Model Reference Control Design by Prediction Error Identification

Campestrini, Lucíola; Eckhard, Diego; Bazanella, Alexandre Sanfelice; Gevers, Michel

doi:10.3182/20120711-3-be-2027.00190

Cited by 13 publications

(31 citation statements)

References 13 publications

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“…However, this approach is basically equivalent to a model-based approach where the system matrices A and B are first reconstructed using a collection of sample trajectories. A crucial observation that emerges from Theorem 2 is that also the controller K can be parametrized through data via (12). Thus for design purposes one can regard G K as a decision variable, and search for the matrix G K that guarantees stability and performance specifications.…”

Section: From Indirect To Direct Data-driven Controlmentioning

confidence: 99%

“…Thus for design purposes one can regard G K as a decision variable, and search for the matrix G K that guarantees stability and performance specifications. In fact, as long as G K satisfies the condition X 0,T G K = I n in (12) we are ensured that X 1,T G K provides an equivalent representation of the closed-loop matrix A+BK with feedback matrix K = U 0,1,T G K . As shown in the next section, this enable design procedures that avoid the need to identify a parametric model of the system.…”

Section: From Indirect To Direct Data-driven Controlmentioning

confidence: 99%

“…We point out that Theorem 2 already gives an identificationfree method for checking whether a candidate controller K is stabilizing or not. In fact, given K, any solution G K to (12) is such that X 1,T G K = A+BK. One can therefore compute the eigenvalues of X 1,T G K to check whether K is stabilizing or not.…”

Section: From Indirect To Direct Data-driven Controlmentioning

confidence: 99%

“…control theory [6], iterative feedback tuning [7], and virtual reference feedback tuning [8]. This topic is now attracting more and more researchers, with problems ranging from PIDlike control [9] to model reference control and output tracking [10], [11], [12], [13], [14], predictive [15], [16], robust [17] and optimal control [18], [19], [20], [21], [22], [23], [24], the latter being one of the most frequently considered problems. The corresponding techniques are also quite varied, ranging from dynamics programming to optimization techniques and algebraic methods.…”

mentioning

confidence: 99%

See 3 more Smart Citations

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

Persis

Tesi

2020

IEEE Trans. Automat. Contr.

578

711

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In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the inputoutput 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.

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Section: From Indirect To Direct Data-driven Controlmentioning

confidence: 99%

Section: From Indirect To Direct Data-driven Controlmentioning

confidence: 99%

Section: From Indirect To Direct Data-driven Controlmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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

Persis

Tesi

2020

IEEE Trans. Automat. Contr.

578

711

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show abstract

“…From Lemma 25, we know that there exist M and P + satisfying (24)- (27) for all (A, B) ∈ Σ i/s . By substituting (27) into (25) and using (24), we obtain…”

Section: B Informativity For Linear Quadratic Regulationmentioning

confidence: 99%

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

Waarde

Eising

Trentelman

et al. 2020

IEEE Trans. Automat. Contr.

315

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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