Research Areas

Compositional Analysis and Synthesis of Interconnected Systems

Compositional Synthesis 

Existing computational tools for control synthesis and verification do not scale well to today’s large scale, networked systems. To overcome this problem we expose the system as an interconnection of subsystems and represent each subsystem with appropriate input-output properties as an abstraction of its detailed dynamical model. We then combine these abstractions to derive system-level stability, performance, and safety guarantees in a compositional fashion, thus decomposing intractably large problems into subproblems of manageable size. 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 exploiting interconnection symmetries for computational savings.

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).

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.

Designing Bacteria-Propelled Microrobots


Together with the Maharbiz, Arkin, and Ajo-Franklin (LBNL) labs, we are working to design millimeter-scale swimming robots propelled by flagellated bacteria. These bacteria will be attached to a synthetic robot hull and will be genetically engineered to accept electronic control signals from a chip embedded in the robot. We are investigating how to take advantage of hydrodynamic interactions between nearby flagella to improve swimming performance at these small size scales. This investigation relies on large-scale numerical simulations of low Reynolds number flows in three dimensions. Is there an optimal spacing between bacteria? Can we generate more thrust by patterning bacteria on the surface in a particular way? Answering these questions will guide our design choices and provide new insights into the locomotion of microorganisms.

Optimal Experiment Design for Metabolic MRI

Metabolic MRI 

In collaboration with the Larson lab at UCSF, we are developing mathematical models and numerical optimization techniques to design imaging sequences for metabolic magnetic resonance imaging (MRI). Techniques for MRI using injected hyperpolarized substrates have enabled researchers to probe the activity of metabolic pathways in living organisms, leading to new noninvasive ways to detect and monitor cancer. But reliance on hyperpolarized substrates leads to fundamental limits on image quality that are not present in conventional MRI. We have been working to improve image quality through dynamical systems modelling, which has allowed us to design injection and flip angle sequences that maximize the Fisher information about metabolic rate parameters in the model. Preliminary experiments have indicated that these optimized imaging sequences provide more reliable metabolic information than existing techniques.