PTC-FOZNN: A Strictly Predefined-Time Convergent Fractional-Order Recurrent Neural Network for Solving Time-Variant Quadratic Programming

This study presents a Predefined-Time Convergent Fractional-Order Zeroing Neural Network (PTC-FOZNN) as an innovative solution for Time-Invariant Quadratic Programming (TIQP) and Time-Variant Quadratic Programming (TVQP) problems. This model represents a noteworthy integration of fractional calculus into recurrent neural networks for cyclic motion planning of robots. The PTC-FOZNN diverges from the conventional Zeroing Neural Network (ZNN) by implementing a conformable fractional derivative that complies with the Leibniz rule-a standard often unmet by existing fractional derivatives. Additionally, it employs a novel predefined-time stabilizer as its activation function. When compared to the traditional ZNN, the PTC-FOZNN, configured with $0 < \alpha\leq 1$, exhibits enhanced convergence speed and greater positional accuracy for both TIQP and TVQP tasks. Through meticulous theoretical and empirical validation, including simulation trials with a Franka Emika Panda robotic arm, the PTC-FOZNN model has proven its effectiveness in precise trajectory tracking and computational efficacy.