Course description:

Control synthesis and performance verification techniques are severely limited in their scalability to large networks of interconnected components.   In this series of lectures we will address this problem with a compositional approach that derives network-level guarantees from structural properties of the components and their interconnection.

First we will review the classical notion of dissipativity and derive conditions under which a large-scale interconnection of dissipative components satisfies a prescribed network performance criterion.  Next we will exhibit practically important interconnection structures and discuss which dissipativity properties are compatible with such structures to verify performance.  We will then present a large-scale optimization technique that searches over dissipativity properties of each component simultaneously for this verification.   Along the way we will define useful variants of the dissipativity notion, such as equilibrium-independent dissipativity and dissipativity with a dynamic supply rate.  We will conclude these lectures with vistas for further research on compositional synthesis, including tools based on formal methods from computer science.  We will illustrate the results presented in these lectures with examples from multi-agent systems, communication networks, and traffic networks.  In doing so, we will exhibit useful structural properties inherent in these networks. 

Biography: 

Murat Arcak is a professor at U.C. Berkeley in the Electrical Engineering and Computer Sciences Department.  He received the B.S. degree from the Bogazici University, Istanbul, Turkey (1996) and the M.S. and Ph.D. degrees from the University of California, Santa Barbara (1997 and 2000). His research is in dynamical systems and control theory with applications to synthetic biology, multi-agent systems, and transportation. He received a CAREER Award from the National Science Foundation in 2003, the Donald P. Eckman Award from the American Automatic Control Council in 2006, the Control and Systems Theory Prize from the Society for Industrial and Applied Mathematics (SIAM) in 2007, and the Antonio Ruberti Young Researcher Prize from the IEEE Control Systems Society in 2014. He is a member of SIAM and a fellow of IEEE.