Recruitment Seminar - Flow Control via PDE Methods Application to Water Resources Management and Smart Manufacturing

Partial Differential Equations (PDEs) are often used to model multi-physics systems. Representative engineering applications are deep oil drilling, road traffic dynamics, multi-phase flow, information diffusion on social media, and even chemical processes governing the state of charge of Lithium-ion battery to mention a few. These applications have tremendous economical and societal benefits. As an illustrative example, water systems governed by multi-phase flow dynamics are in connection with global warming leading to drastic alteration of rainfall patterns, increasing the risk of high floods, rivers ecological instability, and water scarcity as illustrated by the recent situation in Jackson, Mississippi. Generally, these classes of problems involve spatiotemporal dynamics that cannot be approximated straightforwardly by finite-dimensional elements. As such, the development of novel control approaches is needed. During the past few decades, for a large class of engineering processes, several PDE boundary control techniques have emerged to enable the robust stabilization of important engineering processes. I will present recent results related to the exponential stabilization two representative processes:

• The control of rivers and reservoirs sedimentation through the Saint-Venant Exner model. Here, PDE backstepping boundary control is employed to sophisticatedly design gate operating conditions that ensure exponential stabilization of supercritical flow regime, which has not been achieved in previous contributions.

• The event-triggered boundary control of continuum model of highly re-entrant manufacturing systems governed by a nonlinear hyperbolic PDE in connection with the emergence of smart factories operating through wireless communication environments.

I will conclude this talk by providing research avenues related to PDE control and estimation.