A Sound and Complete Proof Rule for Region Stability of Hybrid Systems

Podelski, Andreas; Wagner, Silke

doi:10.1007/978-3-540-71493-4_76

Cited by 21 publications

(21 citation statements)

References 13 publications

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“…Sound and complete proof rules for establishing region stability have been explored and automated [47], as have more efficient encodings of the proof rule that scale better in dimensionality [31]. However, all algorithms we are aware of for checking region stability require linear or simpler (timed or rectangular) ODEs [45,47,46,31,11,48]. Strong attractors are basins of attraction where every state in the state space eventually reaches a region of the state space [45].…”

Section: Related Workmentioning

confidence: 99%

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Sogokon

Jackson

Johnson

2017

Lecture Notes in Computer Science

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We propose a method for verifying persistence of nonlinear hybrid systems. Given some system and an initial set of states, the method can guarantee that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flow-pipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study concerning showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flow-pipes or just reasoning about invariants alone can be insufficient. The case study also nicely shows the richness of systems that the method can handle: the case study features a mode with non-polynomial (nonlinear) ODEs and we manage to prove the persistence property with the aid of an automatic prover specifically designed for handling transcendental functions.

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Section: Related Workmentioning

confidence: 99%

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Sogokon

Jackson

Johnson

2017

Lecture Notes in Computer Science

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“…Instead, they are generated as a finite representation of an infinite path in a control flow graph. For example, in (potentially spurious) counterexamples in termination analysis [9,13,17,18,21,22], non-termination analysis [12], stability analysis [8,23], or cost analysis [1,11].…”

Section: Introductionmentioning

confidence: 99%

Ranking Templates for Linear Loops

Leike

Heizmann

2014

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's Transposition Theorem instead of Farkas Lemma to transform the generated ∃∀-constraint into an ∃-constraint.

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“…To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. used to establish temporal properties of systems such as safety, stability, termination, progress and so on [12,3,18,15]. The invariant generation problem consists of automatically computing useful invariants given the description of a dynamical system.…”

Section: Introductionmentioning

confidence: 99%

Automatic invariant generation for hybrid systems using ideal fixed points

Sankaranarayanan

2010

Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

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We present computational techniques for automatically generating algebraic (polynomial equality) invariants for algebraic hybrid systems. Such systems involve ordinary differential equations with multivariate polynomial right-hand sides. Our approach casts the problem of generating invariants for differential equations as the greatest fixed point of a monotone operator over the lattice of ideals in a polynomial ring. We provide an algorithm to compute this monotone operator using basic ideas from commutative algebraic geometry. However, the resulting iteration sequence does not always converge to a fixed point, since the lattice of ideals over a polynomial ring does not satisfy the descending chain condition.We then present a bounded-degree relaxation based on the concept of "pseudo ideals", due to Colón, that restricts ideal membership using multipliers with bounded degrees. We show that the monotone operator on bounded degree pseudo ideals is convergent and generates fixed points that can be used to generate useful algebraic invariants for non-linear systems. The technique for continuous systems is then extended to consider hybrid systems with multiple modes and discrete transitions between modes.We have implemented the exact, non-convergent iteration over ideals in combination with the bounded degree iteration over pseudo ideals to guarantee convergence. This has been applied to automatically infer useful and interesting polynomial invariants for some benchmark non-linear systems.

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A Sound and Complete Proof Rule for Region Stability of Hybrid Systems

Cited by 21 publications

References 13 publications

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants

Ranking Templates for Linear Loops

Automatic invariant generation for hybrid systems using ideal fixed points

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