Seminar: A Framework for Safe Probabilistic Invariance Verification of Stochastic Dynamical Systems
Abstract: Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This talk will introduce a comprehensive framework for the safe probabilistic invariance verification of both discrete- and continuous-time stochastic dynamical systems over an infinite time horizon. The objective is to ascertain the lower and upper bounds of liveness probabilities for a given safe set and set of initial states. The liveness probability signifies the likelihood of the system remaining within the safe set indefinitely, starting from a state in the initial set. To address this problem, we propose optimizations for verifying safe probabilistic invariance in discrete-time and continuous-time stochastic dynamical systems. These optimizations are constructed via either using the Doob’s nonnegative supermartingale inequality-based method or relaxing the equations proposed in our previous works, which can precisely characterize the probability of reaching a target set while avoiding unsafe states. Finally, we demonstrate the effectiveness of these optimizations through several examples using semi-definite programming tools.
Bio.: Dr. Bai Xue is a Research Professor at Key Laboratory of System Software/State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences (CAS) since September 2021. On September 18, 2024, he was promoted to the position of Deputy Director of the Key Laboratory of System Software. His research interests include, but are not limited to, formal verification and controller synthesis for autonomous systems and AI. Please refer to his homepage (https://lcs.ios.ac.cn/~xuebai/index.html) for his publications on these topics.
He received the B.Sc. degree in Information and Computing Science from Tianjin University of Technology and Education in 2008, and the Ph.D. degree in Applied Mathematics from Beihang University in 2014. Prior to joining Institute of Software as an Associate Research Professor in November 2017, he worked as a research fellow in the Centre for High Performance Embedded Systems at Nanyang Technological University from May, 2014 to September, 2015, and as a postdoc in the Department füer Informatik at Carl von Ossietzky Universität Oldenburg from November, 2015 to October, 2017.