Model (in)validation of switched ARX systems with unknown switches and its application to activity monitoring

Necmiye Ozay, Mario Sznaier, Constantino Lagoa

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

    14 Scopus citations

    Abstract

    Identification of switched linear systems has received considerable attention during the past few years. Since the problem is generically NP-Hard, the majority of existing algorithms are based on heuristics or relaxations. Therefore, it is crucial to check the validity of the identified models against additional experimental data. This paper addresses the problem of model (in)validation for multi-input multioutput switched affine autoregressive exogenous systems with unknown switches. Our main result provides necessary and sufficient conditions for a given model to be (in)validated by the experimental data. In principle, checking these conditions requires solving a sequence of convex optimization problems involving increasingly large matrices. However, as we show in the paper, if in the process of solving these problems either a positive solution is found or the so-called flat extension property holds, then the process terminates with a certificate that either the model has been invalidated or that the experimental data is indeed consistent with the model and a-priori information. By using duality, the proposed approach exploits the inherently sparse structure of the optimization problem to substantially reduce its computational complexity. The effectiveness of the proposed method is illustrated using both academic examples and a non-trivial problem arising in computer vision: activity monitoring.

    Original languageEnglish (US)
    Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
    Pages7624-7630
    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

    All Science Journal Classification (ASJC) codes

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

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    Ozay, N., Sznaier, M., & Lagoa, C. (2010). Model (in)validation of switched ARX systems with unknown switches and its application to activity monitoring. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 7624-7630). [5717330] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717330