This collaborative project studies dynamical systems characterized by a combination of hybrid and probabilistic behavior. Hybrid behavior is characterized by discrete switching between system modes and continuous evolution within a mode. Such systems frequently arise in a wide range of applications, from power electronics and communication networks to economics and biology. In this research, a new modeling framework for such systems is developed, which supports external variables, compositional reasoning, and nondeterministic as well as probabilistic transitions. New stability criteria for such probabilistic hybrid systems are obtained. In contrast with existing results, they are formulated in terms of two independent components: a family of Lyapunov functions (one for each continuous mode) and a slow-switching condition of an average-dwell-time type. This modularity has the benefit of decoupling the search for Lyapunov functions from the verification of the desired properties of the discrete dynamics. The latter task is the focus of the project, and is treated using two complementary methods: one based on proving an invariant property, and another based on solving an optimization problem. These theoretical results are supported by development of new software tools.

Agency
National Science Foundation (NSF)
Institute
Division of Computer and Network Systems (CNS)
Application #
0614993
Program Officer
D. Helen Gill
Project Start
Project End
Budget Start
2006-08-01
Budget End
2010-07-31
Support Year
Fiscal Year
2006
Total Cost
$220,000
Indirect Cost
Name
University of Illinois Urbana-Champaign
Department
Type
DUNS #
City
Champaign
State
IL
Country
United States
Zip Code
61820