10/26/2012 Elise King, Coordinated Science Lab
Written by Elise King, Coordinated Science Lab
ECE Professor Daniel M Liberzon recently won two, 3-year research grants from the National Science Foundation, both related to hybrid systems.
One grant, which is about $240,000, is titled “Hybrid Small-Gain Theorems for Nonlinear Networked and Quantized Control Systems” and will focus on analyzing hybrid systems. The other grant, approximately $280,000, is titled “Limited-Information Control of Hybrid Systems via Reachable Set Propagation” and will focus on developing a novel method for controlling hybrid systems that have limited information.
Although the timing of both grants is coincidental, “they’re related because once you know how to build a system and analyze it, that of course is related to controlling the system,” said Liberzon, a researcher in the Coordinated Science Lab’s Decision and Control group.
A hybrid system is a dynamical system that combines two types of elements: continuous dynamics and discrete events. A car, for example, is a hybrid system because when a person is driving it, the wheels rotate continuously and the car travels on a continuous trajectory, but at the same time, there are pistons firing in the engine and gears shifting at discrete times.
Liberzon’s first grant focuses on the analysis of hybrid systems—in particular, building large interconnected systems from small components and analyzing the resulting large system. For this research, Liberzon will use specific tools such as small-gains theorems to analyze the systems; the main goal behind this research will be to develop new results in stability and robustness.
The second grant deals with controlling such systems.
“When I have a hybrid system I want to induce certain desired behavior,” Liberzon explains. However, sometimes the controller of the system “only has some very rough knowledge of what the system is doing, what state the system is in.”
But, it is more feasible to induce the desired behavior based off of this limited knowledge because it takes less communication between the process and the controller to find a rough answer as opposed to finding out exact quantities, Liberzon said.
“If you can act on more limited information you can do it more efficiently for a larger network of systems,” said, Liberzon.
Better control of these hybrid systems can also improve security. If a controller can use limited knowledge, then the system will not have to reveal important information, such as its exact position. This will be the first time that the research topics of hybrid systems and control with limited information will be brought together.