Adaptive RBF neural network-based prescribed performance control for overhead crane systems using fractional-order MIMO ultra-local model

In this paper, a neural network-based prescribed performance control scheme using fractional-order multi-input multi-output ultra-local models (FO-MIMO-ULM) is proposed to address the problem of anti-swing positioning control of a two-dimensional underactuated overhead crane system. First, in contrast to previous model-free control methodologies that decouple the MIMO system into a series of single-input single-output (SISO) ultra-local models (ULM), an innovative FO-MIMO-ULM with a non-diagonal gain matrix is proposed to approximate the intricate nonlinear dynamics inherent in the overhead crane system. In addition, a fast terminal sliding mode controller with prescribed performance setting is proposed, and an improved symmetric prescribed performance function is introduced to enhance the transient performance and state tracking accuracy, with high-precision convergence of the state error guaranteed. Second, time delay estimation (TDE) is employed to estimate the lumped disturbances in the FO-MIMO-ULM, which can ensure effective model-free characteristics. Furthermore, an radial basis function (RBF) neural network technique is designed to optimize the gain matrix of the MIMO-ULM, thereby improving the control performance. Finally, the stability of the closed-loop control scheme is analyzed by means of Lyapunov stability theory, and the effectiveness and superiority of the proposed method is proved by means of numerical simulation results.