Approximate abstraction of stochastic systems

1
Approximate abstraction of stochastic systems

• A Agung Julius
• Dept. Electrical Systems Engineering
• University of Pennsylvania
• http//www.seas.upenn.edu/agung
• Collaboration with George Pappas, Antoine
  Girard

Stochastic Hybrid Systems Day, U.Twente, 8 Dec
2005
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Talk layout

• Motivational background
• Jump linear stochastic systems
• Stochastic bisimulation function
• Approximate abstraction safety verification
• Examples
• Possible extensions

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Motivational background

4
Talk layout

• Motivational background
• Jump linear stochastic systems
• Stochastic bisimulation function
• Approximate abstraction safety verification
• Examples
• Possible extensions

5
Jump linear stochastic systems (1)

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Jump linear stochastic systems (2)
noise random walk
output
random jump
internal
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Jump linear stochastic systems (3)
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Talk layout

• Motivational background
• Jump linear stochastic systems
• Stochastic bisimulation function
• Approximate abstraction safety verification
• Examples
• Possible extensions

9
Stochastic bisimulation function (1)
internal
should be close
internal
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Stochastic bisimulation function (2)

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Stochastic bisimulation function (3)
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Stochastic bisimulation function (4)
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Stochastic bisimulation function (5)

14
Talk layout

• Motivational background
• Jump linear stochastic systems
• Stochastic bisimulation function
• Approximate abstraction safety verification
• Examples
• Possible extensions

15
Apprx. abstraction safety verification (1)
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Apprx. abstraction safety verification (2)

unsafe
17
Talk layout

• Motivational background
• Jump linear stochastic systems
• Stochastic bisimulation function
• Approximate abstraction safety verification
• Examples
• Possible extensions

18
Examples (1)
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Examples (2)

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Examples (3)
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Examples (4)

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Examples (5)
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Examples (6)

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Examples (7)
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Talk layout

• Motivational background
• Jump linear stochastic systems
• Stochastic bisimulation function
• Approximate abstraction safety verification
• Examples
• Possible extensions

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Nonlinear dynamics

27
Variable rate Poisson processes

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Final words
Thank you for your attention! Veel geluk, Stefan!