An Enhanced Activated Zeroing Neural Dynamics for Solving Complex Matrix Inverse and Tracking Trajectory of Robotic Manipulator

As an important branch of recurrent neural dynamics (RND), zeroing neural dynamics (ZND) can effectively deal with the dynamic complex matrix inverse (DCMI) issues. The convergence and robustness are two key performance indicators of the neuromotor system. For simultaneously realizing faster convergence rate and good noise-tolerance, some variant ZND models combined nonlinear activation function (NL-AF) and modified evolution formula are proposed. Though the performance of these ZND models is improved, the computational burden is sharply increased and some efficiency is lost. Furthermore, existing NL-AFs accelerate the convergence speed but still cannot satisfy the need of rigid time constraint. As we know, many classical NL-AFs have been put forward, few of them synthetically refer to achieving fixed time convergence and robust. Therefore, this work constructs a modified nonlinearly-activated ZND (MNAZND) model by implanting a novel versatile activation function (NV-AF) for solving the noise disturbed DCMI, the designed NV-AF includes the original term, the linear term and the discontinuous term, the original term ensures fixed time convergence, the linear and the discontinuous terms suppress different dynamic noises. Furthermore, with different noise state, the fixed-time convergence upper bound of the MNAZND model is deduced in theoretical proof. The numerical experiment verifies the MNAZND model with the proposed NV-AF has better fixed-time convergence and noise tolerance, the convergence time is less than theoretical fixed time $ 1/(\sigma \tau _{1})$ , and comparative simulation results also demonstrate that the designed NV-AF are advantageous over the previous AFs. Finally, the designed MNAZND is applied to tracking trajectory of robotic manipulator, which further illustrates reliability of the MNAZND.