In this talk, we review recent advances in converse Lyapunov theory and its application to the use of Sum-of-Squares (SOS) optimization for analysis and control of nonlinear systems - a topic which includes, e.g.: Domains of attraction, maximal invariant sets, minimal attractor sets, forward/backward reachable sets and optimal control. In each case, we review the applicable converse Lyapunov functions and show how these can be used to refine and accelerate the search for a corresponding Lyapunov-function-based proof via polynomial optimization methods such as SOS.

Biography: Matthew M. Peet received M.S. and Ph.D. degrees in aeronautics and astronautics from Stanford University. He was a postdoc at INRIA and Asst. Professor at the Illinois Institute of Technology. Currently, he is an Associate Professor of Aerospace Engineering at Arizona State University. His contributions to software development include the SOSTOOLS and PIETOOLS platforms for optimization-based analysis and control of nonlinear, delayed, and PDE systems.