Towards Verifying Cyber- Physical Systems with Structural Dynamism - PowerPoint PPT Presentation

Towards Verifying Cyber- Physical Systems with Structural Dynamism Dagstuhl Seminar 11441-1 Science and Engineering of 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

Application Example: Combine shuttles as a CPS … 2 http://www.railcab.de/ Test track Test shuttle A shuttle system that builds convoys to optimize the energy consumption 02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

1) Modeling with Graph Transformation Systems Apply Graph 3 Track1 Track2 Transformation Systems Shuttle  Map the tracks  Map the shuttles t1:Track t2:Track  Map the shuttle movement to rules (move- ment equals Shuttle reconfiguration) Shuttle Rule: t1:Track t2:Track t1:Track t1:Track s1:Shuttle s1:Shuttle 02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

2) Modeling with Graph Transformation Systems 4 Forbidden Graph Track1 Track2 t:Track Shuttle1 Shuttle2 s1:Shuttle s2:Shuttle t1:Track t2:Track Distance Coordination Shuttle1 Shuttle1 Shuttle2  Correctness: all reachable system graphs do not match the forbidden graph pattern Rule: t1:Track t2:Track t1:Track t2:Track 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 s1:Shuttle s1:Shuttle 02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

Modeling the Railcab System 5 Meta Model: Continuous Behavior: | pos_ref – rear.front.pos_ref | < delta Discrete Behavior (Rule): Forbidden Situation (Graph Pattern): 02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

Basic Verification Idea 6 t:Track Idea (invariant checking): ? s 1 :Shuttle s 2 :Shuttle correct Look only for a transition from a safe to  system move dc:Distance graph an unsafe state Coordinatio n 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

Verification of the Application Example 7 Structural Check returns possible Modelchecking a related hybrid   counterexamples (not taking the automata disproof or conforms continuous behavior and each counterexample constraints into account) 02.11.2011 | Giese & Becker | Towards Verifying CPS with Structural Dynamism

Summary 8  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