Harmonic Noise Rejection Zeroing Neural Network for Time-Dependent Equality-Constrained Quadratic Program and Its Application to Robot Arms

The quadratic program (QP) with equality constraint is widely involved in science and engineering fields. Numerous solutions to the equality-constrained QP (ECQP) have been reported, particularly the zeroing neural network (ZNN) for the time-dependent ECQP. However, such solutions can be severely affected by the harmonic noise and may lose their efficacy. This study aims to address the above limitation by proposing the new ZNN model against harmonic noise with the only known frequency. Such a model, called the harmonic noise rejection ZNN (HNR-ZNN) model, is established by incorporating the dynamics of the harmonic signal (from which the unknown information for the signal's amplitude and phase can be eliminated). Theoretical analysis indicates that the proposed HNR-ZNN model effectively determines the optimal solution of time-dependent ECQP under harmonic noise interference. Comparative computer simulations and real-world robot applications further indicate the validity, excellence, and practicality of the presented HNR-ZNN model.