Prof. Shai Revzen is a member of a five-institution team that will take advantage of recent advances in computation to exploit the promise of the Koopman Theory for modeling and control of dynamic systems.
The research is funded under a $6.25 million, five-year Multi-University Research Initiative (MURI) based at the University of California, Santa Barbara, and called From Data-Driven Operator Theoretic Schemes to Prediction, Inference and Control of Systems (DDOTS to PICS).
Describing the project, Revzen stated that linear systems theory and the consequent tools of control theory have been the workhorse of control theory in virtually every field of engineering since the mid 20th century. However, virtually all real world systems are non-linear, and most existing approaches for linearization are either local or restricted to small regions of a system’s possible range of states.
Koopman Theory, the subject of the DDOTS to PICS MURI, provides a universal framework including all possible linear representations of a dynamical system.
Recent advances in computation have allowed Koopman-theoretic linearization to be computed and applied in some promising cases, providing a novel and promising new avenue for modeling and control. The team hopes to extend these methods into a broadly applicable collection of tools.
While the UCSB team will focus on theory and fluid dynamics, the Michigan team will focus on developing tools for linearization of hybrid systems both offline and on-the-fly, and application of these tools to the control of robots.
Revzen, a professor of Electrical Engineering and Computer Science as well as Ecology and Evolutionary Biology, directs the Biologically Inspired Robotics and Dynamical Systems (BIRDS) Lab. He and his students are working on discovering, modeling, and reproducing the strategies animals use when interacting with physical objects. This work consists of collaboration with biomechanists to analyze experimental data, developing new mathematical tools for modeling and estimation of model parameters, and construction of robots which employ the new principles.
The DDOTS to PICS MURI is one of 23 projects totaling $163 million that the Department of Defense (DoD) will support in academic institutions across the United States. In addition to UCSB and Michigan, the other institutions involved are California Institute of Technology, Massachusetts Institute of Technology, and University of Washington, Seatte.
MURI awards are intended to accelerate research by forming teams of investigators that include more than one traditional science and engineering discipline. They are also intended to support the education and training of graduate students in new, cutting-edge research.