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Variable-gain controllers for nonlinear systems using the T-S fuzzy model.

P Prem Kumar, Indrani Kar, Laxmidhar Behera

    IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
    |December 26, 2006
    PubMed
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    This study introduces two variable state-feedback gain control schemes for stabilizing Takagi-Sugeno (T-S) fuzzy systems with nonlinear disturbances. Both controllers effectively stabilize the T-S fuzzy model, with the second scheme offering relaxed constraints on unmatched state disturbance.

    Area of Science:

    • Control Systems Engineering
    • Fuzzy Logic Systems
    • Nonlinear Dynamics

    Background:

    • Takagi-Sugeno (T-S) fuzzy systems are widely used to model complex nonlinear dynamics.
    • Stabilizing T-S fuzzy systems in the presence of nonlinear disturbances is a significant challenge in control theory.
    • Existing methods often face limitations regarding the bounds of unmatched state disturbances.

    Discussion:

    • Two novel control schemes employing variable state-feedback gain are proposed to address the stabilization of T-S fuzzy systems.
    • Controller I linearizes the T-S fuzzy model around a nominal plant, using a gain parameter to counteract disturbance effects.
    • Controller II focuses on local stabilization of individual linear subsystems, with fuzzy blending ensuring overall Lyapunov stability.

    Key Insights:

    Related Experiment Videos

    • Both proposed controllers demonstrate the ability to stabilize the T-S fuzzy model under nonlinear disturbances.
    • Controller II provides a more relaxed condition concerning the norm bound of unmatched state disturbance compared to Controller I.
    • The efficacy of both control strategies was validated through simulations on two distinct nonlinear systems.

    Outlook:

    • Further research could explore adaptive versions of these controllers to handle time-varying disturbances.
    • Investigating the robustness of these schemes against model uncertainties beyond state disturbances is a potential future direction.
    • Application of these control strategies to real-world complex nonlinear systems could be a valuable extension.