Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs

Sze Zheng Yong, Minghui Zhu, Emilio Frazzoli

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

    2 Citations (Scopus)

    Abstract

    In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.

    Original languageEnglish (US)
    Title of host publicationACC 2015 - 2015 American Control Conference
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages2511-2518
    Number of pages8
    ISBN (Electronic)9781479986842
    DOIs
    StatePublished - Jul 28 2015
    Event2015 American Control Conference, ACC 2015 - Chicago, United States
    Duration: Jul 1 2015Jul 3 2015

    Publication series

    NameProceedings of the American Control Conference
    Volume2015-July
    ISSN (Print)0743-1619

    Other

    Other2015 American Control Conference, ACC 2015
    CountryUnited States
    CityChicago
    Period7/1/157/3/15

    Fingerprint

    Stochastic systems
    State estimation
    Linear systems

    All Science Journal Classification (ASJC) codes

    • Electrical and Electronic Engineering

    Cite this

    Yong, S. Z., Zhu, M., & Frazzoli, E. (2015). Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. In ACC 2015 - 2015 American Control Conference (pp. 2511-2518). [7171109] (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7171109
    Yong, Sze Zheng ; Zhu, Minghui ; Frazzoli, Emilio. / Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 2511-2518 (Proceedings of the American Control Conference).
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    abstract = "In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.",
    author = "Yong, {Sze Zheng} and Minghui Zhu and Emilio Frazzoli",
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    Yong, SZ, Zhu, M & Frazzoli, E 2015, Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. in ACC 2015 - 2015 American Control Conference., 7171109, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 2511-2518, 2015 American Control Conference, ACC 2015, Chicago, United States, 7/1/15. https://doi.org/10.1109/ACC.2015.7171109

    Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. / Yong, Sze Zheng; Zhu, Minghui; Frazzoli, Emilio.

    ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2511-2518 7171109 (Proceedings of the American Control Conference; Vol. 2015-July).

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

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    AB - In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.

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    Yong SZ, Zhu M, Frazzoli E. Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. In ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc. 2015. p. 2511-2518. 7171109. (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2015.7171109