Approximations of Stochastic Hybrid Systems

This paper develops a notion of approximation for a class of stochastic hybrid systems that includes, as special cases, both jump linear stochastic systems and linear stochastic hybrid automata. Our approximation framework is based on the recently developed notion of the so-called stochastic simulat...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2009-06, Vol.54 (6), p.1193-1203
Main Authors: Julius, A.A., Pappas, G.J.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Automata
Biological system modeling
bisimulation
Computational modeling
Computer science
control theory
systems
Computer simulation
Control system analysis
Control theory. Systems
Differential equations
Errors
Exact sciences and technology
Hybrid systems
Mathematical analysis
Mathematical models
Safety
State-space methods
stochastic hybrid systems
Stochastic processes
Stochastic resonance
Stochastic systems
Stochasticity
Systems engineering and theory
verification
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Summary:This paper develops a notion of approximation for a class of stochastic hybrid systems that includes, as special cases, both jump linear stochastic systems and linear stochastic hybrid automata. Our approximation framework is based on the recently developed notion of the so-called stochastic simulation functions. These Lyapunov-like functions can be used to rigorously quantify the distance or error between a system and its approximate abstraction. For the class of jump linear stochastic systems and linear stochastic hybrid automata, we show that the computation of stochastic simulation functions can be cast as a tractable linear matrix inequality problem. This enables us to compute the modeling error incurred by abstracting some of the continuous dynamics, or by neglecting the influence of stochastic noise, or even the influence of stochastic discrete jumps.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2019791