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Bridging direct & indirect data-driven control formulations via regularizations and relaxations
TLDR
In this paper, the authors discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data driven control approach seeking an optimal decision compatible with recorded data assembled in a Hankel matrix and robustified through suitable regularizations.Abstract:
We discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data-driven control approach seeking an optimal decision compatible with recorded data assembled in a Hankel matrix and robustified through suitable regularizations. We formulate these two problems in the language of behavioral systems theory and parametric mathematical programs, and we bridge them through a multi-criteria formulation trading off system identification and control objectives. We illustrate our results with two methods from subspace identification and control: namely, subspace predictive control and low-rank approximation which constrain trajectories to be consistent with a non-parametric predictor derived from (respectively, the column span of) a data Hankel matrix. In both cases we conclude that direct and regularized data-driven control can be derived as convex relaxation of the indirect approach, and the regularizations account for an implicit identification step. Our analysis further reveals a novel regularizer and a plausible hypothesis explaining the remarkable empirical performance of direct methods on nonlinear systems.read more
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Behavioral systems theory in data-driven analysis, signal processing, and control
Ivan Markovsky,Florian Dörfler +1 more
TL;DR: Data-driven analysis, signal processing, and control methods as mentioned in this paper can be broadly classified as implicit and explicit approaches, with the implicit approach being more robust to uncertainty and robustness to noise.
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Distributionally Robust Chance Constrained Data-enabled Predictive Control
TL;DR: This work proposes a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints.
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On the design of terminal ingredients for data-driven MPC
TL;DR: A model predictive control scheme to control unknown linear time-invariant systems using only measured input-output data and no model knowledge is presented.
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Linear tracking MPC for nonlinear systems Part II: The data-driven case.
TL;DR: In this article, a data-driven MPC approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees is presented. But this approach is limited to affine systems.
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Linear Tracking MPC for Nonlinear Systems—Part II: The Data-Driven Case
TL;DR: In this article , a data-driven model predictive control (MPC) approach is proposed to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees.
References
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Book
Subspace Identification for Linear Systems: Theory - Implementation - Applications
Peter Van Overschee,Bart De Moor +1 more
TL;DR: This book focuses on the theory, implementation and applications of subspace identification algorithms for linear time-invariant finitedimensional dynamical systems, which allow for a fast, straightforward and accurate determination of linear multivariable models from measured inputoutput data.
BookDOI
Statistical Learning with Sparsity: The Lasso and Generalizations
TL;DR: Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.
Journal ArticleDOI
N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems
TL;DR: Two new N4SID algorithms to identify mixed deterministic-stochastic systems are derived and these new algorithms are compared with existing subspace algorithms in theory and in practice.
Journal ArticleDOI
Paradigms and puzzles in the theory of dynamical systems
TL;DR: In this article, a self-contained exposition is given of an approach to mathematical models, in particular to the theory of dynamical systems, which leads to a new view of the notions of controllability and observability, and of the interconnection of systems.
Journal ArticleDOI
Iterative feedback tuning: theory and applications
TL;DR: An optimization approach to iterative control design and a direct optimal tuning algorithm that is particularly well suited for the tuning of the basic control loops in the process industry, which are typically PID loops.