A set-membership approach to direct data-driven control design for SISO non-minimum phase plants

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

doi:10.1109/cdc.2017.8263833

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Using the definition of 2-norm of a discrete-time linear transfer function, it is possible to write (36) as…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…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%

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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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“…Using the definition of 2-norm of a discrete-time linear transfer function, it is possible to write (36) as…”

Section: Proof Of Theoremmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…The problem is formulated in terms of set-membership (SM) error-in-variables (EIV) identification in the presence of bounded noise. The approach is extended to the case of non-minimum phase (NMP) plants in [24], where the authors propose an algorithm which guarantees internal stability of the closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

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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Virtual reference feedback tuning for linear discrete-time systems with robust stability guarantees based on set membership

D'Amico

Farina

2023

Automatica

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A set-membership approach to direct data-driven control design for SISO non-minimum phase plants

Cited by 6 publications

References 14 publications

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

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

Adaptive Data-Driven Control for Linear Time Varying Systems

Virtual reference feedback tuning for linear discrete-time systems with robust stability guarantees based on set membership

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