Direct data-driven model-reference control with Lyapunov stability guarantees

Breschi, Valentina; Persis, Claudio De; Formentin, Simone; Tesi, Pietro

doi:10.1109/cdc45484.2021.9683437

Cited by 18 publications

(11 citation statements)

References 31 publications

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“…, M , where Gi , bi , c d,i and Si indicate the rows of G, b, c d and S associated with the i-th set of active constraint, and GW,i is constructed accordingly. Lastly, by selecting the first element of this sequence, it can easily be shown that the control action to be applied is indeed piecewise affine and that it has the structure in (9), thus concluding the proof.…”

Section: The Rows Of G = Gmentioning

confidence: 69%

“…Then, problem (30) is explicitly solved by a piecewise affine law defined as in (9), with χ substituting χ.…”

Section: Handling Changing Set Points In R-eddpcmentioning

confidence: 99%

“…More recently, the regained popularity of results from behavioral theory [41] have lead to the introduction of alternative data-based control schemes that rely on a trajectory-based description of the system dynamics. These range from passivity-based [4,28,31,[35][36][37] and model reference [9] controllers, to optimal [16,17,19] and predictive [5,6,8,14,15,18,33] ones, with the latter built to tackle constraints.…”

Section: Introductionmentioning

confidence: 99%

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On the design of regularized explicit predictive controllers from input-output data

Breschi¹,

Sassella²,

Formentin³

2021

Preprint

Self Cite

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On the wave of recent advances in data-driven predictive control, we present an explicit predictive controller that can be constructed from a batch of input/output data only. The proposed explicit law is build upon a regularized implicit data-driven predictive control problem, so as to guarantee the uniqueness of the explicit predictive controller. As a side benefit, the use of regularization is shown to improve the capability of the explicit law in coping with noise on the data. The effectiveness of the retrieved explicit law and the repercussions of regularization on noise handling are analyzed on two benchmark simulation case studies, showing the potential of the proposed regularized explicit controller.

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Section: The Rows Of G = Gmentioning

confidence: 69%

“…Then, problem (30) is explicitly solved by a piecewise affine law defined as in (9), with χ substituting χ.…”

Section: Handling Changing Set Points In R-eddpcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the design of regularized explicit predictive controllers from input-output data

Breschi¹,

Sassella²,

Formentin³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hence, some studies addressing the stability or stabilization criteria from a data-driven point of view, have been published. In particular several problems related to the design of state/output feedback controllers for linear systems have been revisited [5], [6], [18], [19]. In these works considering the case of exact data experiments for linear time-invariant systems, i.e.…”

Section: Introductionmentioning

confidence: 99%

Robust data-driven control design for linear systems subject to input saturations

Seuret¹,

Tarbouriech²

2023

Preprint

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This paper deals with the problem of providing a data-driven solution to the local stabilization of linear systems subject to input saturation. After presenting a model-based solution to this well-studied problem, a systematic method to transform model-driven into data-driven LMI conditions is presented. This technical solution is demonstrated to be equivalent to the recent advanced results on LMI formulations based on S-procedure or Peterson Lemmas. However, the advantage of the proposed method relies on its simplicity and its potential to be applicable to a wide class of problems of stabilization of (non)linear discrete-time systems. The method is then illustrated on an academic example.

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“…These conditions can be included directly in the algorithm defined for control design. Alternatively, the behavioural framework in [14] has paved the way to the inclusion of data-dependent Linear Matrix Inequalities (LMIs) for closed-loop stability in several data-driven control problems, e.g., direct data-driven linear quadratic regulator design [15], data-enabled predictive control [16], direct data-driven model-reference control [17], dealing also with noisy data [18], [19]. Also, in the field of nonlinear systems, methods for robust control from data have been provided [20], [21].…”

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 model-reference control with Lyapunov stability guarantees

Cited by 18 publications

References 31 publications

On the design of regularized explicit predictive controllers from input-output data

On the design of regularized explicit predictive controllers from input-output data

Robust data-driven control design for linear systems subject to input saturations

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

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