Case Studies in Data-Driven Verification of Dynamical Systems

Kozarev, Alexandar; Quindlen, John F.; How, Jonathan P.; Topcu, Ufuk

doi:10.1145/2883817.2883846

Cited by 28 publications

(30 citation statements)

References 14 publications

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“…In recent years, an increasing number of researchers started addressing various verification and design problems in control of black-box systems [3,2,12,11,15]. In particular, the initial idea behind this paper was influenced by the recent efforts in [2,25,14], and [5] on using simulation traces to find Lyapunov functions for systems with known dynamics.…”

Section: Introductionmentioning

confidence: 99%

Data driven stability analysis of black-box switched linear systems

et al. 2019

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Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius.

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Section: Introductionmentioning

confidence: 99%

Data driven stability analysis of black-box switched linear systems

et al. 2019

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“…The major difference between (2) and the deterministic systems found in earlier problems [8]- [10] is the addition of stochastic noise w(t) in the dynamics. This noise term encapsulates any source of randomness, such as process and/or measurement noise and ultimately breaks the previous works' fundamental assumption of deterministic (noise-free) dynamics.…”

Section: Assumptionmentioning

confidence: 99%

Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties

Quindlen

Topcu

Chowdhary

et al. 2018

2018 Annual American Control Conference (ACC)

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This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulationbased verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the proposed framework constructs a GP regression model and predicts the system's performance over the entire set of possible uncertainties. Included in the framework is a new metric to estimate the confidence in those predictions based on the variance of the GP's cumulative distribution function. This variance-based metric forms the basis of active sampling algorithms that aim to minimize prediction error through careful selection of simulations. In three case studies, the new active sampling algorithms demonstrate up to a 35% improvement in prediction error over other approaches and are able to correctly identify regions with low prediction confidence through the variance metric.

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“…The approach to generalize or learn system behavior from simulations has been used before for computing Lyapunov functions [21,20] and for computing the region of attraction [23]. Simulations can also be used to directly verify system behavior [13,9,8,10].…”

Section: Related Workmentioning

confidence: 99%

Simulation Based Computation of Certificates for Safety of Dynamical Systems

Ratschan¹

2017

Lecture Notes in Computer Science

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In this paper, we present an algorithm for synthesizing certificatesso-called barrier certificates-for safety of hybrid dynamical systems. Unlike the usual approach of using constraint solvers to compute the certificate from the system dynamics, we synthesize the certificate from system simulations. This makes the algorithm applicable even in cases where the dynamics is either not explicitly available, or too complicated to be analyzed by constraint solvers, for example, due to the presence of transcendental function symbols.The algorithm itself allows the usage of heuristic techniques in which case it does not formally guarantee correctness of the result. However, in cases that do allow rigorous constraint solving, the computed barrier certificate can be rigorously verified, if desired. Hence, in such cases, our algorithm reduces the problem of finding a barrier certificate to the problem of formally verifying a given barrier certificate. Problem DescriptionDefinition 1 A (hybrid systems) safety verification problem is a tuple (M, Ω, D, f, Inv, ρ, I, U ) where • M is a finite set (the modes of the safety verification problem),• Ω ⊆ M × R n (the state space of the safety verification problem),• D ⊆ R l where l ∈ N 0 (the set of disturbance inputs of the safety verification problem),

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Case Studies in Data-Driven Verification of Dynamical Systems

Cited by 28 publications

References 14 publications

Data driven stability analysis of black-box switched linear systems

Data driven stability analysis of black-box switched linear systems

Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties

Simulation Based Computation of Certificates for Safety of Dynamical Systems

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