Accession Number:

ADA543485

Title:

Stochastic Differential Dynamic Logic for Stochastic Hybrid Programs

Descriptive Note:

Corporate Author:

CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

Personal Author(s):

Report Date:

2011-04-01

Pagination or Media Count:

27.0

Abstract:

Logic is a powerful tool for analyzing and verifying systems, including programs, discrete systems real-time systems, hybrid systems, and distributed systems. Some applications also have a stochastic behavior, however, either because of fundamental properties of nature, uncertain environments or simplifications to overcome complexity. Discrete probabilistic systems have been studied using logic. But logic has been chronically underdeveloped in the context of stochastic hybrid systems, i.e., systems with interacting discrete, continuous, and stochastic dynamics. We aim at overcoming this deficiency and introduce a dynamic logic for stochastic hybrid systems. Our results indicate that logic is a promising tool for understanding stochastic hybrid systems and can help taming some of their complexity. We introduce a compositional model for stochastic hybrid systems. We prove adaptivity, cadlag, and Markov time properties, and prove that the semantics of our logic is measurable. We present compositional proof rules, including rules for stochastic differential equations, and prove soundness.

Subject Categories:

  • Theoretical Mathematics
  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE