The focus of my research is algorithm design and implementation, specifically in the area of control and optimization. Since my arrival at UC Berkeley, I have been interested in the development of computationally efficient optimization-based control and estimation algorithms. I have applied them to systems modeled by partial differential equations (PDEs). My algorithms have been applied to three areas of Civil and Environmental Engineering:
- Nation-wide air traffic management using aggregate Eulerian flow models
- Online data assimilation for highway traffic flow reconstruction using cellular phone measurements (see also the website of my project Mobile Millennium)
- Inverse modeling for shallow water flows using Lagrangian sensor measurements
- Modeling and Optimization Analysis of Single Flagellum Bacterial Motion
My specific interest is the integration of mobile measurements into distributed parameter systems models such as PDEs. The applications of my work to highway traffic and shallow water flows have benefited from the rapid and recent expansion of the mobile internet. My work on highway traffic is one of the early research instantiations of a location based service, heavily relying on mobile participatory sensing. My research on PDEs has laid some mathematical foundations for Lagrangian sensing. My work is also an example of one the aspects of the “web 2.0” paradigm: user-generated content. In the present case, smartphones carried by humans act as sensors and share information.
My contributions can be summarized in four categories: mathematical results, algorithms, experiments and testbeds. I have produced mathematical proofs as needed (in particular the existence and uniqueness of solutions of PDEs) that are fundamental contributions to the field. Most of the algorithms I have designed rely on the application of specific techniques to the PDEs of interest, such as viability theory, differential flatness, spectral analysis, finite differences and convex optimization. Sometimes, I have used analytic solutions, that were either known, or that I discovered. Almost all my algorithms have been implemented, most of the time with field data collected through experiments using testbeds built by my group.