Comparison of Four Procedures for the Identification of Hybrid Systems

Juloski, A.L.; Heemels, W.P.M.H.; Ferrari-Trecate, Giancarlo; Vidal, René; Paoletti, Simone; Niessen, J.H.G.

doi:10.1007/978-3-540-31954-2_23

Cited by 93 publications

(73 citation statements)

References 16 publications

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“…The four identification procedures described in this section are compared and discussed in [44] (see also [45]). Specific behaviors of the procedures with respect to classification accuracy, noise level, and tuning parameters are pointed out using simple one-dimensional examples.…”

Section: Discussionmentioning

confidence: 99%

“…Hence, the bounded-error procedure fits a PWARX model satisfying (44) to the data, without any assumption on the system generating the data. Since any PWARX model satisfying the bounded-error condition (44) is feasible, an initial guess of the number of submodels s is obtained by addressing Problem 3.2.…”

Section: Bounded-error Proceduresmentioning

confidence: 99%

“…Submodel i is discarded if the cardinality of the set D i of data points classified to mode i is less than βN . Data points that do not satisfy (44) are discarded as infeasible during the classification process, making it possible to detect outliers. In [5] parameter estimates are computed by the ℓ ∞ projection estimator, i.e.…”

Section: Bounded-error Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Identification of Hybrid Systems A Tutorial

Paoletti

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Ferrari-Trecate

et al. 2007

European Journal of Control

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Section: Discussionmentioning

confidence: 99%

Section: Bounded-error Proceduresmentioning

confidence: 99%

Section: Bounded-error Proceduresmentioning

confidence: 99%

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Identification of Hybrid Systems A Tutorial

Paoletti

Juloski

Ferrari-Trecate

et al. 2007

European Journal of Control

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347

268

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“…However, arbitrary linear inequalities can be accommodated simply by refining the polytopic partition -the resulting PWA will have some polytopes with identical dynamics. Fourth, the assumption that A l , l ∈ L are nonsingular is usually satisfied in practice, when the discrete-time PWA description is obtained through identification from experimental data [17], or through discretization of continuous linear dynamics, when A l , l ∈ L are matrix exponentials.…”

Section: Problem Formulation and Approachmentioning

confidence: 99%

“…of Informatics, Masaryk University and are equivalent with other classes of hybrid systems [16]. In addition, there exist techniques for the identification of such models from experimental data, which include Bayesian methods, bounded-error procedures, clustering-based methods, mixed-integer programming, and algebraic geometric methods (see [17] for a review).…”

Section: Introductionmentioning

confidence: 99%

Formal analysis of piecewise affine systems through formula-guided refinement

Yordanov

Tůmová

Belta

et al. 2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-We present a computational framework for identifying a set of initial states from which all trajectories of a piecewise affine (PWA) system satisfy a Linear Temporal Logic (LTL) formula over a set of linear predicates in its state variables. Our approach is based on the construction and refinement of finite abstractions of infinite systems (i.e. systems where states can take infinitely many values). We derive conditions guaranteeing the equivalence of an infinite system and its finite abstraction with respect to a specific temporal logic formula and propose methods aimed at the construction of such formula-equivalent abstractions. We show that the proposed procedure can be implemented using polyhedral operations and analysis of finite graphs. While provably correct, the overall method is conservative and expensive. The proposed algorithms have been implemented as a software tool that is available for download. Illustrative examples for the PWA models of two gene networks are included.

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Simultaneous identification of piecewise affine systems and number of subsystems using mixed logical dynamical systems theory

Zanma

Fuke

Chang

et al. 2008

Elect Comm in Japan

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SUMMARYThis paper addresses system identification of a switched system in which each subsystem is expressed by a piecewise affine system. The system considered is expressed by a mixed logical dynamical system for which some design methods are already known. For identification, in most cases, a number of subsystems, that is, switching points, are given in advance. However, it is not easy to find switching points for multivariable systems. Therefore, in this paper, we propose a simultaneous identification technique that takes into account the number of subsystems and their parameters. The proposed method is applied to several examples to show its effectiveness.

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Comparison of Four Procedures for the Identification of Hybrid Systems

Cited by 93 publications

References 16 publications

Identification of Hybrid Systems A Tutorial

Identification of Hybrid Systems A Tutorial

Formal analysis of piecewise affine systems through formula-guided refinement

Simultaneous identification of piecewise affine systems and number of subsystems using mixed logical dynamical systems theory

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