A note on persistency of excitation

By Jan C. Willems, Paolo Rapisarda, Ivan Markovsky, B. De Moor. IEEE Conference on Decision and Control, 2005

1,336 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/87493bc76f0ee65c7c93657619d4e00d0eb685b5

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In Control and Systems Engineering

Citations in the corpus

Overview of total least-squares methods (2007, background): “Moreover the solution is unique whenever A is of full column rank, which can be translated to a persistency of excitation condition on a, see [79].”
From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma (2020, positive): “Wemention,forinstance, virtualreferencefeedbacktuning[31]andmethodsbasedon Willems’fundamentallemma[32](seealso[33]).”
Bridging Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations (2021, background): “Both lines of work come together in a result known as the fundamental lemma [27]; see also the works in [6], [28], and [29] for recent extensions.”
Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness (2019, methodology): “In this section, we revisit the main result in [27] and state a few auxiliary results inspired by subspace identification [2], which will be useful throughout the article.”
Behavioral systems theory in data-driven analysis, signal processing, and control (2021, methodology): “Regarding the indirect approaches, the fundamental lemma in (Willems et al., 2005) has historically been developed as a foundation for subspace system identification methods based on an experiment design perspective.”
Data Informativity: A New Perspective on Data-Driven Analysis and Control (2019, background): “For example, it is shown in [37] that the rank condition (8) can be imposed by injecting an input sequence that is persistently exciting of order n+ 1.”
Data-Driven Dissipativity Analysis: Application of the Matrix S-Lemma (2021, background): “In both these contributions, a crucial assumption is that the input trajectory is persistently exciting of a sufficiently high order (see [20] and [21]).”
Data-Driven Model Predictive Control With Stability and Robustness Guarantees (2019, methodology): “Moreover, the recent contributions [20]–[22] set up an MPC scheme based on [12], but no guarantees on recursive feasibility or closed-loop stability can be given, since neither terminal ingredients are included in the MPC scheme nor sufficient lower bounds on the prediction horizon are derived.”
Data-driven simulation and control (2008, positive): “Lemma 2 (Fundamental lemma (Willems et al. 2005)) .”
Data-Enabled Predictive Control: In the Shallows of the DeePC (2018, background): “Lemma 4.2: ([36, Theorem 1]): Consider a controllable system B ∈ L m + p .”