Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

By C. De Persis, Pietro Tesi. IEEE Transactions on Automatic Control, 2019

1,095 citations recorded by the source corpus.

In a paper by Willems et al., it was shown that persistently exciting data can be used to represent the input–output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent linear matrix inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/89f9c85719f355d555eaed62efc1b18126e394ea

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In Control and Systems Engineering

Citations in the corpus

Bridging Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations (2021, positive): “This result serves as the theoretic underpinning for work in subspace identification [29]–[31] and data-driven control, in particular subspace predictive control (SPC) based on nonparametric models [32]–[34], explicit feedback policies parameterized by data matrices [35]–[37], and data-enabled predi”
Data-Driven Model Predictive Control With Stability and Robustness Guarantees (2019, methodology): “Recently, Theorem 1 has received increasing attention to develop data-driven controllers [17], verify dissipativity [18], or to design MPC schemes [20]–[22].”
From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma (2020, methodology): “This is in contrast with previous LMI formulations in [37] and [39] that provide sufﬁcient conditions for controller design.”
Behavioral systems theory in data-driven analysis, signal processing, and control (2021, methodology): “The direct approach laid out by De Persis and Tesi (2019) uses the subspace relations (56)-(57) to parametrize the stabilization (54) and LQR (55) problems by raw data matrices.”
Data Informativity: A New Perspective on Data-Driven Analysis and Control (2019, positive): “Therefore, our results provide a theoretic justification for imposing the strong persistency of excitation conditions in prior work on the LQR problem, such as [14] and [40].”