeneous DER Populations,” IEEE Transactions on Control Systems Technology, vol. 29, no. 6, pp. 2427-2443, 2021.
  9. W. S. Gray, G. S. Venkatesh, and L. A. Duffaut Espinosa, “Combining Learning and Model Based Control via Discrete-Time Chen-Fliess Series,” Automatica, vol. 119, 2020, 109085.
  10. L. A. Duffaut Espinosa and M. Almassalkhi, “A Packetized Energy Management Macromodel with Quality of Service Guarantees for Demand-Side Resources,” IEEE Transactions on Power Systems, vol. 35, no. 5, 2020, 3660-3670.
  11. A. Khurram, R. Malhame, L. A. Duffaut Espinosa and M. Almassalkhi, “Identification of Water Demand Process of Electric Water Heaters from Energy Measurements,” Journal Electric Power Systems Research, vol. 189, 2020, 106625.
  12. L. A. Duffaut Espinosa, F. Rosales and A. Posadas, “Embedding Spatial Variability in Rainfall Field Reconstruction,” International Journal of Remote Sensing, vol. 39, no. 9, 2018, pp. 2884-2905.
  13. W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Discrete-Time Approximations of Fliess Operators: The rational case,” Numerische Mathematik, vol. 137, no. 1, 2017, pp. 35-62.
  14. L. A. Duffaut Espinosa, A. Posadas, M. Carbajal, and R. Quiroz, “Multifractal downscaling of rainfall using normalized difference vegetation index (NDVI) in the Andes plateau,” PLOSONE, vol. 12, no. 1, 2017, pp. 1-25.
  15. L. A. Duffaut Espinosa, W. S. Gray, and K. Ebrahimi-Fard, “Dendriform-Tree Setting for Fully Non-commutative Fliess Operators,” IMA Journal of Mathematical Control & Information, vol. 32, 2016, pp. 1-31.
  16. L. A. Duffaut Espinosa, K. Ebrahimi-Fard, and W. S. Gray, “A combinatorial Hopf algebra for nonlinear output feedback control systems”, Journal of Algebra, vol. 453, 2016, pp. 609-643.
  17. L. A. Duffaut Espinosa, Z. Miao, I. R. Petersen, V. Ugrinovskii and M. R. James, “Physical Realizability and Preservation of Commutation and Anticommutation Relations for N -Level Quantum Systems,” SIAM Journal on Control and Optimization, vol. 54, no. 2, 2016, pp. 632-661.
  18. A. Posadas, L. A. Duffaut Espinosa, C. Yarleque´, M. Carbajal, H. Heidinger, L. Carvalho, C. Jones, and R. Quiroz, “Spatial Random Downscaling of Rainfall Signals in Andean Heterogeneous Terrain,” Nonlinear Processes in Geophysics, vol. 22, 2015, pp. 383-402.
  19. L. A. Duffaut Espinosa and W. S. Gray, “Functional series expansions for continuous-time switched systems,” Journal of Dynamical and Control Systems, vol. 21, no. 2, 2015, pp. 211-237.
  20. W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Faa` di Bruno Hopf Algebra of the Feedback Group for Multivariable Fliess Operators,” Systems and Control Letters, vol. 74, 2014, pp. 64-73.
  21. W. S. Gray, L. A. Duffaut Espinosa and M. Thitsa, “Left Inversion of Analytic Nonlinear SISO Systems via Formal Power Series Methods,” Automatica, vol. 50, no. 9, 2014, pp. 2381-2388.
  22. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “On the convergence of Fliess operators driven by L2 -Ito^ processes,” Stochastics: An International Journal of Probability and Stochastic Processes, vol. 84, no. 4, 2012, pp. 507-532.
  23. W. S. Gray and L. A. Duffaut Espinosa, “A Faó di Bruno Hopf algebra for a group of Fliess operators with applications to feedback,” Systems and Control Letters, 2011, pp. 441-449.
  24. W. S. Gray, H. Herencia-Zapana, L. A. Duffaut Espinosa, and O. R. Gonzólez, “Bilinear system interconnections and generating series of weighted Petri nets,” Systems and Control Letters, vol. 58, no. 12, 2009, pp. 841-848.
  25. I. Hafez and L. A. Duffaut Espinosa, “Optimal Funnel Control of an Underactuated System,” ICRA, in preparation.
  26. J. Friz-Trillo and L. A. Duffaut Espinosa, “Data-Driven Cascade Control of Small Quadcopters,” IROS, in preparation.
  27. D. Waleed and L. A. Duffaut Espinosa, “Simultaneous Parameter Estimation in Model-Free Control,” 2024 American Control Conference, Toronto, ON, Canada, 2024, pp. 480-485.
  28. Y. Pedari, D. Waleed, Luis A. Duffaut Espinosa, and H. Ossareh, “Robust State Estimation For Satellite Formations in Presence of Unreliable Measurements,” IEEE International Conference on Systems, Man, and Cybernetics, Maui, Hawaii, 2023.
  29. L. A. Duffaut Espinosa, W .S. Gray and I. Perez Avellaneda, “Critical Points of Chen-Fliess Series with Applications to Optimal Control,” IEEE 62st Conference on Decision and Control, Marina Sands, Singapore, 2023.
  30. I. Perez Avellaneda and Luis A. Duffaut Espinosa, “An Interval Arithmetic Approach to Input-Output Reachability,” 7th IEEE Conference on Control Technology and Applications, Bridgetown, Barbados, 2023, pp. 1-7.
  31. I. Perez Avellaneda and Luis A. Duffaut Espinosa, Output Reachability of Chen-Fliess series: A NewtonRaphson Approach”, 57th Conference on Information Sciences and Systems, Baltimore, Maryland, 2023, pp. 1-7.
  32. I. Perez Avellanado and Luis A. Duffaut Espinosa, “On Mixed-Monotonicity of Chen-Fliess series,” International Conference on System Theory, Control and Computing, Sinaia, Romania, 2022, pp. 98-103.
  33. I. Perez Avellaneda and Luis A. Duffaut Espinosa, “Reachability of Chen-Fliess series: A Gradient Descent Approach,” 58th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois 2022, pp. 1-7.
  34. W. S. Gray, Luis A. Duffaut Espinosa, M. A. Haq, “Estimating Relative Degree of Nonlinear Systems Using Generating Series,” IEEE 61st Conference on Decision and Control, Cancun, Mexico, 2022, , pp. 7333-7338.
  35. A. Khurram, L. A. Duffaut Espinosa, and M. Almassalkhi, “A Group-based Approach for Heterogeneity in Packetized Energy Management Corresponding,” 6th IEEE Conference on Control Technology and Applications, Trieste, Italy, 2022.
  36. D. Waleed and L. A. Duffaut Espinosa, “Integration of a Robust Kalman filter with Model-Free control,” 6th IEEE Conference on Control Technology and Applications, Trieste, Italy, 2022.
  37. W. S. Gray, L. A. Duffaut Espinosa and M. A. Haq, “Universal Zero Dynamics Attacks Using Only InputOutput Data,” American Control Conference, Atlanta, Georgia, 2022, pp. 4985-4991.
  38. W. S. Gray, L. A. Duffaut Espinosa, K. Ebrahimi-Fard, “Additive Networks of Chen-Fliess Series: Local Convergence and Relative Degree,” Conference on Decision and Control, Austin Texas (remote), 2021.
  39. A. Khurram, L. A. Duffaut Espinosa and M. Almassalkhi, “A Methodology for Quantifying Flexibility in a fleet of Diverse DERs”, PowerTech, Madrid, Spain, 2021.
  40. L. A. Duffaut Espinosa, W. S. Gray and G. S. Venkatesh, “Learning Control for Voltage and Frequency Regulation of an Infinite Bus System,” International Conference on System Theory, Control and Computing, Sinaia, Romania, 2020, pp. 800-806.
  41. H. Mavalizadeh, L. A. Duffaut Espinosa and M. Almassalkhi, “Decentralized Frequency Control using Packet-based Energy Coordination,” 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids, 2020.
  42. L. A. Duffaut Espinosa, A. Khurram and M. Almassalkhi, “A Virtual Battery Model for Packetized Energy Management,” 59th IEEE Conference on Decision and Control, Korea, 2020, pp. 42-48.
  43. A. Khurram, R. Malhame, L. A. Duffaut Espinosa and M. Almassalkhi, “Identification of Water Demand Process of Electric Water Heaters from Energy Measurements,” 21st Power Systems Computation Conference, Lisbon, Portugal, 2020.
  44. G. S. Venkatesh, W. S. Gray and L. A. Duffaut Espinosa, “Combining Learning and Model Based Control,” 58th IEEE Conference on Decision and Control, Nice, France, 2019, pp. 1013-1018.
  45. W. S. Gray, G. S. Venkatesh, L. A. Duffaut Espinosa, “Discrete-time Chen Series for Time Discretization and Machine Learning”, Proc. 53rd Conference on Information Sciences and Systems, Baltimore, Maryland, 2019.
  46. L. A. Duffaut Espinosa and Jeff Frolik, “A localized and packetized approach to distributed power inverter management”, 2019 IEEE Power & Energy Society General Meeting, Atlanta, Georgia, 2019.
  47. W. S. Gray, G. S. Venkatesh, L. A. Duffaut Espinosa, “Combining Learning and Model Based Control: Case Study for Single-Input Lotka-Volterra System”, Proc. 2019 American Control Conference, Philadelphia, Pennsylvania, 2019, pp. 928-933.
  48. L. A. Duffaut Espinosa and W. S. Gray, “Fliess Operator Representations of Nonlinear Markov Switched Systems and their Parallel Interconnections”, Proc. 23nd International Symposium on the Mathematical Theory of Networks and Systems, Hong Kong, 2018, pp. 429-434.
  49. W. S. Gray and L. A. Duffaut Espinosa, “Dynamic Output Feedback Invariants of Full Relative Degree Nonlinear SISO Systems”, Proc. 23nd International Symposium on the Mathematical Theory of Networks and Systems, Hong Kong, 2018, pp. 762-768.
  50. L. A. Duffaut Espinosa, M. Almassalkhi, P. Hines, and J. Frolik, “Some Properties of Packetized Energy Management for Different Classes of DERs,” 20th Power Systems Computation Conference, Dublin, Ireland, 2018.
  51. L. A. Duffaut Espinosa, M. Almassalkhi, P. Hines, and J. Frolik, “Aggregate modeling and coordination of diverse energy resources under packetized energy management”, 56th IEEE Conference on Decision and Control, Melbourne, Australia, 2017, pp. 1394-1400.
  52. L. A. Duffaut Espinosa and W. S. Gray, “Integration of Output Tracking and Trajectory Generation Via Analytic Left Inversion,” 21st International Conference on System Theory, Control and Computing, Sinaia, Romania, 2017.
  53. W. S. Gray and L. A. Duffaut Espinosa, “Data-Driven SISO Predictive Control Using Adaptive Discrete-Time Fliess Operator Approximations,” 2016 American Control Conference, Boston, Massachusetts, 2016, pp. 592-597.
  54. L. A. Duffaut Espinosa, M. Almassalkhi, P. Hines, S. Heydari and J. Frolik, “Towards a Macromodel for Packetized Energy Management of Resistive Water Heaters,” Proc. 51st Conference on Information Sciences and Systems, Baltimore, Maryland, 2017.
  55. W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Sensitivity of the Left Inverse of a SISO Analytic Nonlinear System,” Proc. 51st Conference on Information Sciences and Systems, Baltimore, Maryland, 2017.
  56. I. M. Winter-Arboleda, W. S. Gray and L. A. Duffaut Espinosa, “On Global Convergence of Fractional Fliess Operators with Applications to Bilinear Systems,” Proc. 51st Conference on Information Sciences and Systems, Baltimore, Maryland, 2017.
  57. L. Berlin, W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “On the Performance of Antipode Algorithms for the Multivariable Output Feedback Hopf Algebra,” Proc. 51st Conference on Information Sciences and Systems, Baltimore, Maryland, 2017.
  58. I. M. Winter-Arboleda, L. A. Duffaut Espinosa and W. S. Gray, “Nonrecursively Interconnected Fliess Operators Preserve Global Convergence: An Expanded View,” Proc. 22nd International Symposium on the Mathematical Theory of Networks and Systems, Minneapolis, USA, 2016.
  59. I. M. Winter-Arboleda, W. S. Gray and L. A. Duffaut Espinosa, “Expanding the Class of Globally Convergent Fliess Operators” Proc. 22nd International Symposium on the Mathematical Theory of Networks and Systems, Minneapolis, USA, 2016.
  60. W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Discrete-Time Approximations of Fliess Operators,” Proc. 2016 American Control Conference, Boston, USA, 2016, pp. 2433–2439.
  61. W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Analytic Left Inversion of Multivariable Lotka-Volterra Models,” Proc. 54rd IEEE Conference on Decision and Control, Osaka, Japan, 2015, pp. 6472–6477.
  62. W. S. Gray, L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Analytic Left Inversion of SISO Lotka-Volterra Models,” Proc. 49th Conference on Information Sciences and Systems, Baltimore, Maryland, 2015.
  63. I. M. Winter-Arboleda, W. S. Gray and L. A. Duffaut Espinosa, “Fractional Fliess Operators: Two Approaches,” Proc. 49th Conference on Information Sciences and Systems, Baltimore, Maryland, 2015.
  64. L. A. Duffaut Espinosa, W. S. Gray and K. Ebrahimi-Fard, “Dendriform-Tree Setting for Fully Noncommutative Fliess Operators,” Proc. 53rd IEEE Conference on Decision and Control, Los Angeles, California, 2014, pp. 4814–4819.
  65. W. S. Gray, M. Thitsa and L. A. Duffaut Espinosa, “Pre-Lie Algebra Characterization of SISO Feedback Invariants”, Proc. 53rd IEEE Conference on Decision and Control, Los Angeles, California, 2014, pp. 4807–4813.
  66. W. S. Gray and L. A. Duffaut Espinosa and K. Ebrahimi-Fard, “Recursive Algorithm for the Antipode in the SISO FeedbackProduct,” Proc. 21st International Symposium on the Mathematical Theory of Networks and Systems, Groningen, The Netherlands, 2014, pp. 1088–1093.
  67. L. A. Duffaut Espinosa, Z. Miao, I. R. Petersen, V. Ugrinovskii and M. R. James, “Physical Realizability Conditions for Mixed Bilinear-Linear Cascades with Pure Field Coupling,” Proc. 52nd IEEE Conference on Decision and Control, Florence, Italy, 2013, pp. 1866–1871.
  68. W. S. Gray and L. A. Duffaut Espinosa, “Feedback Transformation Groups for Nonlinear Input-output Systems,” Proc. 52nd IEEE Conference on Decision and Control, Florence, Italy, 2013, pp. 2570–2575.
  69. Z. Miao, L. A. Duffaut Espinosa, I. R. Petersen, V. Ugrinovskii and M. R. James, “Coherent observers for finite level quantum systems,” 2013 Australian Control Conference, Perth, Australia, 313–318.
  70. L. A. Duffaut Espinosa, Z. Miao, I. R. Petersen, V. Ugrinovskii and M. R. James, “On the preservation of commutation and anticommutation relations of n-level quantum systems,” Proc. 2013 American Control Conference, Washington D.C., 2013, pp. 2545–2549.
  71. L. A. Duffaut Espinosa, Z. Miao, I. R. Petersen, V. Ugrinovskii and M. R. James, “Preservation of Commutation Relations and Physical Realizability of Open Two Level Quantum Systems,” Proc. 51th IEEE Conference on Decision and Control, Maui, Hawaii, 2012, pp. 3019-3023.
  72. L. A. Duffaut Espinosa, W. S. Gray and M. Thitsa, “Cascaded Analytical Nonlinear Systems Driven By Rough Path Inputs,” Proc. 51th IEEE Conference on Decision and Control, Maui, Hawaii, 2012, pp. 1259-1264.
  73. W. S. Gray, M. Thitsa and L. A. Duffaut Espinosa, “Inversion of Analytic Input-Output Systems via Formal Power Series,” Proc. 15th Latin American Control Conference, Lima, Peru, 2012.
  74. L. A. Duffaut Espinosa, Z. Miao, I. R. Petersen, V. Ugrinovskii and M. R. James, “Physical Realizability of Multi-Level Quantum Systems,” Proc. 2012 Australian Control Conference, Sydney, Australia, 2012, pp. 19-23.
  75. L. A. Duffaut Espinosa, Z. Miao, I. R. Petersen, V. Ugrinovskii and M. R. James, “Physical Realizability of an Open Spin System,” Proc. 20th International Symposium on the Mathematical Theory of Networks and Systems, Melbourne, Australia, 2012.
  76. L. A. Duffaut Espinosa, W. S. Gray and M. Thitsa, “Cascaded Fliess Operators with Rough Path Inputs,” Proc. 20th International Symposium on the Mathematical Theory of Networks and Systems, Melbourne, Australia, 2012.
  77. W. S. Gray and L. A. Duffaut Espinosa, “A Faó di Bruno Hopf algebra for a group of Fliess operators with applications to feedback,” Proc. 50th IEEE Conference on Decision and Control and European Control Conference, Orlando Florida, 2011, pp. 3848-3854.
  78. Danielle C. Tarraf and L. A. Duffaut Espinosa, “On finite memory approximations constructed from Input/Output snapshots,” Proc. 50th IEEE Conference on Decision and Control and European Control Conference, Orlando Florida, 2011, pp. 3966-3973.
  79. L. A. Duffaut Espinosa and W. S. Gray, “Functional series expansions for continuous-time switched systems,” Proc. 2011 American Control Conference, San Francisco, 2011, pp. 2607-2612.
  80. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “On the local convergence of Fliess operators driven by L2-Ito random processes,” Proc. 49th IEEE Conference on Decision and Control, Atlanta, Georgia, 2010, pp. 2631-2637.
  81. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “On the absolute convergence of Fliess operators driven by L2-Ito processes,” Proc. 42nd IEEE Southeastern Symposium on System Theory, Tyler, Texas, 2010, pp. 280-285.
  82. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “On Fliess operators driven by L2-Ito random processes,” Proc. 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, pp. 7478-7484.
  83. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “Growth bounds for iterated integrals of L2-Ito random processes,” Proc. 41st IEEE Southeastern Symposium on System Theory, Tullahoma, Tennessee, 2009, pp. 223-229.
  84. W. S. Gray, H. Herencia-Zapana, L. A. Duffaut Espinosa and O. R. Gonzólez, “On cascades of bilinear system’s and generating series of weighted Petri nets,” Proc. 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008, pp. 4115-4120.
  85. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “On the bilinearity of cascaded bilinear systems,” Proc. 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, pp. 5581-5587.
  86. L. A. Duffaut Espinosa, W. S. Gray and O. R. Gonzólez, “On the rationality of the composition product: a survey,” Proc. 39th IEEE Southeastern Symposium on System Theory, Macon, Georgia, 2007, pp. 238-243.
  87. L. A. Duffaut Espinosa, A. D. Posadas and R. Quiroz, “Extracción de bordes de imágenes digitales a través del análisis multifractal,” Anales del VIII Simposio Nacional de Estudiantes de Física, Universidad Nacional San Antonio Abad del Cusco, Cusco, Perú, 2004.
  88. L. A. Duffaut Espinosa, W. S. Gray, and K. Ebrahimi-Fard, “Combinatorial Hopf algebras for interconnected nonlinear systems: A view towards discretization,” Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series, Springer, 2018.
  89. M. Almassalkhi, L. A. Duffaut Espinosa, P. Hines, J. Frolik, S. Paudyal and M. Amini, “Asynchronous coordination of distributed energy resources with packetized energy management,” Institute for Mathematics and its Applications - Control at Large Scales: Energy Markets and Responsive Grids, 2018.
  90. W. S. Gray and L. A. Duffaut Espinosa, “A Faá di Bruno Hopf Algebra for Analytic Nonlinear Feedback Systems,” in Faá di Bruno Hopf Algebras, Dyson-Schwinger Equations, and Lie-Butcher Series, K. Ebrahimi-Fard and F. Fauvet, Eds., IRMA Lectures in Mathematics and Theoretical Physics, European Mathematical Society, Strasbourg, France, 2015.
  91. M. Almassalkhi, H. Mavalizadeh, and L. A. Duffaut Espinosa, “Decentralized frequency control with packet-based energy management,” pat., (U.S. Patent Application No. 17/305,491), Jul. 2021.
  92. A. Posadas, C. Yarlequ´e, M. Carbajal, H. Heidinger, L. Carvalho, C. Jones, L. A. Duffaut Espinosa and R. Quiroz, Climate-Smart Agriculture: Global Science Conference, “The random cascade model: an approach for spatial downscaling of rainfall signals in heterogeneous terrain,” University of California Davis, Davis, California, 2013.
  93. L. A. Duffaut Espinosa, W. S. Gray and M. Thitsa, 8th International Purdue Symposium on Statistics, “Cascade of nonlinear systems driven by rough paths,” Purdue University, West Lafayette, Indiana, 2012.
  94. J. R. Donat, G. Carrasco, L. A. Duffaut Espinosa and P. L. Morton, “Sources and transport of Zinc and Cadmium and their complexing ligands in the Atlantic and Pacific oceans: differential ligand decay in specific water masses,” Ocean Sciences Meeting, Salt Lake City, Utah, 2012.
  95. G. Carrasco, L. A. Duffaut Espinosa, P. L. Morton and J. R. Donat, “Evaluating Sources and Transport of Zinc and Cadmium and Their Complexing Ligands in the Atlantic and Pacific Oceans,” Mineralogical Magazine, vol. 75,no. 3, 2011, pp. 627.
  96. L. A. Duffaut Espinosa, “On the Well-posedness of Cascades of Analytic Nonlinear Input-output Systems Driven by Noise,” Workshop on Rough Paths and Combinatorics in Control Theory, San Diego, California, 2011.
  97. L. A. Duffaut Espinosa and W. S. Gray, “A Rota-Baxter like algebra for Fliess operators with Poisson inputs and its applications to switched nonlinear systems,” The 7th International Congress on Industrial & Applied Mathematics, Vancouver, Canada, 2011 (invited).
  98. W. S. Gray and L. A. Duffaut Espinosa, “A Fa´a di Bruno Hopf Algebra for a group of Fliess operators with applications to feedback,” The 7th International Congress on Industrial & Applied Mathematics, Vancouver, Canada, 2011.

Teaching


Teaching Philosophy

As an engineering educator, I strive to foster critical thinking, creativity, and problem-solving skills in my students by providing hands-on, real-world challenges. I believe in empowering students with both theoretical knowledge and practical tools, preparing them to be adaptable, ethical engineers who can innovate in an ever-changing technological landscape.


Courses at the University of Vermont (2019 - present)


Upcoming Courses


Past Courses


Courses at George Mason University (2014 - 2016)


Team


Current Students

Undergraduate


Master


PhD


Graduated/Past Students

Contact


I am always looking for talented and hard working students who want to work in systems, control, estimation, autonomy, and robotics.


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