Path-complete Lyapunov functions: graph-theory and algebraic geometry for controlling complex systems

28^th February 2023, 13:00 Ashton Lecture Theatre
Prof. Raphaël Jungers
Institute for Information and Communication Technologies, Electronics and Applied Mathematics, Université Catholique de Louvain

Abstract

I'll present recent results on Path-Complete control, a meta-optimization technique aiming at designing efficient optimization programs, initially introduced for stability analysis, but later generalized to other control problems. These optimization programs are conveniently represented by an automaton. While we understand correctly now the characterization of all valid automata for stability analysis, many elementary questions remain open.

For practical purpose, it is crucial to understand when a particular optimization program is less conservative than another one. I'll focus on this problem, which is essentially an algebraic geometry problem. I will mention recent advances, which take into account the used template of candidate Lyapunov functions in the comparison problem. We solve the problem for several templates, making use of tools from automata theory (simulation,...), graph theory (Hall's marriage theorem), and convex geometry (duality,...).