Simulation-guided lyapunov analysis for hybrid dynamical systems

The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are "close" to each other. In the semi-formal approach to conformance testing, the two systems are simulated on a large set of tests, and a metric, defined on pairs of real-valued, real-timed trajectories, is used to determine a lower bound on the distance. We show how the Skorokhod metric on continuous dynamical systems can be used as the foundation for conformance testing of complex dynamical models. The Skorokhod metric allows for both state value mismatches and timing distortions, and is thus well suited for checking conformance between idealized models of dynamical systems and their implementations. We demonstrate the robustness of the metric by proving a transference theorem: trajectories close under the Skorokhod metric satisfy "close" logical properties in the timed linear time logic FLTL (Freeze LTL) containing a rich class of temporal and spatial constraint predicates involving time and value freeze variables. We provide efficient window-based streaming algorithms to compute the Skorokhod metric for both piecewise affine and piecewise constant traces, and use these as a basis for a conformance testing tool for Simulink. We experimentally demonstrate the effectiveness of our tool in finding discrepant behaviors on a set of control system benchmarks, including an industrial challenge problem.

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“…We check conformance with respect to the system output λ. For the dynamical system equations, please refer to [23,24].…”

Section: Skorokhod Distance Between Systems: Case Studiesmentioning

confidence: 99%

“…In [24], the authors present a version of this system We scale the signals such that 0.5 s of time-jitter is treated equivalent to 10% of the steady-state value (14.7) of the A/F ratio signal. The simulation traces correspond to a time horizon of 10 s and the window size is 300…”

Section: Skorokhod Distance Between Systems: Case Studiesmentioning

confidence: 99%

Quantifying conformance using the Skorokhod metric

Deshmukh¹,

Majumdar

Prabhu

2017

Form Methods Syst Des

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“…Therefore, stability of complex industrial designs are often "verified" by extensive simulations. Recent work by Kapinski et al argues that Lyapunov functions can be of practical values for automotive designs, provided they can be discovered easily, and certified using formal verification tools [32]. We hope that the use of linear relaxations can provide us with more approaches to synthesize Lyapunov functions that can serve as certificates for stability.…”

Section: Resultsmentioning

confidence: 97%

Linear relaxations of polynomial positivity for polynomial Lyapunov function synthesis

Sassi

Sankaranarayanan

Chen

et al. 2015

IMA J Math Control Info

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We examine linear programming (LP) based relaxations for synthesizing polynomial Lyapunov functions to prove the stability of polynomial ODEs. Our approach starts from a desired parametric polynomial form of the polynomial Lyapunov function. Subsequently, we encode the positive-definiteness of the function, and the negation of its derivative, over the domain of interest. We first compare two classes of relaxations for encoding polynomial positivity: relaxations by sum-of-squares (SOS) programs, against relaxations based on Handelman representations and Bernstein polynomials, that produce linear programs. Next, we present a series of increasingly powerful LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials. Subsequently, we show how these LP relaxations can be used to search for Lyapunov functions for polynomial ODEs by formulating LP instances. We compare our techniques with approaches based on SOS on a suite of automatically synthesized benchmarks. Posi-

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“…The ideas presented can be considered as a starting point for a methodology to verify analog designs, yet important extensions should be studied more, like avoiding informal linearization, in addition to tackling more complex verification issues especially related to AC analysis. Similar but more elaborate research was done in [18]. The author proposed an approach for specifying and reasoning about implementations of digital systems that are described at the analog level of abstraction.…”

Section: Related Work Of Proof Based and Symbolic Methodsmentioning

confidence: 99%

Research Trends in Formal Verification Process for Analog and Mixed Signal Design

S¹,

Manjunath²

2015

IJCA

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Formal verification is one of the crucial stages of design phase that ensure the preciseness of the circuit design and its corresponding behavior with respect to specific system design. From last decade, there has been an abundant formal verification techniques introduced by the research community for analog and mixed signal circuits that used as an interface between analog and digital components. Owing to the maximized sophistication, and shrinking sizes of chip, analog, and mixed signal verification is encountering challenges in increasing verification requirement that calls for analyzing the prior techniques. The prime purpose of this paper is to discuss the most standard models, and techniques introduced till date and to excavate the various facts about their effectiveness in the area circuit design principles. The paper also discusses some of the critical research gaps explored from the study.

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Simulation-guided lyapunov analysis for hybrid dynamical systems

Cited by 109 publications

References 21 publications

Quantifying conformance using the Skorokhod metric

Quantifying conformance using the Skorokhod metric

Linear relaxations of polynomial positivity for polynomial Lyapunov function synthesis

Research Trends in Formal Verification Process for Analog and Mixed Signal Design

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