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A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates

Prajna, Stephen and Jadbabaie, Ali and Pappas, George J. (2007) A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates. IEEE Transactions on Automatic Control, 52 (8). pp. 1415-1428. ISSN 0018-9286. http://resolver.caltech.edu/CaltechAUTHORS:PRAieeetac07

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Abstract

This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings. In the worst-case setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes it possible to handle nonlinearity, uncertainty, and constraints directly within this framework. In the stochastic setting, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, barrier certificates can be constructed using convex optimization, and hence the method is computationally tractable. Some examples are provided to illustrate the use of the method.


Item Type:Article
Additional Information:© Copyright 2007 IEEE. Reprinted with permission. Manuscript received March 4, 2005; revised May 17, 2006. [Posted online: 2007-08-13] Recommended by Associate Editor C. T. Abdallah. The work of S. Prajna was supported by AFOSR, NIH/NIMGS Alliance for Cellular Signalling, DARPA, Kitano ERATO Systems Biology Project, and URI.
Subject Keywords:Barrier certificates, hybrid systems, nonlinear systems, safety verification, stochastic systems, sum of squares optimization
Record Number:CaltechAUTHORS:PRAieeetac07
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:PRAieeetac07
Alternative URL:http://dx.doi.org/10.1109/TAC.2007.902736
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9022
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:22 Oct 2007
Last Modified:15 Jan 2015 20:41

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