On data-driven stabilization of systems with nonlinearities satisfying quadratic constraints

Luppi, Alessandro; Persis, Claudio De; Tesi, Pietro

doi:10.1016/j.sysconle.2022.105206

Cited by 24 publications

(9 citation statements)

References 27 publications

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“…Of course, when changing the model class one needs to balance the benefits of more general model classes and the tractability of the resulting robust control problems. Some classes of systems have shown a favorable trade-off in this regard, such as bilinear systems [44], [49], polynomial systems [45], [48], rational systems [46] and systems with quadratic or sector bounded nonlinearities [47], [70]. As was shown in the aforementioned works, a thorough understanding of the linear case often remains invaluable for the proposal of nonlinear extensions.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Data Informativity: A New Perspective on Data-Driven Analysis and Control

Waarde

Eising

Trentelman

et al. 2020

IEEE Trans. Automat. Contr.

334

354

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The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Data Informativity: A New Perspective on Data-Driven Analysis and Control

Waarde

Eising

Trentelman

et al. 2020

IEEE Trans. Automat. Contr.

334

354

View full text Add to dashboard Cite

show abstract

“…To avoid this conflict, the concept of contractive sets [27] can be leveraged for linear systems with convex safe sets to unify the safe and stable control design. This idea is leveraged in previous studies [28][29][30] to directly design data-driven safe controllers for linear time-invariant systems. The data-based safe control design is also considered in Ahmadi et al [31] using only measured data collected from open-loop system trajectories.…”

Section: Introductionmentioning

confidence: 99%

Data‐driven safe gain‐scheduling control

Modares

Sadati

Modares

2023

Asian Journal of Control

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Data‐based safe gain‐scheduling controllers are presented for discrete‐time linear parameter‐varying systems (LPV) with polytopic models. First, ‐contractivity conditions are provided under which the safety and stability of the LPV systems are unified through Minkowski functions of the safe sets. Then, a data‐based representation of the closed‐loop LPV system is provided, which requires less restrictive data richness conditions than identifying the system dynamics. This sample‐efficient closed‐loop data‐based representation is leveraged to design data‐driven gain‐scheduling controllers that guarantee ‐contractivity and, thus, invariance of the safe sets. It is also shown that the problem of designing a data‐driven gain‐scheduling controller for a polyhedral (ellipsoidal) safe set amounts to a linear program (a semi‐definite program). The motivation behind direct learning of a safe controller is that identifying an LPV system requires satisfying the persistence of the excitation (PE) condition. It is shown in this paper, however, that directly learning a safe controller and bypassing the system identification can be achieved without satisfying the PE condition. This data‐richness reduction is of vital importance, especially for LPV systems that are open‐loop unstable, and collecting rich samples to satisfy the PE condition can jeopardize their safety. A simulation example is provided to show the effectiveness of the presented approach.

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“…By integrating noisy data and side information, [13] showed that unknown polynomial dynamics can be learnt via semidefinite programming. When the nonlinearities satisfy quadratic constraints, data-driven stabilizer was developed in [14]. With certain knowledge and assumptions on the nonlinear basis function, systems containing more general types of nonlinearities have also been studied in recent works.…”

Section: Introductionmentioning

confidence: 99%