Finite Abstractions for Robust Synthesis

Abstraction-based control synthesis gained popularity in recent years for its ability to handle nontrivial dynamics and rich specifications at the same time. In practice, control systems are often affected by imperfections. Synthesis of robust control strategies thus becomes essential. In this talk, I will present a notion of finite abstractions that can be used for robust control synthesis. I will focus on nonlinear dynamical systems described by differential equations, with specifications expressible in linear temporal logics. I will present computationally efficient procedures for abstracting nonlinear dynamics into finite-state transitions and discuss how analytical tools from dynamical system theory can provide correctness and robustness guarantees for these abstractions. Connections with reachability analysis will also be discussed, where I will focus on how computation of better over-approximations of local reachable sets can lead to less conservative abstractions. Finally, some preliminary results on feasibility guarantees for discrete synthesis resulting from finite abstractions will be discussed.
Jun Liu received his B.Sc. degree in Applied Mathematics from Shanghai Jiao-Tong University, Shanghai, China, in 2002, his M.Sc. degree in Mathematics from Peking University, Beijing, China, in 2005, and his Ph.D. degree in Applied Mathematics from the University of Waterloo, Waterloo, Ontario, Canada, in 2010. Between 2012 and 2015, he was a Lecturer in the Department of Automatic Control and Systems Engineering at the University of Sheffield, Sheffield, UK. From 2011 and 2012, he was a Postdoctoral Scholar in Control and Dynamical Systems at the California Institute of Technology, Pasadena, California, USA. In 2015, he returned to the University of Waterloo, where he is currently an Assistant Professor in Applied Mathematics. His research is mainly in hybrid systems and control.