Hybrid Control and Estimation of Semi-Dissipative Systems- Analysis, Computation, and Machine Learning
Abstract
The proposed research is aimed at developing a rigorous theoretical and computational framework for hybrid control and optimization of fluid transport and mixing problems, combining applied mathematics and machine learning (ML) techniques. Understanding mass transport, fluid mixing, and their asymptotic behaviors via active control of the flow advection leads to fundamental, yet highly challenging problems often found in industrial and engineering applications. In this project, the PI focuses on the problem of optimal mixing of an inhomogeneous distribution of a scalar �eld via active control of the flow velocity, governed by the Stokes or the Navier-Stokes equations, where molecular diffusion is negligible. In the absence of diffusion, transport and mixing occur due to pure advection. This essentially leads to a nonlinear control problem of a semi-dissipative system. One of the most prominent mathematical challenges encountered in control and estimation of such systems arises through the presence of nonlinearities and strong couplings between the scalar and flow equations, as well as their mixed parabolic-hyperbolic nature. The classic tools for treating parabolic systems, based in its intrinsic regularizing effects and model reduction, are no longer applicable. Small-scale structures and large gradients of the scalar �eld develop in the mixing process, posing a major obstacle in numerical simulation, as the mesh size must be re�ned sufficiently to capture the smallest spatial scales of the thin �laments arising in the evolution of the scalar distribution. These problems are rich and challenging, both in theory and their computational aspects, and call for novel analytical and numerical treatments.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 05, 2025
- Source ID
- FA86552417027
Entities
People
- Enrique Zuazua Iriondo
Organizations
- Air Force Office of Scientific Research
- Friedrich-Alexander-Universität Erlangen-Nürnberg
- United States Air Force