Hybrid Systems

algorithm For example consider forward breadth-first search. F=Init repeat F=F ∪ SuccFlow(F) ∪ SuccJump(F) until fixpoint |(F∩ Bad 6= ∅) | tired A standard verification (semi-)algorithm. EJCMI Nancy 2007 – p. 58/67 How to implement it Needed data structure for (over-)approximate representation of subsets of R, and algorithms for efficient computing of • unions, intersections; • inclusion tests; • SuccFlow; • SuccJump. EJCMI Nancy 2007 – p. 59/67 Known implementations • Polyhedra (HyTech exact. Checkmate) • “Griddy polyhedra” (d/dt) • Ellipsoids (Kurzhanski, Bochkarev) • Level sets of functions (Tomlin) • Zonotopes (Girard) f(x)<0 EJCMI Nancy 2007 – p. 60/67 Does it work? Up to 10 dimensions. Sometimes. EJCMI Nancy 2007 – p. 61/67 Using advanced verification techniques • Searching for better data-structures (SOS, *DD) • Abstraction and refinement • Combining model-checking and theorem proving • Acceleration • Bounded model-checking EJCMI Nancy 2007 – p. 62/67 Beyond verification Generic verification algorithms + hybrid data structures allow: • Model-checking • Controller synthesis • Phase portrait generation EJCMI Nancy 2007 – p. 63/67