Timed Relational Abstractions for Sampled Data Control Systems

Computer Aided Verification

2012

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Abstract. In this paper, we present the HybridSAL relational abstracter -a tool for verifying continuous and hybrid dynamical systems. The input to the tool is a model of a hybrid dynamical system and a safety property. The output of the tool is a discrete state transition system and a safety property. The correctness guarantee provided by the tool is that if the output property holds for the output discrete system, then the input property holds for the input hybrid system. The input is in HybridSal input language and the output is in SAL syntax. The SAL model can be verified using the SAL tool suite. This paper describes the HybridSAL relational abstracter -the algorithms it implements, its input, its strength and weaknesses, and its use for verification using the SAL infinite bounded model checker and k-induction prover.

Section: Discussion: Strengths and Weaknessesmentioning

confidence: 99%

“…Next, consider the quadratic relations added to φ in Step (11). Let p 1 , p 2 be as defined in Step (10).…”

Section: A Supplementary Materialsmentioning

confidence: 99%

HybridSAL Relational Abstracter

Computer Aided Verification

2012

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“…There exists several ways to compute relational abstractions. However, the current techniques used to compute a relational abstraction [28,33,35] are not suitable to verify real-time properties or to analyze a network of hybrid systems.…”

Section: Related Workmentioning

confidence: 99%

“…The timed relational abstraction [35] is suitable to analyze control systems that sample the physical plant at fixed time intervals. In that case, the relation is precise over time since it relates the current values with the future values of the variables after a continuous transition of fixed duration (the sampling interval).…”

Section: Related Workmentioning

confidence: 99%

Time-aware relational abstractions for hybrid systems

Mover

Cimatti

2013 Proceedings of the International Conference on Embedded Software (EMSOFT)

et al. 2013

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Hybrid Systems model both discrete switches and continuous dynamics and are suitable to represent embedded systems where discrete controllers interact with a physical plant.Relational abstraction is a new approach for verifying hybrid systems. In relational abstraction, the continuous dynamics in each location of the hybrid system is abstracted by a binary relation that relates the current value of the continuous variables with all future values of the variables that are reachable after a time elapse (continuous) transition. The abstract system is an infinite-state system, which can be verified using k-induction or abstract interpretation.Existing techniques for computing relational abstractions are time-agnostic: they do not construct any relationship between the state variables and the time elapsed during the continuous evolution. Time-agnostic abstractions cannot verify timing properties.We present a technique to compute a time-aware relational abstraction for verifying (timing-related) safety properties of cyber-physical systems. We show the effectiveness of the new abstraction on several case studies on which the previous techniques fail.

“…This relation has been called timed relational abstraction before [5,6]. The relation ψtra is computed as a conjunction of equality constraints.…”

Section: Checking If Abstract Counterexample Is Spuriousmentioning

confidence: 99%

Safety verification for linear systems

Duggirala

2013 Proceedings of the International Conference on Embedded Software (EMSOFT)

2013

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An embedded software controller is safe if the composition of the controller and the plant does not reach any unsafe state starting from legal initial states (in an unbounded time horizon). Linear systems -specified using linear ordinary differential or difference equations -form an important class of models for such control systems. We present a new decidability result for safety verification of linear systems. Our decidability result assumes that the set of initial states and the set of unsafe states satisfy some conditions. When the set of initial and unsafe states do not satisfy these conditions, they can be overapproximated by sets that do satisfy the conditions. We thus get a counterexample guided abstraction refinement (CEGAR) procedure for the unconstrained safety verification of linear systems. Our new procedure performs abstraction-refinement on the initial and unsafe region, and not on the system itself. We present the new procedure and describe experimental results that demonstrate its effectiveness.