Robust identification of switched affine systems via moments-based convex optimization

Necmiye Ozay, Constantino Manuel Lagoa, Mario Sznaier

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    26 Citations (Scopus)

    Abstract

    This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information. Our method builds upon an algebraic procedure proposed by Vidal et al. for noise free measurements. In the presence of norm bounded noise, this algebraic procedure leads to a very challenging nonconvex polynomial optimization problem. Our main result shows that this problem can be reduced 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) probability distribution function with finite support. Appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem that can be efficiently solved. These results are illustrated with two examples showing substantially improved identification performance in the presence of noise.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
    Pages4686-4691
    Number of pages6
    DOIs
    StatePublished - Dec 1 2009
    Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
    Duration: Dec 15 2009Dec 18 2009

    Publication series

    NameProceedings of the IEEE Conference on Decision and Control
    ISSN (Print)0191-2216

    Other

    Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
    CountryChina
    CityShanghai
    Period12/15/0912/18/09

    Fingerprint

    Affine Systems
    Convex optimization
    Switched Systems
    Convex Optimization
    Moment
    Semidefinite Optimization
    Optimization Problem
    Convex Relaxation
    Convex Constraints
    Probability Distribution Function
    Hybrid systems
    Hybrid Systems
    Probability distributions
    Distribution functions
    Subsystem
    Discrete-time
    Polynomials
    Rank of a matrix
    Norm
    Unknown

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Modeling and Simulation
    • Control and Optimization

    Cite this

    Ozay, N., Lagoa, C. M., & Sznaier, M. (2009). Robust identification of switched affine systems via moments-based convex optimization. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 4686-4691). [5399962] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399962
    Ozay, Necmiye ; Lagoa, Constantino Manuel ; Sznaier, Mario. / Robust identification of switched affine systems via moments-based convex optimization. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. pp. 4686-4691 (Proceedings of the IEEE Conference on Decision and Control).
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    title = "Robust identification of switched affine systems via moments-based convex optimization",
    abstract = "This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information. Our method builds upon an algebraic procedure proposed by Vidal et al. for noise free measurements. In the presence of norm bounded noise, this algebraic procedure leads to a very challenging nonconvex polynomial optimization problem. Our main result shows that this problem can be reduced 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) probability distribution function with finite support. Appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem that can be efficiently solved. These results are illustrated with two examples showing substantially improved identification performance in the presence of noise.",
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    Ozay, N, Lagoa, CM & Sznaier, M 2009, Robust identification of switched affine systems via moments-based convex optimization. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399962, Proceedings of the IEEE Conference on Decision and Control, pp. 4686-4691, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5399962

    Robust identification of switched affine systems via moments-based convex optimization. / Ozay, Necmiye; Lagoa, Constantino Manuel; Sznaier, Mario.

    Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. p. 4686-4691 5399962 (Proceedings of the IEEE Conference on Decision and Control).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    Ozay N, Lagoa CM, Sznaier M. Robust identification of switched affine systems via moments-based convex optimization. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. p. 4686-4691. 5399962. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399962