Control of PDEs

I have worked on the feedback stabilization problem for various PDEs. 

You can find certain stabilization results in the book:

I. Karafyllis and M. Krstic, Input-to-State Stability for PDEs, Springer-Verlag, London (Series: Communications and Control Engineering), 2019.

Below is a list of papers that contain feedback stabilization results for systems that involve PDEs. I have not included papers with event-triggered or sampled-data stabilization results (this topic is analyzed separately).  

• I. Karafyllis, P. D. Christofides and P. Daoutidis, "Dynamics of a Reaction-Diffusion System with Brusselator Kinetics Under Feedback Control", Physical Review E, 59(1), 1999, pp. 372-380.

• I. Karafyllis and P. Daoutidis, "Control of Hot Spots in Plug Flow Reactors", Computers and Chemical Engineering, 26, 2002, pp. 1087–1094.

• I. Karafyllis and M. Krstic, “On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations”, ESAIM Control, Optimisation and Calculus of Variations, 20(3), 2014, pp. 894 - 923.

• I. Karafyllis and M. Krstic, “Stability of Integral Delay Equations and Stabilization of Age-Structured Models”, ESAIM Control, Optimisation and Calculus of Variations, 23(4), 2017, pp. 1667-1714.

• I. Karafyllis and M. Krstic, “An ODE Observer for Lyapunov-Based Global Stabilization of a Bioreactor Nonlinear PDE”, Feedback Stabilization of Controlled Dynamical Systems, Nicolas Petit (Ed.), Lecture Notes in Control and Information Sciences, Vol. 473, Springer, 2017. 

• K. Schmidt, I. Karafyllis and M. Krstic, “Yield Trajectory Tracking for Hyperbolic Age-Structured Population Systems”, Automatica, 90, 2018, pp. 138-146.

• I. Karafyllis and M. Papageorgiou, “Feedback Control of Scalar Conservation Laws with Application to Density Control in Freeways by Means of Variable Speed Limits”, Automatica, 105, 2019, pp. 228-236.

• I. Karafyllis and M. Krstic, “Small-Gain-Based Boundary Feedback Design for Global Exponential Stabilization of 1-D Semilinear Parabolic PDEs”, SIAM Journal on Control and Optimization, 57(3), 2019, pp. 2016-2036.

• I. Karafyllis, N. Bekiaris-Liberis and M. Papageorgiou, “Feedback Control of Nonlinear Hyperbolic PDE Systems Inspired by Traffic Flow Models”, IEEE Transactions on Automatic Control, 64(9), 2019, pp. 3647-3662.

• I. Karafyllis and M. Krstic, “Global Stabilization of a Class of Nonlinear Reaction-Diffusion PDEs by Boundary Feedback”, SIAM Journal on Control and Optimization, 57(6), 2019, pp. 3723-3748.

• I. Karafyllis and M. Krstic, “Stability Results for the Continuity Equation”, Systems & Control Letters, 135, 2020, 104594.

• I. Karafyllis, “Lyapunov-Based Boundary Feedback Design For Parabolic PDEs”, International Journal of Control, 94(5), 2021, pp. 1247–1260.

• I. Karafyllis, D. Theodosis and M. Papageorgiou, “Analysis and Control of a Non-Local PDE Traffic Flow Model”, International Journal of Control, 95(3), 2022, pp. 660-678.

• I. Karafyllis and M. Krstic, “Global Stabilization of Compressible Flow Between Two Moving Pistons”, SIAM Journal on Control and Optimization, 60(2), 2022, pp. 1117-1142.

• I. Karafyllis and M. Krstic, “Spill-Free Transfer and Stabilization of Viscous Liquid”, IEEE Transactions on Automatic Control, 67(9), 2022, pp. 4585-4597.

• I. Karafyllis, F. Vokos and M. Krstic, “Feedback Stabilization of Tank-Liquid System with Robustness to Wall Friction”, ESAIM Control, Optimisation and Calculus of Variations, 28, 2022, 81.

• I. Karafyllis, F. Vokos and M. Krstic, “Output-Feedback Control of Viscous Liquid-Tank System and its Numerical Approximation”, Automatica, 149, 2023, 110827.

• I. Karafyllis and M. Krstic, “Control of a Linearized Viscous Liquid-Tank System with Surface Tension”, SIAM Journal on Control and Optimization, 62(2), 2024, pp. 1034-1059.

• P.-E. Haacker, I. Karafyllis, M. Krstic and M. Diagne, “Stabilization of Age-Structured Chemostat Hyperbolic PDE with Actuator Dynamics”, International Journal of Robust and Nonlinear Control, 34(10), 2024, pp. 6741-6763.

• G. A. de Andrade, R. Vazquez, I. Karafyllis and M. Krstic, “Backstepping Control of a Hyperbolic PDE System with Zero Characteristic Speed States”, IEEE Transactions on Automatic Control, 69(10), 2024, pp. 6988-6995.

• I. Karafyllis, F. Vokos and M. Krstic, “Feedback Stabilisation of Tank-Liquid System with Robustness to Surface Tension”, International Journal of Control, 98(10), 2025, pp. 2469–2480.

• I. Karafyllis, F. Vokos and M. Krstic, “A Complete Inverse Optimality Study for a Tank-Liquid System”, Systems and Control Letters, 207, 2026, 106293.

• C. Veil, M. Krstic, I. Karafyllis, M. Diagne and O. Sawodny, “Stabilization of Predator-Prey Age-Structured Hyperbolic PDE when Harvesting both Species is Inevitable”, IEEE Transactions on Automatic Control, 71(1), 2026, pp. 123-138.

• I. Karafyllis and M. Krstic, “Partial-State DADS Control for Matched Unmodeled Dynamics”, Automatica, 188, 2026, 112930.

• I. Karafyllis, E. Loko, M. Krstic and A. Chaillet, “Global Stabilization of Chemostats with Nonzero Mortality and Substrate Dynamics”, submitted to the International Journal of Control (see also arXiv:2502.09310 [math.OC]).