A new class of robust and predefined-time consensus protocol based on noise-tolerant ZNN models

Zeroing neural network (ZNN) is a powerful tool in designing suitable control schemes since it is a systematic approach. It has been used in fields like robot manipulator control and tracking control, but few researchers have investigated the possible application of the ZNN in multi-agent systems. Based on the elegant zeroing neural network (ZNN) scheme, in this paper, two novel noise-tolerant ZNN (NTZNN) models are proposed to achieve consensus, which is a crucial problem in the field of cooperative control of the multi-agent systems. Besides, the novel noise-tolerant sign-bi-power (NTSBP) and noise-tolerant sign-exp-power (NTSEP) activation functions are used in this study. The NTZNN models activated by NTSBP and NTSEP are more robust than traditional ZNN models activated by the traditional sign-bi-power (SBP) and sign-exp-power (SEP) activation functions, respectively. The detailed mathematical analysis is presented to prove the robustness and predefined-time stability of the NTZNN models, and the upper bounds of the settling-time function are also estimated by a novel method based on improper integral. Combining the traditional Polyakov method and the proposed method based on improper integral, we can estimate the upper bounds of the settling-time function in a more precise way. Then, the robustness of the NTZNN models under both dynamic bounded vanishing noise and dynamic bounded non-vanishing noise is further evaluated by numerical experiments, and results show that the models are effective at both situations. We also present several practical examples of formation control, and parallel experiments are provided to further demonstrate that our results are general. All the theoretical and numerical verification results show that the NTZNN models are more robust than the traditional ZNN models activated by SBP or SEP activation functions, and it is also predefined-time stable.