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Open accessPosted Content

Data-Based System Analysis and Control of Flat Nonlinear Systems.

04 Mar 2021-
Abstract: Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In this paper, we extend this result to the class of discrete-time single-input single-output flat nonlinear systems. We propose a data-based parametrization of all trajectories using only input-output data. Further, we use this parametrization to solve the data-based simulation and output-matching control problems for the unknown system without explicitly identifying a model. Finally, we illustrate the main results with numerical examples.

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Topics: Parametrization (56%), Nonlinear system (54%), Linear combination (53%) ... read more
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7 results found


Open accessPosted Content
Abstract: In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data-driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.

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6 Citations


Open accessPosted Content
Abstract: We present a novel data-driven MPC approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parametrization provided by the Fundamental Lemma of Willems et al. We use new input-output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference. As intermediate results of independent interest, we extend the Fundamental Lemma to affine systems and we propose a data-driven tracking MPC scheme with guaranteed robustness. The theoretical analysis of this MPC scheme relies on novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor.

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4 Citations


Open accessJournal ArticleDOI: 10.1016/J.ARCONTROL.2021.09.005
Ivan Markovsky1, Florian Dörfler2Institutions (2)
Abstract: The behavioral approach to systems theory, put forward 40 years ago by Jan C. Willems, takes a representation-free perspective of a dynamical system as a set of trajectories. Till recently, it was an unorthodox niche of research but has gained renewed interest for the newly emerged data-driven paradigm, for which it is uniquely suited due to the representation-free perspective paired with recently developed computational methods. A result derived in the behavioral setting that became known as the fundamental lemma started a new class of subspace-type data-driven methods. The fundamental lemma gives conditions for a non-parametric representation of a linear time-invariant system by the image of a Hankel matrix constructed from raw time series data. This paper reviews the fundamental lemma, its generalizations, and related data-driven analysis, signal processing, and control methods. A prototypical signal processing problem, reviewed in the paper, is missing data estimation. It includes simulation, state estimation, and output tracking control as special cases. The direct data-driven control methods using the fundamental lemma and the non-parametric representation are loosely classified as implicit and explicit approaches. Representative examples are data-enabled predictive control (an implicit method) and data-driven linear quadratic regulation (an explicit method). These methods are equally amenable to certainty-equivalence as well as to robust control. Emphasis is put on the robustness of the methods under noise. The methods allow for theoretical certification, they are computationally tractable, in comparison with machine learning methods require small amount of data, and are robustly implementable in real-time on complex physical systems.

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Topics: Robust control (53%), Model predictive control (51%), Robustness (computer science) (51%) ... read more

4 Citations


Open accessPosted Content
23 Nov 2020-
Abstract: In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial dynamics, our approach allows to design controllers for unknown systems with rational or general non-polynomial dynamics. We first derive a data-driven parametrization of unknown nonlinear systems with rational dynamics. By applying robust control techniques to this parametrization, we obtain sum-of-squares based criteria for designing controllers with closed-loop robust stability and performance guarantees for all systems which are consistent with the measured data and the assumed noise bound. We then apply this approach to control systems whose dynamics are linear in general non-polynomial basis functions by transforming them into polynomial systems. Finally, we apply the developed approaches to numerical examples.

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Topics: Polynomial (57%), Robust control (57%), Nonlinear system (56%) ... read more

3 Citations


Open accessPosted Content
30 Mar 2021-
Abstract: In data-driven analysis and control, the so-called Fundamental Lemma by Willems et al. has gained a lot of interest in recent years. Using behavioural system theory, the Fundamental Lemma shows that the full system behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single sequence of data of the system, as long as the input is persistently exciting. In this work, we aim to generalize this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems'. This implies that the result is also applicable to nonlinear system behaviour that can be captured with an LPV representation. We show the applicability of our result by connecting it to earlier works on data-driven analysis and control for LPV systems.

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3 Citations


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30 results found


Open accessBook
01 Jan 1987-
Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...

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20,022 Citations


Open accessJournal Article

4,138 Citations


Journal ArticleDOI: 10.1109/MCS.2006.1636313
Abstract: This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.

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2,261 Citations


Open accessJournal ArticleDOI: 10.1214/009053607000000677
Abstract: We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.

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1,534 Citations


Open accessJournal ArticleDOI: 10.1007/S12532-018-0139-4
Joel Andersson1, Joris Gillis2, Greg Horn, James B. Rawlings1  +1 moreInstitutions (3)
Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

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Topics: AMPL (52%), Software framework (52%), Optimization problem (51%) ... read more

879 Citations


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No. of citations received by the Paper in previous years
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