Data-Driven LQR Control Design

Silva, Gustavo R. Gonçalves da; Bazanella, Alexandre Sanfelice; Lorenzini, Charles; Campestrini, Lucíola

doi:10.1109/lcsys.2018.2868183

Cited by 64 publications

(37 citation statements)

References 11 publications

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“…This is useful since the minimal cost associated to any initial condition x 0 can be computed as x ⊤ 0 P + x 0 . The data-driven LQR approach in [16] is quite different from Theorem 29 since the solution to the Riccati equation is approximated using a batch-form solution to the Riccati difference equation. A similar approach was used in [9]- [11], [13] for the finite horizon data-driven LQR/LQG problem.…”

Section: From Data To Lq Gainmentioning

confidence: 99%

“…A similar approach was used in [9]- [11], [13] for the finite horizon data-driven LQR/LQG problem. In the setup of [16], the approximate solution to the Riccati equation is exact only if the number of data points tends to infinity. The main difference between our approach and the one in [16] is hence that the solution P + to the Riccati equation can be obtained exactly from finite data via Theorem 29.…”

Section: From Data To Lq Gainmentioning

confidence: 99%

See 1 more Smart Citation

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: From Data To Lq Gainmentioning

confidence: 99%

Section: From Data To Lq Gainmentioning

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

“…The online adaptation of the control strategy or its employed model is well understood for parametric models [6], [7]. In particular for linear systems, data-driven approaches are extensively researched, see [8], and [9]. For nonlinear systems, model reference adaptive control (MRAC) is designed to effectively deal with model uncertainties or only little prior knowledge using online parameter estimation [10].…”

Section: A Related Workmentioning

confidence: 99%

Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning

Umlauft

Hirche

2020

IEEE Trans. Automat. Contr.

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Combining control engineering with nonparametric modeling techniques from machine learning allows to control systems without analytic description using data-driven models. Most existing approaches separate learning, i.e. the system identification based on a fixed dataset, and control, i.e. the execution of the model-based control law. This separation makes the performance highly sensitive to the initial selection of training data and possibly requires very large datasets. This article proposes a learning feedback linearizing control law using online closed-loop identification. The employed Gaussian process model updates its training data only if the model uncertainty becomes too large. This event-triggered online learning ensures high data efficiency and thereby reduces the computational complexity, which is a major barrier for using Gaussian processes under realtime constraints. We propose safe forgetting strategies of data points to adhere to budget constraint and to further increase data-efficiency. We show asymptotic stability for the tracking error under the proposed event-triggering law and illustrate the effective identification and control in simulation.

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“…The classic model-based approach [8] consists of (i) identifying a model of the system from the available data, and (ii) using the estimated model to design the optimal control inputs. Data-driven algorithms have been proposed in [9]- [12] for the LQR/LQG problem. In particular, the approach pursued in these papers relies on the estimation of the Markov parameters of the system, thereby bypassing the identification step of the model-based approach.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Minimum-Energy Controls for Linear Systems

Baggio

Katewa

Pasqualetti

2019

IEEE Control Syst. Lett.

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In this paper we study the problem of computing minimum-energy controls for linear systems from experimental data. The design of open-loop minimum-energy control inputs to steer a linear system between two different states in finite time is a classic problem in control theory, whose solution can be computed in closed form using the system matrices and its controllability Gramian. Yet, the computation of these inputs is known to be ill-conditioned, especially when the system is large, the control horizon long, and the system model uncertain. Due to these limitations, open-loop minimum-energy controls and the associated state trajectories have remained primarily of theoretical value. Surprisingly, in this paper we show that open-loop minimum-energy controls can be learned exactly from experimental data, with a finite number of control experiments over the same time horizon, without knowledge or estimation of the system model, and with an algorithm that is significantly more reliable than the direct model-based computation. These findings promote a new philosophy of controlling large, uncertain, linear systems where data is abundantly available.

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Data-Driven LQR Control Design

Cited by 64 publications

References 11 publications

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

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

Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning

Data-Driven Minimum-Energy Controls for Linear Systems

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