Computer Science and Engineering, Department of
First Advisor
Dung Hoang 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 Dung Hoang 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: Dung Hoang Tran
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons
Comments
Copyright 2024, Qing Liu. Used by permission