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The Complex Systems Scholar
“Complex systems are made of a multitude of interdependent parts that interact in intricate and uncertain ways,” explains Siljak. And they exist everywhere. Siljak and his collaborators have studied “fields as diverse as electric power systems and the arms race, ecosystems and large space structures, competitive economic equilibrium and artificial neural networks,” he says.
“Of particular interest in our studies was the fundamental question: Does increased complexity make for diminished stability? Or is it the other way around, and increased complexity begets increased system stability? No universal answer to this question has been found in complex systems, whether natural or man-made,” he explains. “Our mathematical analysis has shown that if interactions between parts of a complex system are properly bounded, then the stability of the parts either can, or can be made to, imply the stability of the overall system.”
Siljak’s research has shown that, for complex systems, decentralized control is superior to centralized control; the former is more suitable for preventing possible (or, he might argue, probable) failures of a complex system or coping with those occurring during operation.
A prolific scholar, he has published an array of books and papers, including three books (Decentralized Control of Complex Systems, Large-Scale Dynamic Systems, and Nonlinear Systems) and more than 180 papers in scholarly and scientific journals. In 1999, the
The University Environment
“This University is an open place,” says Siljak. “Its engineering department is not driven by an emphasis on factory-style productivity. It allows you to develop basic research that is not driven by peer pressure to do something ‘modern.’ You can take your time and develop answers to the fundamental questions. That is what I have found in these 40 years…that I can do activities not under direct pressure to develop what is fashionable,” he explains.
In addition, says Siljak, the human factor at SCU is a powerful one. “It is a more personable, friendlier environment. You don’t have a huge bureaucracy to deal with. This is important for developing new ideas and presenting them when they are ‘ready to see the world.’”
He adds, “I like to teach young people.” And from all reports, they like him as a teacher. Siljak’s elective courses are among the most popular in the engineering school. Teaching, explains Siljak, requires the same dedication as high-level athletics. “I was brought up in an environment where there was a heavy emphasis on how a teacher taught. …I was always challenged by that model. It is almost like a sporting event. You have to plan the lectures and execute them well, and, above all, you have to be dedicated to it.”
When he likens teaching to an athletic event, it’s no empty comparison. Born in
While still on the team, Siljak entered the
Siljak has applied his research to many areas, including population biology, where he has published in respected journals such as Nature, Mathematical Biosciences, and Journal of Mathematical Biology. He studied nonlinear population models and developed conditions for the robust stability of ecosystems under structural perturbations, whereby species change their interactions over time.
In the social sciences, he applied his mathematical methods to study the stability of the arms race, investigating how uncertainty in interactions among belligerent countries affects the overall stability of the race. He expanded the analysis to include competitive-cooperative arms race models and studied the influence of alliance formations on the arms race process.
In the mid-1960s, applying his theories to the development of control strategies for aerospace structures, Siljak initiated NASA-funded research on parameter space methods with G.J. Thaler, a former SCU professor. These methods were used in the control design of spacecraft, including the Saturn V rocket that carried astronauts to the moon.
In collaboration with Alex Zecevic, a colleague in the electrical engineering department, he has conducted basic research on the stability of large electric power systems. The two developed control and computer algorithms for stabilization of large-scale systems. This joint research has been supported by grants from the National Science Foundation and the Department of Energy, to name a few. In a recent NSF panel on the power blackout in the northern
Siljak’s research has attracted scientists from more than a dozen countries. “The University is a place that is open to the collaboration of people from all over the world,” he says. “Our activities and results have established
"Regardless of what size institution it comes from," says Siljak, "good work stands on its own two feet."