Provably robust verification of dissipativity properties from data

Koch, Anne; Berberich, Julian; Allgöwer, Frank

doi:10.48550/arxiv.2006.05974

Cited by 16 publications

(45 citation statements)

References 30 publications

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“…Whereas, there exist only few comprising approaches for nonlinear systems and several approaches tailored for certain classes of nonlinear systems. For example, [5] generalizes, among others, the results from [4] for nonlinear polynomial systems. For general nonlinear systems, [6] proposes Gaussian process optimization including statistical guarantees.…”

Section: Introductionmentioning

confidence: 64%

“…This kind of system properties, such as dissipativity [2], provides insight into the system and facilitates a controller design by stabilizing control laws without knowledge of the system. [3] and [4] treat data-driven determining dissipativity properties for linear time-invariant (LTI) systems by a trajectorybased non-parametric and a set-membership representation of LTI systems, respectively. Whereas, there exist only few comprising approaches for nonlinear systems and several approaches tailored for certain classes of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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Data-driven system analysis of nonlinear systems using polynomial approximation

Martin¹,

Allgöwer²

2021

Preprint

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In the context of data-driven system analysis of general nonlinear systems, there exist only few approaches which often lack on rigorous guarantees, call for nonconvex optimization, or require the knowledge of the basis functions of the system dynamics. In this paper, we establish a novel data-based non-parametric representation of nonlinear functions based on Taylor series which are derived from finite many noisy samples. By incorporating the measurement noise and the error of polynomial approximation, we provide computationally tractable conditions for sum of squares optimization, e.g., to verify dissipativity properties with rigorous guarantees and without an explicitly identified model.

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Section: Introductionmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Data-driven system analysis of nonlinear systems using polynomial approximation

Martin¹,

Allgöwer²

2021

Preprint

Self Cite

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“…We will specifically build upon ideas used in [19]- [21] and [22]- [25] for data-driven analysis and data-driven controller design, respectively. In these works, data is used to characterize all models that are consistent with the data.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Reachability Analysis from Noisy Data

Alanwar¹,

Koch²,

Allgöwer³

et al. 2021

Preprint

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We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented, and their accuracy is shown to depend on the underlying system generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and under the assumption of Lipschitz continuity to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximative reachable set containing the true reachable set. Multiple numerical examples show the applicability of the introduced algorithms, and accuracy comparisons are made between algorithms.

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“…These features are a priori known for many systems due to their inherent physical nature, e.g., the electrical circuits where the energy is dissipated by the resistors [42]. In addition, they can be verified using recently developed data-driven methods [45]- [49]. Information about these attributes is potentially available for later use as side-information.…”

Section: Introductionmentioning

confidence: 99%

Kernel-Based Identification with Frequency Domain Side-Information

Khosravi¹,

Smith²

2021

Preprint

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This paper discusses the problem of system identification when frequency domain side-information is available. Initially, we consider the case where the side-information is provided as the H∞-norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification approach for estimating the impulse response of the system under the given side-information. The estimation problem is formulated as a constrained optimization in a stable reproducing kernel Hilbert space, where suitable constraints are considered for incorporating the desired frequency domain features. The resulting optimization has an infinite-dimensional feasible set with an infinite number of constraints. We show that this problem is a well-defined convex program with a unique solution. We propose a heuristic that tightly approximates this unique solution. The proposed approach is equivalent to solving a finite-dimensional convex quadratically constrained quadratic program. The efficiency of the discussed method is verified by several numerical examples.

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Provably robust verification of dissipativity properties from data

Cited by 16 publications

References 30 publications

Data-driven system analysis of nonlinear systems using polynomial approximation

Data-driven system analysis of nonlinear systems using polynomial approximation

Data-Driven Reachability Analysis from Noisy Data

Kernel-Based Identification with Frequency Domain Side-Information

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