New Double Integral Reinforcing Recurrent Neural Network for Solving Matrix Pseudoinverse Problem

Recurrent neural network (RNN) is a neurodynamic method designed to tackle time-varying problems in various technical domains, which are widely derived from scientific research and practical applications. It should be noted that traditional models often lack an effective capability to suppress nonlinear time-varying noise during the design process, and thus may encounter many difficulties in practical applications. This article presents a novel RNN model for solving the continuous time-varying matrix pseudoinverse, which has a significant characteristic of double integral-reinforcing (DIR) term and is termed DIR continuous-time RNN (DIR-CT-RNN) model. Correspondingly, using the discretization formula, a DIR discrete-time RNN (DIR-DT-RNN) is presented for solving the discrete time-varying matrix pseudoinverse. The theoretical results present that the DIR-DT-RNN model converges toward the theoretical solution under the discrete time-unvarying constant (DTU-C) noise or discrete time-varying linear (DTV-L) noise interference. Under the discrete time-varying quadratic (DTV-Q) noise interference, the proposed model converges to a constant that relates to the design parameters. In addition, simulation results, including an application for trajectory tracking of three-link robotic manipulator, which come from practical engineering background, verify the effectiveness and superiority of DIR-DT-RNN model for solving the time-varying matrix pseudoinverse under various types of noise interference.