AVERIST: An Algorithmic VERifier for STability AVERIST ARCHITECTURE - - PowerPoint PPT Presentation

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AVERIST: An Algorithmic VERifier for STability AVERIST ARCHITECTURE - - PowerPoint PPT Presentation

Feb 28, 2023 228 likes •449 views

AVERIST: An Algorithmic VERifier for STability AVERIST ARCHITECTURE AVERIST architecture Linear PSS expressions AVERIST State-space partition Weighted ABSTRACTION MODEL-CHECKING Graph analysis graph Graph construction Counterexample

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AVERIST: An Algorithmic VERifier for STability

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AVERIST ARCHITECTURE

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AVERIST architecture

AVERIST

ABSTRACTION State-space partition Graph construction MODEL-CHECKING Graph analysis Weighted graph PSS Linear expressions Stable Counterexample

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Model-checking

1 1 1 2 2 3 1 1 2 1 1 1 2 2 1 2 1

Abstract counterexample H stable

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Interactive dialog

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ANALYSIS RESULTS

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Stable PSS

x y quad1 quad2 quad3 quad4

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Stable PSS

Linear expressions Polyhedral switched system x=0, y=0 STABILITY ANSWER = Stable

AVERIST

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Unstable PSS - Blow-up

x y quad1 quad2 quad3 quad4

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Unstable PSS

Linear expressions Polyhedral switched system x=0, y=0 STABILITY ANSWER = Unstable (blow-up)

AVERIST

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Unstable PSS - Counterexample

x y quad1 quad2 quad3 quad4

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Unstable PSS - Counterexample

AVERIST

Linear expressions Polyhedral switched system x=0, y=0 [('quad2', 'Constraint_System {x1==0, -x0>0}’), ('quad3', 'Constraint_System {x0==0, -x1>0}’), ('quad1', 'Constraint_System {x1==0, x0>0}’), ('quad1', 'Constraint_System {x0==0, x1>0}’), ('quad2', 'Constraint_System {x1==0, -x0>0}')] STABILITY ANSWER = Abstract counterexample

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DEPENDENCIES

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Parma Polyhedra Library - PPL

x y

x − y = 0 P x = Variable(0)

1

y = Variable(1)

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P = NNC Polyhedron(2,’universe’)

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P.add constraint(y>0)

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P.add constraint(x-y>0)

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Parma Polyhedra Library - PPL

x y

x − y = 0 P x = Variable(0) y = Variable(1) P = NNC Polyhedron(2,’universe’) P.add constraint(x>0) P.add constraint(x-y>0)

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GNU Linear Programming Kit - GLPK

x y

x − y = 0 P

2 1

sage: P.maximize(1*x) {'bounded': True, 'generator': point(2/1, 1/1), 'maximum': True, 'sup_d': 1, 'sup_n': 2} sage: P.maximize(1*y) {'bounded': True, 'generator': closure_point(2/1, 2/1), 'maximum': False, 'sup_d': 1, 'sup_n': 2}

  • 'sup_n': Integer. The numerator of the supremum value.
  • 'sup_d': Non-zero integer. The denominator of the supremum value.
  • 'maximum': Boolean. True if and only if the supremum is also the maximum value.
  • 'generator': a Generator. A point or closure point where expr reaches its supremum value.
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SLIDE 17

NetworkX

import networkx as nx G=nx.DiGraph() G.add nodes from([1,2,3,4]) G.add weighted edges from([(1,2,1), (2,3,1),(3,4,1),(4,1,1),(2,1,1.2)]) negative cycle = greater than one edge cycle(G)

greater_than_one_edge_cycle() uses a modified Bellman-Ford algorithm in order to consider the product of weights instead the sum of them.

1 2 3 4

1.2 1 1 1 1

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HYBRIDIZATION SLIDES

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Hybridization

  • Hybrid system with linear dynamics is transformed into a hybrid system

with polyhedral dynamics.

  • Lyapunov (asymptotic) stability is preserved.
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Hybridization

  • Hybrid system with linear dynamics is transformed into a hybrid system

with polyhedral dynamics.

  • Lyapunov (asymptotic) stability is preserved.
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SLIDE 21

Hybridization

  • Hybrid system with linear dynamics is transformed into a hybrid system

with polyhedral dynamics.

  • Lyapunov (asymptotic) stability is preserved.