Associate Professor

## Research

**Research Areas:**

**Research Interests:**

- Approximation and mathematical control theory of partial differential equations
- Optimal control of transport and mixing via fluid flows
- Well-posedness and long-time behavior of mathematical fluid dynamics
- Data-driven optimal control and estimation for network dynamics
- Computational methods for optimal control design and model reduction
- Reliability of renewable systems

**Grants:**

- Humboldt Research Fellowship for Experienced Researchers, Nov. 2023
- 2023–2026, AFOSR, FA9550-23-1-0675, “Hybrid Control and Estimation of Semi-Dissipative Systems: Analysis, Computation, and Machine Learning”, $442,285 (single PI).
- 2023–2026, NSF, DMS-2229345, “Collaborative Research: AMPS: Deep-Learning-Enabled Distributed Optimization Algorithms for Stochastic Security Constrained Unit Commitment”, \$320,000 (PI at UGA, \$120,000), jointly with Hongyu Wu (PI at Kansas State University), and Ashesh Sinha (Co-PI at Kansas State University).
- 2022–2025, NSF, DMS-2205117, “Nonlinear Control and Observer Designs for Flow-Transport Systems”, $120,000 (single PI).
- 2021–2024, NSF, DMS-2232526, Supplemental Funding for Research Collaboration in Europe for NSF Awardees, $9,060 (PI at UGA).

- 2021–2024, NSF, DMS-2111486, “Collaborative Research: Computational Methods for Optino-costmal Transport via Fluid Flows”, \$398,050 (PI at UGA, \$145,597), jointly with John Singler (PI at Missouri S&T), Yangwen Zhang (PI at CMU).
- 2018–2023, NSF, DMS-2005696 (previously DMS-1813570), “Control and Optimization of Semi-Dissipative Systems”, $108,734 (single PI, no-cost extension from 2021 to 2023).
- Interdisciplinary Research Pre-Seed Program on “The Integration of PDE Modeling, Machine Learning and Topology Analysis in MRIs Analysis”, $3,500, UGA, 2020.
- 2018–2019, DARPA, HR001117S0039-Lagrange-FP-014, “Robust Optimization & Control of Dynamic Sensor Systems” \$749,999 (PI at OSU, \$98,000), jointly with J. Burns (PI at VT), M. Demetriou (PI at WPI), and N. Gatsonis (Co-PI at WPI).

## Selected Publications

**Selected Publications:**

- X. Zheng, W. Hu and J. Wu, Numerical algorithms and simulations of boundary dynamic control for optimal mixing in unsteady Stokes flows, Computer Methods in Applied Mechanics and Engineering, vol. 417, Part A, 1 December 2023, 116455. doi.org/10.1016/j.cma.2023.116455.
- W. Hu, C. N. Rautenburg and X. Zheng, Feedback Control for Fluid Mixing via Advection, Journal of Differential Equations, 374, 2023. 126–153. doi.org/10.1016/j.jde.2023.07.009.
- W. Hu, Global regularity and stability analysis of the Patlak-Keller-Segel system with flow advection in a bounded domain: a semigroup approach. Nonlinear Analysis, Vol. 234, Sep. 2023, 113319. https://doi.org/10.1016/j.na.2023.113319.
- A. N. Ceretani, W. Hu, and C. Rautenburg, Optimal Conduit Shape for Stokes Flow, System & Control Letter, Vol. 173, Mar. 2023, 105461. doi.org/10.1016/j.sysconle.2023.105461.
- W. Hu, J. Liu and Z. Wang, Bilinear Control of Convection-Cooling and Computation: From Open-Loop to Closed-Loop, Applied Mathematics & Optimization, 86(5), 2022. doi.org/10.1007/s00245-022-09876-x.
- S. Afshar and W. Hu, Permeability Estimation of a Porous Structure based on Sampled Velocity Measurements, Inverse Problems, 38(6), 065002, 2022.
- W. Hu and J. Liu, Optimal Bilinear Control of a Reparable Multi-State System, International Journal of Control, 95:4, 851-866, 2022. DOI: 10.1080/00207179.2020.1825819.
- K. Huhtala, L.Paunonen, and W.Hu, Robust output regulation of the linearized Boussi- nesq equations with boundary control and observation, Mathematics of Control, Signals, and Systems, 34, 361–391, 2022.
- W. Hu, M. A. Demetriou, X. Tian, N. A. Gatsonis, Hybrid Domain Decomposition Filters for Advection-Diffusion PDEs with Mobile Sensors, Automatica, Vol.138, April 2022, 110109. https://doi.org/10.1016/j.automatica.2021.110109.
- C. He, W. Hu and L. Mu, Optimal Control of Convection-Cooling via Flow Advection and Numerical Implementation, Computers and Mathematics with Applications, 92 (2021), 48-61.
- W. Gong, W. Hu, M. Mateos, J. Singler, and Y. Zhang*, Analysis of an hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system, ESAIM: Mathematical Modelling and Numerical Analysis, 54(2020), 2229–2264. DOI: 10.1051/m2an/2020015.
- Y. Dai, W. Hu, J. Wu and B. Xiao, The Littlewood-Paley Decomposition for Periodic Functions and Applications to the Boussinesq Equations, Analysis and Applications, 18 (4), 2020, 639–682.
- W. Hu, J. Shen, J.Singler, Y. Zhang, and X.Zheng, A Superconvergent Hybridizable Discontinuous Galerkin Method for Dirichlet Boundary Control of Elliptic PDEs, Numerische Mathematik, 144(2), 375–411, 2020.
- W. Hu, An Approximating Control Design for Optimal Mixing by Stokes Flows, Applied Mathematics & Optimization, 82, 2020, 471--498. doi.org/10.1007/s00245-018-9535-4.

## Education

**Education:**

Ph.D., Mathematics, Virginia Tech, 2012.