Robust moving horizon H-8: control of discrete time-delayed systems with interval time-varying delays

F. Yildiz Tascikaraoglu, I. B. Kucukdemiral, J. Imura

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    Abstract

    In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.
    Original languageEnglish
    Article number462983
    Number of pages13
    JournalMathematical Problems in Engineering
    Volume2014
    DOIs
    Publication statusPublished - 27 Aug 2014

    Fingerprint

    Interval Time-varying Delay
    Disturbance rejection
    Linear matrix inequalities
    Closed-loop
    Horizon
    Discrete-time
    Disturbance Rejection
    Delay-dependent
    Matrix Inequality
    Linear Inequalities
    Asymptotic stability
    State feedback
    Feedback control
    Norm-bounded Uncertainties
    Time delay
    Dissipativity
    Dynamical systems
    Discrete-time Linear Systems
    Actuators
    State Feedback Control

    Keywords

    • moving horizon state-feedback control
    • MHHC
    • Lyapunov-Krasovskii functional
    • Linear matrix inequality

    Cite this

    @article{65e8e34a113e4de4973dc137e88e6a7a,
    title = "Robust moving horizon H-8: control of discrete time-delayed systems with interval time-varying delays",
    abstract = "In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.",
    keywords = "moving horizon state-feedback control, MHHC, Lyapunov-Krasovskii functional, Linear matrix inequality",
    author = "{Yildiz Tascikaraoglu}, F. and Kucukdemiral, {I. B.} and J. Imura",
    year = "2014",
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    doi = "10.1155/2014/462983",
    language = "English",
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    Robust moving horizon H-8: control of discrete time-delayed systems with interval time-varying delays. / Yildiz Tascikaraoglu, F.; Kucukdemiral, I. B.; Imura, J.

    In: Mathematical Problems in Engineering, Vol. 2014, 462983, 27.08.2014.

    Research output: Contribution to journalArticle

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    AU - Yildiz Tascikaraoglu, F.

    AU - Kucukdemiral, I. B.

    AU - Imura, J.

    PY - 2014/8/27

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    AB - In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

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