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Towards Verifying Cyber- Physical Systems with Structural Dynamism

Dagstuhl Seminar 11441-1 Science and Engineering

• f Cyber-Physical Systems, 02.11.2011

Holger Giese and Basil Becker System Analysis & Modeling Group, Hasso Plattner Institute for Software Systems Engineering at the University of Potsdam, Germany holger.giese@hpi.uni-potsdam.de

02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

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Application Example:

Combine shuttles as a CPS …

A shuttle system that builds convoys to optimize the energy consumption Test shuttle Test track

http://www.railcab.de/

02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

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1) Modeling with Graph Transformation Systems

Apply Graph Transformation Systems

 Map the tracks  Map the shuttles  Map the shuttle

movement to rules (move- ment equals reconfiguration)

Track1 Track2

t1:Track t2:Track

Shuttle Shuttle Shuttle t1:Track t2:Track s1:Shuttle t1:Track t1:Track s1:Shuttle

Rule:

02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

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2) Modeling with Graph Transformation Systems

Track1 Track2

t1:Track t2:Track

Shuttle1 Shuttle1 Shuttle2 Shuttle2 Shuttle1

t:Track s1:Shuttle s2:Shuttle Distance Coordination

Forbidden Graph

t1:Track t2:Track s1:Shuttle t1:Track t2:Track s1:Shuttle

Rule:

 Correctness: all reachable system graphs do not match the forbidden graph pattern

Idea for hybrid behavior: continuous attributes and modes with continuous laws

 Correctness: all reachable hybrid system graphs do not match the forbidden hybrid

graph pattern

Modeling the Railcab System

Meta Model: Continuous Behavior: Forbidden Situation (Graph Pattern): Discrete Behavior (Rule):

| pos_ref – rear.front.pos_ref | < delta

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02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

Basic Verification Idea

Idea (invariant checking):



Look only for a transition from a safe to an unsafe state



Found a case leading from a safe to a forbidden graph pattern Timed:



Found a case leading from a safe to a forbidden graph pattern also fulfilling the time constraints that is not prevented by other rules (system of linear inequality; CPLEX solver) Hybrid:



Construct hybrid automata for the check (PHAVer)

02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

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t:Track s1:Shuttle s2:Shuttle dc:Distance Coordinatio n

move correct system graph ?

Verification of the Application Example



Structural Check returns possible counterexamples (not taking the continuous behavior and constraints into account)



Modelchecking a related hybrid automata disproof or conforms each counterexample

02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

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Summary

 Very expressive model in form of hybrid graph transformation

model containing ■ Discrete behavior with structural dynamism (which potentially leads to a discrete infinite states paces in form of graphs) ■ Continuous behavior in form of mode nodes and their continuous laws that can in principle reference all continuous variables of reachable other nodes

 Invariant checker for restricted variant where for all counter-

examples a closed continuous system of inequalities can be derived.

 Tool support is still under development … 02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

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