Region Stability Proofs for Hybrid Systems

Podelski, Andreas; Wagner, Silke

doi:10.1007/978-3-540-75454-1_23

Cited by 28 publications

(18 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…In addition to probabilistic state reachability being investigated in the previous section, we now address the problem of probabilistic region stability. For that purpose, we take into account the notion of region stability as introduced for non-probabilistic hybrid systems by Podelski and Wagner in [PW07a,PW07b]. According to their definition, given some set R of states called region, a (non-probabilistic) system is called stable with respect to region R iff for every infinite run s 0 , s 1 , .…”

Section: 2mentioning

confidence: 99%

“…The latter problem is motivated by the notion of region stability for nonprobabilistic hybrid systems [PW07a,PW07b], where a system is called stable with respect to some region R iff all system runs eventually reach R and finally stay in R forever. In this article, we suggest an adaptation of region stability to the probabilistic case along with a symbolic, interpolation-based procedure for the verification of probabilistic stability properties like "the probability that the system stabilizes within region R is at least 99.9%".…”

Section: Introductionmentioning

confidence: 99%

Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability

Teige¹,

Fränzle²

2012

Logical Methods in Computer Science

View full text Add to dashboard Cite

Abstract. The stochastic Boolean satisfiability (SSAT) problem has been introduced by Papadimitriou in 1985 when adding a probabilistic model of uncertainty to propositional satisfiability through randomized quantification. SSAT has many applications, among them probabilistic bounded model checking (PBMC) of symbolically represented Markov decision processes. This article identifies a notion of Craig interpolant for the SSAT framework and develops an algorithm for computing such interpolants based on a resolution calculus for SSAT.As a potential application area of this novel concept of Craig interpolation, we address the symbolic analysis of probabilistic systems. We first investigate the use of interpolation in probabilistic state reachability analysis, turning the falsification procedure employing PBMC into a verification technique for probabilistic safety properties. We furthermore propose an interpolation-based approach to probabilistic region stability, being able to verify that the probability of stabilizing within some region is sufficiently large.

show abstract

“…Note that this proof is related to the idea of region stability [15] and can be thought of as a stabilization proof for an unknown (and maybe hard to characterize) sub-region A inv ⊆ A into which all trajectories from A stabilize, and which is an invariant region for the system. Table 2 summarizes runtimes for this proof using iSAT and the different enclosure methods.…”

mentioning

confidence: 99%

Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods

Eggers

Ramdani

Nedialkov

et al. 2011

Software Engineering and Formal Methods

View full text Add to dashboard Cite

Abstract. Aiming at automatic verification and analysis techniques for hybrid systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art enclosure method for ODEs, and with bracketing systems which exploit monotonicity properties to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply our method to the analysis of a non-linear hybrid system by solving predicative encodings of an inductive stability argument and evaluate the impact of different methods and their combination.

show abstract

Region Stability Proofs for Hybrid Systems

Cited by 28 publications

References 24 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

Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability

Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods

Contact Info

Product

Resources

About