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Claire Tomlin earned her PhD from UC Berkeley in 1998.

Whether UC Berkeley engineer Claire Tomlin is studying air traffic patterns or genetic switches, the secrets she seeks are in the mathematics underlying the systems. Tomlin, a professor of electrical engineering and computer sciences, is a control theorist. Her aim is to learn how complex systems can be controlled to achieve a particular goal, such as preventing planes from crashing into each other. In September, Tomlin was honored with one of this year's MacArthur Foundation Fellowships, better known as a "genius grant."

"I work with mathematical models and try to manipulate their parameter or inputs in a principled way to control the system," says Tomlin who also holds a faculty position at Stanford University's Department of Aeronautics and Astronautics.

The classic application of control theory is the auto-pilot feature that's ubiquitous on today's airplanes, Tomlin explains. But she and her colleagues are now facing much more challenging control problems involving hybrid systems that may consist of thousands of components. To control these "systems of systems," the researchers must develop software algorithms that take into account a mix of constant and changing conditions. For example, at any given time there are 3,000 to 5,000 aircraft flying in US airspace. Controlling those aircraft is a multi-level problem compounded by myriad static and dynamic conditions such as highly-localized traffic around a particular airport, regional traffic, rerouted aircraft, and planes on auto pilot.

"It's a wonderful control problem to try and avoid bottlenecks that can lead to huge delays," says Tomlin, who is affiliated with the Center for Information Technology Research in the Interest of Society (CITRIS). "You want to keep all of the aircraft separated from each other but maintain a kind of optimal flow of aircraft through the system so you're not subject to delays."

This .avi video clip depicts air traffic over a period of ten hours in several sectors covered by the Oakland Air Route Traffic Control Center. Aircraft flying above 33,000 feet are displayed. Aircraft that appear to collide are actually traveling at different altitudes. The visualization was created using Enhanced Traffic Management System data provided by NASA Ames. [Video]

Eventually, such a system should enable airports to run like clockwork while improving the safety of the skyways. An advanced collision avoidance system would provide aircraft with the computational smarts to automatically avoid each other while flying in tighter formations. Still, Tomlin stresses, pilots and air traffic controllers will remain in the loop. A computer tool would complement radar data by giving air traffic controllers a sense of the twenty-minute time horizon and offer hints to optimize air traffic flow. The controllers would then relay that information to pilots.

In collaboration with NASA, Tomlin and her students tested the collision avoidance algorithms on unmanned air vehicles. On the heels of those experiments, the researchers outfitted Boeing military jets with laptop computers running the algorithms. With F-15s in the sky nearby, the pilots took their hands off the yoke and the system passed the test with flying colors. Recently, Tomlin won another grant with the space agency to investigate how the technology could be implemented in the national airspace system.

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Back on the ground, Tomlin is also applying her hybrid control theory innovations to biological problems. In collaboration with Stanford pathology professor Jeffrey Axelrod, Tomlin and her students developed mathematical models of protein regulatory networks involved in the development of a fruit fly's wings. Genes that produce certain proteins are activated or deactivated by other proteins in the vicinity. Once again, Tomlin was faced with a large complex system of continuous dynamics. After developing the models, she used them to predict protein concentrations based on genetic variables. The results were strikingly similar to Axelrod's real world data. Understanding these kinds of genetic systems could shed light on how birth defects in humans may arise.

For Tomlin, the difference between networks of genes and skyways of planes is in the details. From her vantage point, it's all about getting the numbers right.

"My projects are connected by the use of mathematical models as a method to get a system to do something desirable," she says.

Claire Tomlin's home page

Hybrid Systems Laboratory at Stanford University

"Air Traffic Control Algorithms Take Off" by David Pescovitz (June/July 2005)

"Aviation engineer wins MacArthur 'genius' award" by Sarah Yang (Public Affairs, September 20, 2006)

"'Out of the blue,' a MacArthur award for aeronautics scholar Claire Tomlin" (Stanford News Service, September 19, 2006)

Center for Information Technology Research in the Interest of Society (CITRIS)

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