Research Areas

An Input-Output Approach to Networks

Input Out Approach 

We are developing a broadly applicable methodology that employs control-theoretic input-output concepts to predict and engineer collective behavior in networked dynamical systems. Existing methods for certifying stability and performance of dynamical systems do not scale to large networks of tightly coupled subsystems. To overcome this problem, we represent the subsystems with input-output properties as abstractions of their detailed models, and exploit these properties together with the interconnection structure to ascertain desirable behaviors. This approach has enabled systematic design and analysis tools for multi-agent systems, biochemical reaction networks, and resource allocation in communication networks. Current research topics include leveraging large-scale optimization techniques to detect useful input-output properties of the subsystems, and employing tools from graph theory and computational algebra to identify symmetries in the interconnection.

Spatial Pattern Formation in Biology

Biomolecular Network 

In collaboration with the Maharbiz and Arkin Labs, we are investigating how critical processes in natural multicellular organisms can be reestablished in a bacterial medium to enable synthetic multicellular systems. A problem of particular interest is spatial gene expression patterns that allow distinct cell types to emerge in early development. The mechanisms underlying such differentiation are not fully understood and synthetic gene networks that achieve patterning would provide insights about design principles. We recently proposed a new network architecture that generates such patterns with the help of a diffusible molecule establishing cell-to-cell communication. We are now pursuing a contact-mediated signaling mechanism as an alternative to diffusion-driven patterning. We have developed an efficient mathematical approach to predict patterns with this mechanism and are leveraging the results to engineer a programmable multicellular patterning system.

A Formal Methods Approach to Traffic Management

Traffic Management 

We are developing tools for traffic management and control using formal methods. By applying techniques such as model-checking and correct-by-construction synthesis, we ensure that traffic flow satisfies high-level objectives expressed using temporal logics that guarantee desirable behavior such as avoiding congestion, maintaining high throughput, ensuring fairness of ramp metering strategies, and reacting to incidents or unexpected conditions. Our techniques take advantage of inherent structure in traffic networks such as monotonicity properties, decomposability into sparsely connected subsystems, and hybrid dynamics. Exploiting such structure allows scalable and efficient design methodologies applicable to freeway ramp metering and traffic signal timing. We are applying these approaches to ongoing field tests in connection with California Partners for Advanced Transportation Technology (PATH).