Zhang Neural Network for Linear Time-Varying Equation Solving and its Robotic Application

Different from gradient-based neural networks, a special kind of recurrent neural network has been proposed by Zhang et al for real-time matrix inversion. In this paper, we generalize such a design method to solving online a set of linear time-varying equations. In comparison with gradient-based neural networks, the resultant Zhang neural network for time-varying equation solving is designed based on a vector-valued error function, instead of a scalar-valued error function. It is depicted in an implicit dynamics, instead of an explicit dynamics. Furthermore, Zhang neural network globally exponentially converges to the exact solution of linear time-varying equations. Simulation results, including the application to robot kinematic control, substantiate the theoretical analysis and demonstrate the efficacy of Zhang neural network on linear time-varying equation solving, especially when using a power-sigmoid activation function.