Research | Florent Koudohode

Most of the systems we care about in engineering, flexible structures, chemical reactors, traffic networks, networks of distributed sensors, do not live in a finite-dimensional state space. Their natural language is that of partial differential equations: state and dynamics are infinite-dimensional, propagation is bounded by physics, and control acts most often through the boundary. The classical control toolbox, built for ordinary differential equations and continuous communication, does not directly transfer.

My research lives at this intersection. I design control laws for PDEs that remain robust under the constraints that the real world imposes, namely, that measurements arrive only at discrete instants, that they are quantized to finitely many levels, that control signals are subject to transmission delay, and that bandwidth must be used parsimoniously. The tools I rely on are Lyapunov analysis, backstepping transformations, predictor feedback, observer design, and a careful treatment of event-triggering rules. The result, when it works, is a control law that does more with less, provably stable, computationally honest, and ready to be deployed.

Event-triggered control

Classical feedback updates the control signal continuously, which is impossible on a digital platform and wasteful on a networked one. Event-triggered control replaces that continuous update with a triggering rule, a condition on the state, the error, or both, that determines, intrinsically, when the next update is needed. The challenge is to design rules that guarantee stability, exclude Zeno behaviour, and remain robust to disturbances. I have worked on event-triggered laws for the wave, Schrödinger and reaction–diffusion equations, as well as for 2×2 hyperbolic systems.

Boundary control of PDEs

When a physical system is described by a PDE, control acts most often at the boundary, a heated wall, a regulated valve, an end actuator. Stabilising such a system requires designing feedback laws that propagate through the spatial domain in finite time. The backstepping methodology, pioneered by Krstic and collaborators, transforms the open-loop PDE into a chosen target system via an invertible Volterra transformation. I use this framework in conjunction with Lyapunov functionals and observer design for measurement-output settings.

Predictor feedback for delay and quantization

Input delay is endemic to networked control: control signals reach the plant only after a transmission lag. Predictor feedback compensates this delay by acting on a future prediction of the state. Quantization, the unavoidable rounding induced by digital sensors and actuators, adds a second layer of imperfection, and the two effects interact. My recent work designs switched predictor-feedback laws that simultaneously compensate both, with semiglobal stability guarantees for nonlinear plants.

Related papers: IEEE TAC 2025, IMA JMCI 2025, SCL 2024, IFAC 2025, ACC 2025, CDC 2024.

European Research Council Consolidator Grant · 2022 #101088147

ERC Consolidator Grant, C-NORA

My current research is supported by the European Research Council under the Consolidator Grant C-NORA (#101088147), led at the Technical University of Crete by Prof. Nikolaos Bekiaris-Liberis. The project addresses micro-macro secure control of infinite-dimensional transport systems.

Project website

Control, at the edge of the possible.

ERC Consolidator Grant, C-NORA