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Journal ArticleDOI

Behavioral systems theory in data-driven analysis, signal processing, and control

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.
About: This article is published in Annual Reviews in Control.The article was published on 2021-11-10 and is currently open access. It has received 38 citations till now. The article focuses on the topics: Robust control & Model predictive control.
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TL;DR: 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.

49 citations

Journal ArticleDOI
TL;DR: In this article , 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: In this article, 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 multicriteria 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 nonparametric 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.

34 citations

Journal ArticleDOI
TL;DR: A tailored variant of Willems’ fundamental lemma is given, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints.
Abstract: In this letter we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems’ fundamental lemma, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.

15 citations

Journal ArticleDOI
TL;DR: In this paper , a distributed event-triggered transmission strategy based on periodic sampling is proposed, under which a model-based stability criterion for the closed-loop network system is derived, by leveraging a discrete-time looped-functional approach.
Abstract: The present paper deals with data-driven event-triggered control of a class of unknown discrete-time interconnected systems (a.k.a. network systems). To this end, we start by putting forth a novel distributed event-triggering transmission strategy based on periodic sampling, under which a model-based stability criterion for the closed-loop network system is derived, by leveraging a discrete-time looped-functional approach. Marrying the model-based criterion with a data-driven system representation recently developed in the literature, a purely data-driven stability criterion expressed in the form of linear matrix inequalities (LMIs) is established. Meanwhile, the data-driven stability criterion suggests a means for co-designing the event-triggering coefficient matrix and the feedback control gain matrix using only some offline collected state-input data. Finally, numerical results corroborate the efficacy of the proposed distributed data-driven ETS in cutting off data transmissions and the co-design procedure.

9 citations

Journal ArticleDOI
TL;DR: A survey of sequential decision-making problems that involve optimizing over probability functions is presented in this article , where the authors discuss the relevance of these problems for learning and control, and present a framework that combines a problem formulation and a set of resolution methods.

8 citations

References
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TL;DR: Time Series Analysis and Forecasting: principles and practice as mentioned in this paper The Oxford Handbook of Quantitative Methods, Vol. 3, No. 2: Statistical AnalysisTime-Series ForecastingPractical Time-Series AnalysisApplied Bayesian Forecasting and Time Series AnalysisSAS for Forecasting Time SeriesApplied Time Series analysisTime Series analysisElements of Nonlinear Time Series analyses and forecastingTime series analysis and forecasting by Example.
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Book
27 Nov 2013
TL;DR: The many different interpretations of proximal operators and algorithms are discussed, their connections to many other topics in optimization and applied mathematics are described, some popular algorithms are surveyed, and a large number of examples of proxiesimal operators that commonly arise in practice are provided.
Abstract: This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Here, we discuss the many different interpretations of proximal operators and algorithms, describe their connections to many other topics in optimization and applied mathematics, survey some popular algorithms, and provide a large number of examples of proximal operators that commonly arise in practice.

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Book
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TL;DR: In this article, an augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems, with step-by-step explanations that show clearly how to make practical use of the material.
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3,254 citations

Trending Questions (2)
How do behavior approaches and data-driven methods relate to each other?

The paper explains that the behavioral approach to systems theory, which takes a representation-free perspective, has gained renewed interest in the data-driven paradigm due to its compatibility with computational methods.

What is behavioral analysis theory?

Behavioral analysis theory is a representation-free perspective of a dynamical system as a set of trajectories, which is suited for data-driven analysis, signal processing, and control.