Adaptive Fuzzy LMS Control for Positioning and Anti-Sway of an Overhead Crane System

Abstract This paper formulates an adaptive fuzzy control approach for the overhead crane positioning and anti-sway problem. The crane is treated as an underactuated nonlinear system with four states, one horizontal force input, and two controlled outputs: trolley position and load swing angle. The introductory part of the paper is extended with a crane control-oriented literature overview that distinguishes open-loop input shaping and command smoothing, model-based feedback control, fuzzy and LMI-based control, data-driven and model-free adaptive control, reinforcement learning, and machine learning-based approaches. The control design is then developed from a compact Takagi–Sugeno fuzzy state-space representation of the nonlinear cart–pendulum crane dynamics. The fuzzy model is obtained by sector nonlinearity and local approximation in fuzzy partition spaces, resulting in two local rules scheduled by the load swing angle. A parallel distributed fuzzy controller is parameterized as a linear-in-the-parameters control law, and its local parameters are adapted online by a teacher-based normalized least mean squares (LMS) rule. The adaptive controller learns the control signal of a virtual supervisory fuzzy controller and then remains active as the controller in the test phase. Projection, leakage regularization, force saturation, and a smooth transfer from the supervisory signal to the learned LMS signal are included to obtain an implementation-oriented closed-loop formulation. The proposed approach is intended as a physically interpretable bridge between robust fuzzy crane modeling and data-driven adaptive control. The novelty is clarified as the integration of a compact fuzzy crane model, a supervisory teacher signal, normalized LMS learning, leakage/projection, input saturation, and command-governed anti-sway tuning in one simulation-oriented framework. The study is explicitly presented as a numerical benchmark; formal nonlinear stability certification and laboratory validation are identified as future work rather than as claims of the present contribution.