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Statistical Model Checking , Refinement Checking , Optimization , .. for Stochastic Hybrid Systems

Statistical Model Checking , Refinement Checking , Optimization , .. for Stochastic Hybrid Systems. Kim G. Larsen Peter Bulychev , Alexandre David , Dehui Du, Axel Legay , Guangyuan Li, Marius Mikucionis , Danny B. Poulsen , Amalie Stainer , Zheng Wang.

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Statistical Model Checking , Refinement Checking , Optimization , .. for Stochastic Hybrid Systems

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  1. StatisticalModel Checking, Refinement Checking, Optimization, .. for Stochastic Hybrid Systems Kim G. Larsen Peter Bulychev, Alexandre David, Dehui Du, Axel Legay, Guangyuan Li, Marius Mikucionis, Danny B. Poulsen, Amalie Stainer, Zheng Wang TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA

  2. IDEA4CPS Foundations for CPS Inst. of Software Chinese Academy of Sciences, Beijing, China I D TechnicalUniversity of Denmark, Lyngby, Denmark E East China Normal University, Shanghai, China Aalborg University, Denmark A FORMATS, Sep 2012

  3. Cyber-Physical Systems • Complex systems that tightly integrate multiple, networked computing elements (hardware and software) with non-computing physical elements such as electrical or mechanical components. Hybrid Systems Smart X FORMATS, Sep 2012

  4. Trustworthiness Probabilities Confidence (TCPS) .. by which we mean CPS on which reliance can justifiably be placed. (wiki) .. of a component is .. defined by how well it secures a set of functional and non-functional properties, deriving from its architecture, construction, and environment, and evaluated as appropriate. FORMATS, Sep 2012

  5. Current State Probabilistic Temporal Logic Stochastic Hybrid Systems Statistical Model Checking FORMATS, Sep 2012

  6. Overview Stochastic Hybrid Systems WeightedMetric Interval Temporal Logic UPPAAL SMC (Demo) Energy Aware Buildings SMC and RefinementChecking SMC and Optimization Conclusion FORMATS, Sep 2012

  7. Stochastic HybridSystems Simulate 5 [<=20] {p} Pr[<=20](<>(time >=12 && p >= 4)) A Bouncing Ball FORMATS, Sep 2012

  8. HybridAutomata H=(L, l0,§, X,E,F,Inv)where • L set of locations • l0 initial location • §=§i[§o set of actions • X set of continuous variablesvaluationº: X!R (=RX) • E set of edges(l,g,a,Á,l’) with gµRXand ÁµRX£RX and a2§ • For each l a delayfunctionF(l): R>0£RX ! RX • For each l an invariantInv(l)µRX FORMATS, Sep 2012

  9. HybridAutomata Semantics • States(l,º) whereº2RX • Transitions (l,º) !d (l,º’) whereº’=F(l)(d)(º) providedº’2Inv(l)(l,º) !a (l’,º’) if thereexists (l,g,a,Á,l’)2E with º2g and (º,º’)2Á and º’2Inv(l’) FORMATS, Sep 2012

  10. StochasticHybridAutomata StochasticSemantics For eachstates=(l,º) Delaydensityfunction* ¹s: R>0!R Output Probability Function °s: §o! [0,1] Next-state density function* ´as: St!R where a2§. * Dirac’s delta functions for deterministicdelays / nextstate FORMATS, Sep 2012

  11. StochasticHybridAutomata StochasticSemantics For eachstates=(l,º) Delaydensityfunction* ¹s: R>0!R Output Probability Function °s: §o! [0,1] Next-state density function* ´as: St!R where a2§. UPPAAL Uniform distributions (boundeddelay) Exponential distributions (unboundeddelay) Syntax for discreteprobabilisticchoice Distribution on nextstate by use of random Hybrid flow by use of ODEs Networks Repeated races between components for outputting * Dirac’s delta functions for deterministicdelays / nextstate FORMATS, Sep 2012

  12. Stochastic Semantics NTAs Pr[time<=2](<> T.T3) ? Pr[time<=T](<> T.T3) ? Pr[c<=C](<> T.T3) ? Composition = Race between components for outputting FORMATS, Sep 2012

  13. Stochastic Semantics of NHAs • Assumptions: • Component SHAs are: • Input enabled • Deterministic • Disjoint set of output actions ¼ ( s , a1a2 …. an ) : the set of maximal runs from s with a prefix t1a1t2a2 … tnak for some t1,…,tn2R. FORMATS, Sep 2012

  14. Metric Interval Temporal Logic • MITL≤ syntax: ϕ ::=σ | ¬ϕ|ϕ1∧ ϕ2| Oϕ | ϕ1U≤dϕ2 where d ∈ ℕ is a natural number. • MITL≤ semantics [ r=(a1,t1)(a2,t2)(a3,t3)… ]: • r⊨σif a1= σ • r⊨¬ϕ ifr ⊭ ϕ • r⊨ ϕ1∧ ϕ2ifr⊨ ϕ1andr ⊨ ϕ2 • r⊨Oϕif(a2,t2)(a3,t3)… ⊨ϕ • r⊨ϕ1U≤dϕ2if 9i. (ai,ti)(ai+1,ti+1)…⊨ϕ2 with t1+t2 +…+ti≤d and (aj,tj)(aj+1,tj+1)… ⊨ϕ1for j<i FORMATS, Sep 2012

  15. Logical Properties– WMITL Á = MODEL M PrM(Á) = ?? FORMATS, Sep 2012

  16. [FORMATS11, RV12] Statistical Model Checking M Generator }<T p Á Inconclusive Validator µ, ² p,® Core Algorithm PrM(Á) ¸p at significancelevel® PrM(Á) 2 [a-²,a+²] with confidenceµ FORMATS, Sep 2012

  17. Logical Properties– WMITL Á = OBSERVER (det) MODEL M 95% confidence interval: [0.215,0.225] FORMATS, Sep 2012

  18. Statistical Model Checking[LPAR2012] M | OÁ M Generator M | UÁ OÁ UÁ AÁ Á Inconclusive CASAAL Validator }acc µ, ² p,® Core Algorithm PrM(Á) ¸p at significancelevel® PrM(Á) 2 [a-²,a+²] with confidenceµ FORMATS, Sep 2012

  19. Experiments • How exact is the O/U? • 1000 random formulas • 2, 3, 4 actions • 15 connectives New exactmethod for fullMITL[a,b] usingrewriting [RV12] FORMATS, Sep 2012

  20. EnergyAwareBuildings With Alexandre David, Dehui Du Marius Mikucionis Arne Skou Fehnker, Ivancic. Benchmarks for Hybrid Systems Verification. HSCC04

  21. Stochastic HybridSystems Room1 simulate 1 [<=100]{Temp(0).T, Temp(1).T} simulate 10 [<=100]{Temp(0).T, Temp(1).T} Pr[<=100](<> Temp(1).T<=5 and time>30) >= 0.2 on/off Heater Pr[<=100](<> Temp(0).T >= 10) Room 2 on/off FORMATS, Sep 2012

  22. Framework Design Space Exploration FORMATS, Sep 2012

  23. Rooms & Heaters – MODELS FORMATS, Sep 2012

  24. Control Strategies – MODELS Temperature Threshold Strategies FORMATS, Sep 2012

  25. Weather & User Profile – MODELS FORMATS, Sep 2012

  26. Results – Simulations simulate 1 [<=2*day] { T[1], T[2], T[3], T[4], T[5] } simulate 1 [<=2*day] { Heater(1).r, Heater(2).r, Heater(3).r } FORMATS, Sep 2012

  27. Results – Discomfort Pr[<=2*day](<> time>0 && Monitor.Discomfort) FORMATS, Sep 2012

  28. Results – Comfort Pr[comfort<=2*day] (<> time>=2*day) FORMATS, Sep 2012

  29. Results – Energy Pr[Monitor.energy<=1000000](<> time>=2*day) FORMATS, Sep 2012

  30. Result – User Profile Pr[Monitor.energy<=1000000](<> time>=2*day) FORMATS, Sep 2012

  31. Refinement FORMATS, Sep 2012

  32. Controller Synthesis Heater Room on/off Room ?? constintTenv=7; constintk=2; constintH=20; constintTB[4]= {12, 18, 25, 28}; constintTenv=7; constintk=2; constintH=20; constint TB[4]= {12, 18, 25, 28}; criticalhigh 28 high 25 normal 18 low 12 criticallow FORMATS, Sep 2012

  33. Unfolding criticalhigh 28 high 25 normal 18 low 12 criticallow FORMATS, Sep 2012

  34. Timing criticalhigh 28 high 25 normal 18 low 12 criticallow FORMATS, Sep 2012

  35. TA Abstraction constintuL[3]={3,5,2}; constintuU[3]={4,6,3}; constintdL[3]={3,9,15}; constintdU[3]={4,10,16} FORMATS, Sep 2012

  36. Validation by Simulation FORMATS, Sep 2012

  37. Validation by Simulation constintuL[3]={3,8,2}; constintuU[3]={4,9,3}; constintdL[3]={3,9,15}; constintdU[3]={4,10,16} FORMATS, Sep 2012

  38. Optimization FORMATS, Sep 2012

  39. Time Bounded L-problem [Qest12] simulate 1 [time<=5] {C, x, y} Problem: Determineschedulethatmaximizes time until out of energy WATA, Dresden, May 30, 2012

  40. Time Bounded L-problem [Qest12] Pr[time<=30] (<> C<0 ) WATA, Dresden, May 30, 2012

  41. Time Bounded L-problem [Qest12] simulate 10000 [time<=10] {C,x,y}: 1 : time>=7 && Test.GOOD TEST Can we do better? Pr [time<=10] (<> time>=7 && Test.GOOD WATA, Dresden, May 30, 2012

  42. RESTART Method FORMATS, Sep 2012

  43. Meta Modeling RESTART Approach FORMATS, Sep 2012

  44. Meta Modeling Direct Approach FORMATS, Sep 2012

  45. Meta Analysis Direct Approach RESTART Approach FORMATS, Sep 2012

  46. Meta Analysis FORMATS, Sep 2012

  47. Meta Analysis FORMATS, Sep 2012

  48. Other Case Studies BLUETOOTH 10 node LMAC FIREWIRE ROBOT Schedulability Analysis for Mix Cr Sys Energy Aware Buildings Genetic Oscilator (HBS) Passenger Seating in Aircraft FORMATS, Sep 2012

  49. Contribution & More • Natural stochastic semantics of networks of stochastic hybrid systems. • Efficient implementation of SMC algorithms: • Estimation of • Sequential testing ¸ p • Sequential probability comparison ¸ • Parameterized comparison • Distributed Implementation of SMC ! FORMATS, Sep 2012

  50. Thank You ! FORMATS, Sep 2012

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