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Primal-dual tests for safety and reachability

Prajna, S and Rantzer, Anders LU (2005) In Hybrid Systems: Computation and Control (Lecture Notes in Computer Science) 3414. p.542-556
Abstract
A methodology for safety verification using barrier certificates has been proposed recently, Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from convex duality and the concept of density functions, in this paper we show that reachability can also be verified through convex programming. Several convex programs for verifying safety,... (More)
A methodology for safety verification using barrier certificates has been proposed recently, Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from convex duality and the concept of density functions, in this paper we show that reachability can also be verified through convex programming. Several convex programs for verifying safety, reachability, and other properties such as eventuality are formulated. Some examples are provided to illustrate their applications. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Hybrid Systems: Computation and Control (Lecture Notes in Computer Science)
volume
3414
pages
542 - 556
publisher
Springer
external identifiers
  • wos:000229036300035
  • scopus:24344500489
ISSN
1611-3349
0302-9743
ISBN
978-3-540-25108-8
DOI
10.1007/b106766
language
English
LU publication?
yes
id
607af536-3918-4590-8d8d-b0aec2ec5878 (old id 238740)
date added to LUP
2007-08-22 15:17:45
date last changed
2017-11-12 03:30:17
@inbook{607af536-3918-4590-8d8d-b0aec2ec5878,
  abstract     = {A methodology for safety verification using barrier certificates has been proposed recently, Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from convex duality and the concept of density functions, in this paper we show that reachability can also be verified through convex programming. Several convex programs for verifying safety, reachability, and other properties such as eventuality are formulated. Some examples are provided to illustrate their applications.},
  author       = {Prajna, S and Rantzer, Anders},
  isbn         = {978-3-540-25108-8},
  issn         = {1611-3349},
  language     = {eng},
  pages        = {542--556},
  publisher    = {Springer},
  series       = {Hybrid Systems: Computation and Control (Lecture Notes in Computer Science)},
  title        = {Primal-dual tests for safety and reachability},
  url          = {http://dx.doi.org/10.1007/b106766},
  volume       = {3414},
  year         = {2005},
}