Computer-assisted proofs for Lyapunov stability via Sums of Squares certificates and Constructive Analysis

Devadze, Grigory; Magron, Victor; Streif, Stefan

doi:10.48550/arxiv.2006.09884

Cited by 1 publication

(2 citation statements)

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“…The authors rely on the framework of the so-called Lyapunov invariants and employ the convex optimization for their construction. Recently, Devadze et al used computerassisted proofs and program extraction techniques for the formalization of initial value problem for ODE and sum-ofsquares certificates for stability of polynomial systems [8], [9]. An alternative direction of algorithmic verification is FLUCTUAT, which allows to propagate the errors of function on variables with an uncertainty margin using statistical analysis.…”

Section: Related Workmentioning

confidence: 99%

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Formal verification of a controller implementation in fixed-point arithmetic

Flessing¹,

Devadze²,

Streif³

2021

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For the implementations of controllers on digital processors, certain limitations, e.g. in the instruction set and register length, need to be taken into account, especially for safety-critical applications. This work aims to provide a computer-certified inductive definition for the control functions that are implemented on such processors accompanied with the fixed-point data type in a proof assistant. Using these inductive definitions we formally ensure correct realization of the controllers on a digital processor. Our results guarantee overflowfree computations of the implemented control algorithm. The method presented in this paper currently supports functions that are defined as polynomials within an arbitrary fixed-point structure. We demonstrate the verification process in the case study on an example with different scenarios of fixed-point type implementations.

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Section: Related Workmentioning

confidence: 99%

“…−10s 2 −10.3s−5 and a multiplicative uncertainty that can be compensated with the weighting function W 2 (s) = −3. To obtain a robust controller with respect to these uncertainties, we use the H ∞ synthesis [11] that results in the following transfer function: 9 .…”

Section: B Examplementioning

confidence: 99%