Computing, School of
School of Computing: Dissertations, Theses, and Student Research
First Advisor
Hoang-Dung Tran
Committee Members
Hamid Bagheri, Bhuvana Gopal
Date of this Version
2024
Document Type
Thesis
Citation
A thesis presented to the faculty of the Graduate College at the University of Nebraska in partial fulfilment of requirements for the degree of Master of Science
Major: Computer Science
Under the supervision of Professor Hoang-Dung Tran
Lincoln, Nebraska, December 2024
Abstract
The verification of linear systems has been an active area of research for decades. Reachability analysis is a key component in verification problems. It involves computing the system’s reachable set, the set of reachable states in the state space from a given set of initial states. Most verification methods primarily focus on qualitative verification, which answers whether or not a system may violate specified safety conditions. This paper extends this qualitative verification to quantitative verification by introducing a novel approach, employing probabilistic stars (Probstars) to compute reachable sets, which augment traditional star sets by integrating Gaussian-distributed random variables with predicates. This quantitative verification enables a probabilistic understanding of reachability in high-dimensional systems, providing the probability of violation for discrete-time, linear time-invariant (LTI) systems within a bounded time. Based on the proposed probstar representation, we present a method to compute approximations of the reachable set, employing Krylov subspace methods like Arnoldi and Lanczos iterations to enhance computational efficiency in terms of memory and time.
Advisor: Hoang-Dung Tran
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons
Comments
Copyright 2024, Qing Liu. Used by permission