Assurances of safety in dynamical systems are complicated by inevitable stochasticity, from human-in-the-loop actions, disturbance effects, and modeling errors. Computational challenges arise for almost any non-Gaussian stochasticity. We have created computationally efficient approaches to construct stochastic reach-avoid sets, based in Fourier transforms, chance constrained optimization, and Lagrangian methods. Some of our approaches enable exact results, without gridding, sampling, or recursion, while others provide under-approximations that can still ensure safety. Our methods have been applied to problems in verification, planning, and control. We demonstrate these methods to problems in robot navigation, dynamic target capture, satellite rendezvous and docking, and circadian entrainment. Our ultimate goal is construction of run-time methods for prediction, verification, and control of high-dimensional dynamical systems.

Meeko Oishi is an Associate Professor of Electrical and Computer Engineering at the University of New Mexico. She received the Ph.D. (2004) and M.S. (2000) in Mechanical Engineering from Stanford University, and a B.S.E. in Mechanical Engineering from Princeton University (1998). Her research interests include hybrid dynamical systems, control of human-in-the-loop systems, reachability analysis, and modeling of motor performance and control in Parkinson’s disease. She previously held a faculty position at the University of British Columbia at Vancouver. She is the recipient of the NSF CAREER Award, the UNM Regents’ Lecturer Award, the UNM Teaching Fellowship, the Peter Wall Institute Early Career Scholar Award, the Truman Postdoctoral Fellowship in National Security Science and Engineering, and the George Bienkowski Memorial Prize, Princeton University. She was a Summer Faculty Fellow at AFRL Space Vehicles Directorate 2013–2015, and is a member of the 2020-2021 Defense Science Study Group.