Adaptive Fuzzy Fractional-Order Sliding Mode Control Using an RBF Neural Network Observer for Robotic Manipulators
Year: 2026
Type: article
Abstract: This paper develops an observer-based adaptive fuzzy fractional sliding mode control (AFFSMC) approach for trajectory tracking of a four-degree-of-freedom robotic manipulator subject to nonlinear coupling, parametric uncertainty, unmodeled friction, and external disturbances. The approach integrates three components within a single design: a fractional-order PID-type sliding surface that shapes the transient and steady-state error response through Caputo operators, a Mamdani fuzzy reaching law whose gain is scheduled online by a supervisory fuzzy system, and a radial basis function (RBF) neural network estimator that approximates the lumped uncertainty online. The control law is derived with respect to a nominal model, so that inertia, Coriolis, gravity, and friction mismatches, together with the external disturbance, are collected into one lumped uncertainty whose reduced sliding dynamics are derived explicitly. The RBF weight-adaptation law is obtained from the same composite Lyapunov function used for the sliding variable, and the analysis establishes uniform ultimate boundedness with an explicit ultimate bound that depends on the ideal-weight bound, the leakage gain, the reconstruction residual, and the damping gain. Actuator torque limits are incorporated through a saturation-aware gain bound, a conditional-integration anti-windup, and a boundedness result under saturation. Numerical studies on the four-link platform cover four uncertainty scenarios and include a comparison with computed-torque PID, sign-based fractional sliding mode, and fuzzy fractional sliding mode control without the estimator, a study of the estimator regressor, a sensitivity study of the design parameters, and a saturation study. With realistic torque limits, the tracking errors of all four joints converge to a sub-milliradian band within about one second in every scenario, with steady-state errors of 1.4–16 microradians. In the combined-uncertainty scenario, the proposed approach reduces the steady-state error by factors of 4.8, 4.1, and 15 relative to the controller without the estimator, sign-based fractional sliding mode control, and computed-torque PID, while its control-torque total variation is about 190 times lower than that of sign-based fractional sliding mode control.
Source: Mathematics
DOI: 10.3390/math14224150
Author: Siddig M. Elkhider
Institution: King Faisal University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7225797509
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