Quelling Chaos Through Clever Control System Construction

Control systems are all around us in the modern world. If they’re doing their jobs right, nobody ever notices them. But once they begin to break down, the modern conveniences we have all become so accustomed to begin to fail.

Computers within our cars ensure that power is distributed correctly to all four wheels while maintaining cruising speed and avoiding immediate threats. HVAC systems distribute heating and cooling throughout enormous spaces using dozens of individual units at once. Our nation’s power grid is constantly balancing the supply and demand of hundreds of gigawatts produced by a complex network of power plants of various capabilities.

The techniques that prevent control systems’ failures usually couple all the individual pieces of a control system together. But as these networks become larger and more complex, incorporating many different types of technologies with different goals, they start to struggle. Just imagine how complex it would be to model and understand every element of our national power grid, all at once; nobody knows how to do that!

For the past three years, Leila Bridgeman has been mining the ideas of past control theorists for new approaches to these increasingly complicated problems. Just because these ideas were not chosen for development in simpler systems does not mean their approaches aren’t applicable to modern complexities.

“The main idea we chose to pursue essentially breaks one big problem down into small separate problems,” said Bridgeman, whose work has been supported by a prestigious Office of Naval Research (ONR) Young Investigator Award. “It was described in some papers from the 1970s that people mostly forgot, but it’s been a treasure trove for my group, and I’m continually surprised at how well the framework performs.”

“We recently realized that the approach provides simple rules to check that changing communications don’t cause controllers to spiral out of control,” Bridgeman said. “It made an enormous problem into one that suddenly doesn’t seem so bad.”

Another prong of Bridgeman’s work in collaboration with researchers at the University of New Mexico focuses on the data-driven analysis of invariant sets. While the term sounds like a mouthful, it essentially means using direct observations rather than ground-up mathematics to develop conditions where a system is safe.

Imagine a hockey player zipping across an ice rink. Ideally, that skater wants to avoid crashing into the walls whenever possible. If that player were operated by an autonomous control system, we’d want it to protect the player from harm as long as they remained on the ice.

There would clearly be, however, locations and speeds that, when combined, would inevitably lead to disaster. On the other hand, there would be a large set of locations and speeds that the player could recover from no matter what. In control theory terms, that mathematical safe space is known as an invariant set.

“Even if a control system is 99.999999% perfect for each step, it’s not good enough if there are a million steps involved,” Bridgeman explained. “Finding invariant sets is pretty much the only way to certify safety. The big goal of this research is to allow the design of AI controllers that won’t accidentally break the world—or the people—they interact with.”