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 of coupled parabolic equations.
Control problems for fractional PDEs.
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.
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. 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.
Internship Report, Lur'e systems stability properties and numerical simulations.