A General Recurrent Neural Network Model for Time-Varying Matrix Inversion

Abstract

This paper presents a general recurrent neural network model for online inversion of time-varying matrices. Utilizing the first-order time-derivative, the neural model guarantees its state trajectory globally converge to the exact inverse of a given time-varying matrix. In addition, exponential convergence can be achieved if linear or sigmoid activation function is used. Network sensitivity is also studied to show the desirable robustness property of this neural approach. Simulation results, including the application to kinematic control of redundant manipulators, are used to demonstrate the effectiveness and performance of the proposed neural model.