My research centers on the study of Partial Differential Equations (PDEs) with a particular focus on control theory, including the well-posedness of boundary value problems, controllability, and stabilization. My main research interests are:
Control problems for PDEs on graphs
Stabilization of PDEs in the presence of delay, saturation, or disturbances.
Controllability and stabilization of coupled systems.
Preprints:
2024 E. Cerpa, K. Morris, H. Parada, Feedback control of an unstable parabolic-elliptic system with input delay. Submitted.
2025 F. Boyer, H. Parada, Null controllability of coupled parabolic equations with first-order perturbations. Submitted.
2025 R. de A. Capistrano-Filho, H. Parada, J. S. da Silva, An analysis of the entire functions associated with the operator of the KdV equation. Submitted. Preprint version.
2025 C. Negulescu, H. Parada, Spectral scheme for an energetic Fokker-Planck equation with kappa-distribution steady states. Submitted. Preprint version.
2025 P. Guzmán, A. Huerta, H. Parada, Rapid stabilization for a wave equation with boundary disturbance. Submitted. Preprint version.
Journal articles:
2025 H. Parada, Observer-based exponential stabilization of fractional heat equation. Applied Mathematics & Optimization 91, 67 (2025). Preprint version.
2025 G. Arias, H. Parada, Boundary stabilization of a class of coupled reaction-diffusion system with one control. SIAM, Journal of Control and Optimization, vol. 63 (4), pp 2783-2808. Preprint version.
2025 S. Majumdar, H. Parada, Stabilization of Kawahara equation with input saturation and saturated boundary feedback. Mathematical Control and Related Fields, 15(3): 845-875. Preprint version.
2024 E. Crépeau, H. Parada, C. Prieur, Stability of KdV equation on a network with bounded and unbounded lengths. ESAIM: Control, Optimisation and Calculus of Variations, vol. 30, 84, 2024. Preprint version.
2024 H. Parada, Null controllability of KdV equation in a star-shaped network. Evolution Equations and Control Theory, vol. 13 (3), pp 719-750. Preprint version.
2023 H. Parada, C. Timmimoun, J. Valein, Stability results for the KdV equation with time-varying delay. Systems & Control Letters, vol. 177, pp105547. Preprint version.
2022 E. Crépeau, H. Parada, C. Prieur, Global well-posedness of the KdV equation on a star shaped network and stabilization with saturated controllers. SIAM, Journal of Control and Optimization, vol. 60 (4), pp 2268-2296. Preprint version.
2022 E. Crépeau, H. Parada, C. Prieur, Delayed stabilization of KdV equation on a star shaped network. Mathematics of Control, Signals, and Systems, vol. 34, pp. 559–605. Preprint version.
Conferences papers:
2023 E. Crépeau, H. Parada, C. Prieur, Stability of linear KdV equation in a star shaped network with bounded and unbounded lengths. 62nd IEEE Conference on Decision and Control, Singapore. Preprint version.
2022 H. Parada, Stability analysis of a Korteweg-de Vries equation with saturated boundary feedback. IFAC CPDE 2022 Workshop on Control of Systems Governed by Partial Differential Equations, Kiel, Germany. Full version.
Control and Stabilization of PDE on networks. I defended my PhD thesis on the 5th of July 2023.
PhD Commite:
Emmanuelle Crépeau (Advisor), Christophe Prieur (Co-advisor).
Reviwers: Franck Boyer, Bing-Yu Zhang. Report 1, report 2.
Emmanuel Witrant (President), Eduardo Cerpa, Julie Valein, Hoai-Minh Nguyen.
Report of the PhD commitee here.
Master Thesis, Feedback control of an unstable parabolic-elliptic system with input delay.
Internship Report, Lur'e systems stability properties and numerical simulations.