Direct data-driven control design through set-membership errors-in-variables identification techniques

Cerone, V.; Regruto, D.; Abuabiah, Mohammad

doi:10.23919/acc.2017.7962984

Cited by 20 publications

(26 citation statements)

References 13 publications

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“…First let us introduce the time-varying feasible controller set (FCS), which is inspired by the feasible parameter set (FPS) for LTV systems proposed in [26] and the FCS definition for LTI controllers presented in [23]. The time-varying FCS, for the case of LTV systems, is defined as follows.…”

Section: Adaptive Ddc For Ltv Systems In the Set-membership Frameworkmentioning

confidence: 99%

“…where K * (t) is the ideal controller and follows the same definition as in [23]. Now thanks to (29), Equation ( 27) becomes…”

Section: Proofmentioning

confidence: 99%

“…A robust data-driven model predictive control is proposed in [22] for LTI systems. A novel non-iterative DDC scheme for LTI systems is introduced in [23]. The problem is formulated in terms of set-membership (SM) error-in-variables (EIV) identification in the presence of bounded noise.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Data-Driven Control for Linear Time Varying Systems

Abdalla

2021

Machines

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In this paper, we propose an adaptive data-driven control approach for linear time varying systems, affected by bounded measurement noise. The plant to be controlled is assumed to be unknown, and no information in regard to its time varying behaviour is exploited. First, using set-membership identification techniques, we formulate the controller design problem through a model-matching scheme, i.e., designing a controller such that the closed-loop behaviour matches that of a given reference model. The problem is then reformulated as to derive a controller that corresponds to the minimum variation bounding its parameters. Finally, a convex relaxation approach is proposed to solve the formulated controller design problem by means of linear programming. The effectiveness of the proposed scheme is demonstrated by means of two simulation examples.

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Section: Adaptive Ddc For Ltv Systems In the Set-membership Frameworkmentioning

confidence: 99%

“…where K * (t) is the ideal controller and follows the same definition as in [23]. Now thanks to (29), Equation ( 27) becomes…”

Section: Proofmentioning

confidence: 99%

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Adaptive Data-Driven Control for Linear Time Varying Systems

Abdalla

2021

Machines

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“…In this case, the ∆ A and ∆ y are exactly known if the properties of the transmitter are known. Within the automatic control framework, the UBB paradigm is exploited and studied in EIV system identification [40], state estimation [1], model predictive control [3,36], direct data-driven control [13], and factor analysis [14]. In these applications, the error bound can be estimated either from previous information on the model and on the measurement devices or from available training datasets.…”

Section: Problem Statementmentioning

confidence: 99%

Sparse linear regression from perturbed data

Fosson

Cerone

Regruto

2020

Preprint

Self Cite

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The problem of sparse linear regression is relevant in the context of linear system identification from large datasets. When data are collected from real-world experiments, measurements are always affected by perturbations or low-precision representations. However, the problem of sparse linear regression from fully-perturbed data is scarcely studied in the literature, due to its mathematical complexity. In this paper, we show that, by assuming bounded perturbations, this problem can be tackled by solving low-complex 2 and 1 minimization problems. Both theoretical guarantees and numerical results are illustrated in the paper.

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“…On the other hand, with respect to classic VRFT, our method has the merit to provide theoretical stability conditions, by only enforcing linear constraints on the controller gain in the design phase. Note that in [35], [36] a non-iterative direct data-driven control approach which relies on SM errors-in-variables identification techniques is proposed. However, such an approach is inspired by a different direct method, i.e., the correlation based tuning framework.…”

Section: Introductionmentioning

confidence: 99%

Virtual Reference Feedback Tuning for linear discrete-time systems with robust stability guarantees based on Set Membership

D'Amico¹,

Farina²

2022

Preprint

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In this paper we propose a novel methodology that allows to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant reference signals. The approach uses both (i) Virtual Reference Feedback Tuning for enforcing suitable performances and (ii) the Set Membership framework for providing a-priori robust stability guarantees. Indeed, an uncertainty set for the system parameters is obtained through Set Membership identification, where an algorithm based on the scenario approach is proposed to estimate the inflation parameter in a probabilistic way. Based on this set, robust stability conditions are enforced as Linear Matrix Inequality constraints within an optimization problem whose linear cost function relies on Virtual Reference Feedback Tuning. To show the generality and effectiveness of our approach, we apply it to two of the most widely used yet simple control schemes, i.e., where tracking is achieved thanks to (i) a static feedforward action and (ii) an integrator in closed-loop. The proposed method is not fully direct due to the Set Membership identification. However, the uncertainty set is used with the only objective of providing robust stability guarantees for the closed-loop system and it is not directly used for the performances optimization, which instead is totally based on data. The effectiveness of the developed method is demonstrated with reference to two simulation examples. A comparison with other data-driven methods is also carried out.

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Direct data-driven control design through set-membership errors-in-variables identification techniques

Cited by 20 publications

References 13 publications

Adaptive Data-Driven Control for Linear Time Varying Systems

Adaptive Data-Driven Control for Linear Time Varying Systems

Sparse linear regression from perturbed data

Virtual Reference Feedback Tuning for linear discrete-time systems with robust stability guarantees based on Set Membership

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