Identification of Hybrid Systems A Tutorial

Paoletti, Simone; Juloski, A.L.; Ferrari-Trecate, Giancarlo; Vidal, René

doi:10.3166/ejc.13.242-260

Cited by 347 publications

(268 citation statements)

References 78 publications

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“…Additionally, most of the published methods for switched systems identification are batch algorithms (see also the survey paper [6] and some more recent techniques presented in [7][8][9]) except the algebraic algorithm derived in [10] and further extended in [11]. However, this latter method inherits from its batch version appeared in [3], a problem of dimensionality induced by the polynomial embedding.…”

Section: Introductionmentioning

confidence: 99%

Switched affine models for describing nonlinear systems

Bako

Boukharouba

Duviella

et al. 2009

IFAC Proceedings Volumes

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In this work, a recursive procedure is derived for the identification of switched affine models from input-output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in term of the prediction error, appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. Finally performance is tested through some computer simulations and the modeling of an open channel system.

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Section: Introductionmentioning

confidence: 99%

Switched affine models for describing nonlinear systems

Bako

Boukharouba

Duviella

et al. 2009

IFAC Proceedings Volumes

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“…Such systems can be described by a PWS function f as y i = f (x i ), where x i is built from past inputs u i and outputs y i of the system [3]. We consider the PWA system studied in the Example 1 of [10], where…”

Section: Piecewise Smooth Dynamical System Identificationmentioning

confidence: 99%

“…However, such approaches rely on nonconvex optimization, which implies that despite the existence of efficient algorithms such as expectation-maximization, these algorithms are only guaranteed to converge to a local solution and are sensitive to their initialization. Other works in control theory consider switching regression, either for linear [3]) or nonlinear [4] submodels, and suffer from similar issues. Except for [5], the situation is often worse since these methods do not constrain the submodels to be active in different regions of input space, which creates local solutions that are not consistent with piecewise models.…”

Section: Introductionmentioning

confidence: 99%

Learning smooth models of nonsmooth functions via convex optimization

Lauer

Bloch

2012

2012 IEEE International Workshop on Machine Learning for Signal Processing

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This paper proposes a learning framework and a set of algorithms for nonsmooth regression, i.e., for learning piecewise smooth target functions with discontinuities in the function itself or the derivatives at unknown locations. In the proposed approach, the model belongs to a class of smooth functions. Though constrained to be globally smooth, the trained model can have very large derivatives at particular locations to approximate the nonsmoothness of the target function. This is obtained through the definition of new regularization terms which penalize the derivatives in a location-dependent manner and training algorithms in the form of convex optimization problems. Examples of application to hybrid dynamical system identification and image reconstruction are provided.

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“…Thus, in these cases, the goal is to obtain a model that explains the data with s subsystems. Unfortunately it is known that, in the presence of unknownbut-bounded noise, this scenario leads to an NP-hard problem [21,8]. Several approaches have been proposed to address this difficulty [14,3,23,12].…”

Section: Introductionmentioning

confidence: 99%

Set membership identification of switched linear systems with known number of subsystems

2015

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This paper addresses the problem of robust identification of a class of discrete-time linear hybrid systems, switched linear models, in a set membership framework. Given a finite collection of noisy input/output data the objective is twofold: (i) establish whether this data was generated by a system that switches amongst an a-priori known number of subsystems, and (ii) in that case identify a suitable set of linear models along with a switching sequence that can explain the available experimental information. Our main result shows that these problems are equivalent to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) Borel measure with finite support. The use of well known (tight) convex relaxations of rank allows for further reducing the problem to a semidefinite optimization that can be efficiently solved. In the second part of the paper we extend these results to handle sensor failures that result in corrupted input/output measurements. Assuming that these failures are infrequent, we show that the problem can be recast into an optimization form where the objective is to simultaneously minimize the rank of a matrix and the number of nonzero rows of a second one. In both cases, appealing to well known convex relaxations of rank and sparsity leads to overall semidefinite optimization problems that can be efficiently solved. These results are illustrated with multiple examples showing substantially improved identification performance in the presence of noise and sensor faults.

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Identification of Hybrid Systems A Tutorial

Cited by 347 publications

References 78 publications

Switched affine models for describing nonlinear systems

Switched affine models for describing nonlinear systems

Learning smooth models of nonsmooth functions via convex optimization

Set membership identification of switched linear systems with known number of subsystems

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