AVERIST Algorithmic Verifier for Stability of Linear Hybrid Systems - PowerPoint PPT Presentation

AVERIST Algorithmic Verifier for Stability of Linear Hybrid Systems Miriam García Soto and Pavithra Prabhakar HSCC, April 2018

AVERIST ✤ Formal stability verification of hybrid systems ✤ Classes considered: ✤ polyhedral hybrid systems ( PHS ) ✤ linear hybrid systems ( LHS ) ✤ Techniques implemented: ✤ Counterexample Guided Abstraction Refinement ( CEGAR ) for state-space reduction ✤ Hybridization for dynamics simplification

<latexit sha1_base64="kPkwc1xN7+45lGzyKO1kene/4=">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</latexit> <latexit sha1_base64="kPkwc1xN7+45lGzyKO1kene/4=">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</latexit> <latexit sha1_base64="kPkwc1xN7+45lGzyKO1kene/4=">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</latexit> <latexit sha1_base64="kPkwc1xN7+45lGzyKO1kene/4=">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</latexit> Input & Stability property ✤ A system is Lyapunov stable with respect to the var: x,y; location: quad1, quad2, quad3, quad4; equilibrium point 0 if for every ε > 0 there loc: quad1; exists δ > 0 such that for every execution σ inv: x>=0 AND y>=0; dyn: dx==y AND dy==-4*x; starting from B δ (0) , σ (t) ∈ B ε (0), for all time t. guards: when y==0 goto quad4; loc: quad2; inv: x<=0 AND y>=0; dyn: dx==10*y AND dy==-x; guards: when x==0 goto quad1; loc: quad3; inv: x<=0 AND y<=0; dyn: dx==y AND dy==-4*x; guards: when y==0 goto quad2; loc: quad4; inv: x>=0 AND y<=0; dyn: dx==10*y AND dy==-x; guards: when x==0 goto quad3;

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