An Informativity Approach to the Data-Driven Algebraic Regulator Problem

Trentelman, Harry L.; Waarde, Henk J. van; Camlibel, M. Kanat

doi:10.1109/tac.2021.3129457

Cited by 22 publications

(15 citation statements)

References 25 publications

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“…Its associated behavior, denoted by B(P ), is then a finite dimensional linear space. This paper deals with analysis and control design for systems of the form (2), where the polynomial matrices P (ξ) and Q(ξ) are unknown. We do assume that the order L and the dimensions m and p are known.…”

Section: Systems Represented By Ar Modelsmentioning

confidence: 99%

A behavioral approach to data-driven control with noisy input-output data

Waarde¹,

Eising²,

Camlibel³

et al. 2022

Preprint

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This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of inputoutput AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

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Section: Systems Represented By Ar Modelsmentioning

confidence: 99%

A behavioral approach to data-driven control with noisy input-output data

Waarde¹,

Eising²,

Camlibel³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This completes the proof. Remark 2: Note that Lemma 4 considers a version of the output regulation problem with known disturbances, which is slightly different from the results in [26,Theorem 8]. Although the proof of Lemma 4 is similar to that of [26,Theorem 8], we include a proof to make this paper selfcontained.…”

Section: Data-driven Output Synchronization For Multi-agent Systemsmentioning

confidence: 99%

Data-driven output synchronization of heterogeneous leader-follower multi-agent systems

Jiao¹,

Waarde²,

Trentelman³

et al. 2021

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This paper deals with data-driven output synchronization for heterogeneous leader-follower linear multiagent systems. Given a multi-agent system that consists of one autonomous leader and a number of heterogeneous followers with external disturbances, we provide necessary and sufficient data-based conditions for output synchronization. We also provide a design method for obtaining such output synchronizing protocols directly from data. The results are then extended to the special case that the followers are disturbance-free. Finally, a simulation example is provided to illustrate our results.

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“…Remark 2: Note that Lemma 3 considers a version of the output regulation problem with known disturbances, which is slightly different from the results in [29, Theorem 8]. Although the proof of Lemma 3 is similar to that of [29,Theorem 8], we include a proof to make this paper selfcontained.…”

Section: Data-driven Output Synchronization For Multi-agent Systemsmentioning

confidence: 99%