Two Neural Dynamics Approaches for Computing System of Time-Varying Nonlinear Equations

Abstract The problem of solving time-varying nonlinear equations has received much attention in many fields of science and engineering. In this paper, firstly, considering that the classical gradient-based neural dynamics (GND) might result in nonnegligible residual error in handling time-varying nonlinear equations, an adaptive coefficient GND (AGND) model is constructed as an improvement. Besides, the secondly new designed model is the projected zeroing neural dynamics (PZND) to relieve the limitation on the available activation function, which can be of saturation and non-convexity different from that should be unbounded and convex described in the traditional zeroing neural dynamics (ZND) approach. Moreover, theoretical analyses on the AGND model and PZND model are provided to guarantee their effectiveness. Furthermore, computer simulations are conducted and analyzed to illustrate the efficacy and superiority of the two new neural dynamics models designed for online solving time-varying nonlinear equations. Finally, applications to robot manipulator motion generation and Lorenz system are provided to show the feasibility and practicability of the proposed approaches.