A robust zeroing neural network for solving dynamic nonlinear equations and its application to kinematic control of mobile manipulator

Nonlinear phenomena are often encountered in various practical systems, and most of the nonlinear problems in science and engineering can be simply described by nonlinear equation, effectively solving nonlinear equation (NE) has aroused great interests of the academic and industrial communities. In this paper, a robust zeroing neural network (RZNN) activated by a new power versatile activation function (PVAF) is proposed and analyzed for finding the solutions of dynamic nonlinear equations (DNE) within fixed time in noise polluted environment. As compared with the previous ZNN model activated by other commonly used activation functions (AF), the main improvement of the presented RZNN model is the fixed-time convergence even in the presence of noises. In addition, the convergence time of the proposed RZNN model is irrelevant to its initial states, and it can be computed directly. Both the rigorous mathematical analysis and numerical simulation results are provided for the verification of the effectiveness and robustness of the proposed RZNN model. Moreover, a successful robotic manipulator path tracking example in noise polluted environment further demonstrates the practical application prospects of the proposed RZNN models.