Validated Simulation-Based Verification of Delayed Differential Dynamics

Chen, Mingshuai; Fränzle, Martin; Li, Yangjia; Mosaad, Peter Nazier; Zhan, Naijun

doi:10.1007/978-3-319-48989-6_9

Cited by 12 publications

(28 citation statements)

References 22 publications

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“…The work in [18] presents a technique for simulation-based time-bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections by computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. A similar simulation method integrating error analysis of the numeric solving and the sensitivity-related state bloating algorithms was proposed in [6] to obtain safe enclosures of time-bounded reach sets for systems modelled by DDEs.…”

Section: Related Workmentioning

confidence: 99%

“…We initialize the system variable x and the Taylor coefficients in INIT part according to the given initial condition(s) in our example. Then, in the TRANS part, we state the interval Taylor form of degree 2, i.e., f n (t) corresponds to the solution x of DDE (5), as shown in line 22, and the relation between Taylor coefficients in the current (unprimed variables) and the next segment (primed variables) according to the generated operator (6), where the segments are of duration 1 each. a2 ' = -0.5* a1 -xi * a2 ; 20 21 --x ( t ) is given by a Taylor form of degree 2 22…”

Section: Model Checking Delay Differential Equationsmentioning

confidence: 99%

“…where f n is the underlying Taylor form and A n,0 to A n,k are the intervals Taylor coefficients stemming from the n-th iteration of the operator (6). As this Taylor form provides an over-approximation of the solution x over time frame [nδ, (n + 1)δ], the condition (7) implies ∀t ∈ [nδ, (n + 1)δ] : x(t) ∈ Safe.…”

Section: Proving Continuous-time Properties On the Time Discretizationmentioning

confidence: 99%

“…It requires polynomial constraint solving due to the Taylor forms, i.e., polynomial expressions involved in the statement f n (t) ∈ Safe. Different proof schemes can be implemented using such a solver: using kinduction [39] or interpolation-based unbounded proof schemes [29], absence of any time point in the sequence of valuations generated by operator (6) satisfying ∃n ∈ N, ∃t ∈ [0, 1], ∃ξ ∈ [0, 1], ∃a 0 ∈ A n,0 , . .…”

Section: Proving Continuous-time Properties On the Time Discretizationmentioning

confidence: 99%

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Model Checking Delay Differential Equations Against Metric Interval Temporal Logic

Mosaad¹,

Fränzle²,

Xue³

2017

SACS

Self Cite

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Delay differential equations (DDEs) play an important role in the modeling of dynamic processes. Delays arise in contemporary control schemes like networked distributed control and can cause deterioration of control performance, invalidating both stability and safety properties. This induces an interest in DDE especially in the area of modeling and verification of embedded control. In this article, we present an approach aiming at automatic safety verification of a simple class of DDEs against requirements expressed in a linear-time temporal logic. As requirements specification language, we exploit metric interval temporal logic (MITL) with a continuous-time semantics evaluating signals over metric spaces. We employ an over-approximation method based on interval Taylor series to enclose the solution of the DDE and thereby reduce the continuous-time verification problem for MITL formulae to a discrete-time problem over sequences of Taylor coefficients. We encode sufficient conditions for satisfaction as SMT formulae over polynomial arithmetic and use the iSAT3 SMT solver in its bounded model-checking mode for discharging the resulting proof obligations, thus proving satisfaction of time-bounded MITL specifications by the trajectories induced by a DDE. In contrast to our preliminary work in [44], we can verify arbitrary time-bounded MITL formulae, including nesting of modalities, rather than just invariance properties.

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Section: Related Workmentioning

confidence: 99%

Section: Model Checking Delay Differential Equationsmentioning

confidence: 99%

Section: Proving Continuous-time Properties On the Time Discretizationmentioning

confidence: 99%

Section: Proving Continuous-time Properties On the Time Discretizationmentioning

confidence: 99%

See 2 more Smart Citations

Model Checking Delay Differential Equations Against Metric Interval Temporal Logic

Mosaad¹,

Fränzle²,

Xue³

2017

SACS

Self Cite

View full text Add to dashboard Cite

show abstract

“…Huang et al presents a technique for simulation based time-bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections by computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system [18]. A similar simulation method integrating error analysis of the numeric solving and the sensitivity-related state bloating algorithms was proposed in [11] to obtain safe enclosures of time-bounded reach sets for systems modelled by DDEs.…”

Section: Introductionmentioning

confidence: 99%

Synthesizing SystemC Code from Delay Hybrid CSP

Yan

Wang

et al. 2017

Programming Languages and Systems

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Abstract. Delay is omnipresent in modern control systems, which can prompt oscillations and may cause deterioration of control performance, invalidate both stability and safety properties. This implies that safety or stability certificates obtained on idealized, delay-free models of systems prone to delayed coupling may be erratic, and further the incorrectness of the executable code generated from these models. However, automated methods for system verification and code generation that ought to address models of system dynamics reflecting delays have not been paid enough attention yet in the computer science community. In our previous work, on one hand, we investigated the verification of delay dynamical and hybrid systems; on the other hand, we also addressed how to synthesize SystemC code from a verified hybrid system modelled by Hybrid CSP (HCSP) without delay. In this paper, we give a first attempt to synthesize SystemC code from a verified delay hybrid system modelled by Delay HCSP (dHCSP), which is an extension of HCSP by replacing ordinary differential equations (ODEs) with delay differential equations (DDEs). We implement a tool to support the automatic translation from dHCSP to SystemC.

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Taming Delays in Dynamical Systems

Feng

Chen

Zhan

et al. 2019

Computer Aided Verification

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Delayed coupling between state variables occurs regularly in technical dynamical systems, especially embedded control. As it consequently is omnipresent in safety-critical domains, there is an increasing interest in the safety verification of systems modelled by Delay Differential Equations (DDEs). In this paper, we leverage qualitative guarantees for the existence of an exponentially decreasing estimation on the solutions to DDEs as established in classical stability theory, and present a quantitative method for constructing such delaydependent estimations, thereby facilitating a reduction of the verification problem over an unbounded temporal horizon to a bounded one. Our technique builds on the linearization technique of nonlinear dynamics and spectral analysis of the linearized counterparts. We show experimentally on a set of representative benchmarks from the literature that our technique indeed extends the scope of bounded verification techniques to unbounded verification tasks. Moreover, our technique is easy to implement and can be combined with any automatic tool dedicated to bounded verification of DDEs.

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Validated Simulation-Based Verification of Delayed Differential Dynamics

Cited by 12 publications

References 22 publications

Model Checking Delay Differential Equations Against Metric Interval Temporal Logic

Model Checking Delay Differential Equations Against Metric Interval Temporal Logic

Synthesizing SystemC Code from Delay Hybrid CSP

Taming Delays in Dynamical Systems

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