Hybrid system identification: An SDP approach

C. Feng, Constantino Manuel Lagoa, N. Ozay, M. Sznaier

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

    8 Citations (Scopus)

    Abstract

    The problem of identifying discrete time affine hybrid systems with noisy measurements is addressed in this paper. Given a finite number of measurements of input/output and a bound on the measurement noise, the objective is to identify a switching sequence and a set of affine models that are compatible with the a priori information, while minimizing the number of affine models. While this problem has been successfully addressed in the literature if the input/output data is noise-free or corrupted by process noise, results for the case of measurement noise are limited, e.g., a randomized algorithm has been proposed in a previous paper [3]. In this paper, we develop a deterministic approach. Namely, by recasting the identification problem as polynomial optimization, we develop deterministic algorithms, in which the inherent sparse structure is exploited. A finite dimensional semi-definite problem is then given which is equivalent to the identification problem. Moreover, to address computational complexity issues, an equivalent rank minimization problem subject to deterministic LMI constraints is provided, as efficient convex relaxations for rank minimization are available in the literature. Numerical examples are provided, illustrating the effectiveness of the algorithms.

    Original languageEnglish (US)
    Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
    Pages1546-1552
    Number of pages7
    DOIs
    StatePublished - Dec 1 2010
    Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
    Duration: Dec 15 2010Dec 17 2010

    Publication series

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

    Other

    Other2010 49th IEEE Conference on Decision and Control, CDC 2010
    CountryUnited States
    CityAtlanta, GA
    Period12/15/1012/17/10

    Fingerprint

    System Identification
    Hybrid systems
    Hybrid Systems
    Identification (control systems)
    Identification Problem
    Convex Relaxation
    Affine Systems
    Output
    Deterministic Algorithm
    Randomized Algorithms
    Minimization Problem
    Computational complexity
    Computational Complexity
    Discrete-time
    Polynomials
    Numerical Examples
    Polynomial
    Optimization
    Model

    All Science Journal Classification (ASJC) codes

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

    Cite this

    Feng, C., Lagoa, C. M., Ozay, N., & Sznaier, M. (2010). Hybrid system identification: An SDP approach. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 1546-1552). [5718082] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5718082
    Feng, C. ; Lagoa, Constantino Manuel ; Ozay, N. ; Sznaier, M. / Hybrid system identification : An SDP approach. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 1546-1552 (Proceedings of the IEEE Conference on Decision and Control).
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    abstract = "The problem of identifying discrete time affine hybrid systems with noisy measurements is addressed in this paper. Given a finite number of measurements of input/output and a bound on the measurement noise, the objective is to identify a switching sequence and a set of affine models that are compatible with the a priori information, while minimizing the number of affine models. While this problem has been successfully addressed in the literature if the input/output data is noise-free or corrupted by process noise, results for the case of measurement noise are limited, e.g., a randomized algorithm has been proposed in a previous paper [3]. In this paper, we develop a deterministic approach. Namely, by recasting the identification problem as polynomial optimization, we develop deterministic algorithms, in which the inherent sparse structure is exploited. A finite dimensional semi-definite problem is then given which is equivalent to the identification problem. Moreover, to address computational complexity issues, an equivalent rank minimization problem subject to deterministic LMI constraints is provided, as efficient convex relaxations for rank minimization are available in the literature. Numerical examples are provided, illustrating the effectiveness of the algorithms.",
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    Feng, C, Lagoa, CM, Ozay, N & Sznaier, M 2010, Hybrid system identification: An SDP approach. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5718082, Proceedings of the IEEE Conference on Decision and Control, pp. 1546-1552, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5718082

    Hybrid system identification : An SDP approach. / Feng, C.; Lagoa, Constantino Manuel; Ozay, N.; Sznaier, M.

    2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 1546-1552 5718082 (Proceedings of the IEEE Conference on Decision and Control).

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

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    AB - The problem of identifying discrete time affine hybrid systems with noisy measurements is addressed in this paper. Given a finite number of measurements of input/output and a bound on the measurement noise, the objective is to identify a switching sequence and a set of affine models that are compatible with the a priori information, while minimizing the number of affine models. While this problem has been successfully addressed in the literature if the input/output data is noise-free or corrupted by process noise, results for the case of measurement noise are limited, e.g., a randomized algorithm has been proposed in a previous paper [3]. In this paper, we develop a deterministic approach. Namely, by recasting the identification problem as polynomial optimization, we develop deterministic algorithms, in which the inherent sparse structure is exploited. A finite dimensional semi-definite problem is then given which is equivalent to the identification problem. Moreover, to address computational complexity issues, an equivalent rank minimization problem subject to deterministic LMI constraints is provided, as efficient convex relaxations for rank minimization are available in the literature. Numerical examples are provided, illustrating the effectiveness of the algorithms.

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    Feng C, Lagoa CM, Ozay N, Sznaier M. Hybrid system identification: An SDP approach. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 1546-1552. 5718082. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5718082