Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion

As inspired by revising (Zhang and Ge, 2003), the traditional gradient-based neural system (also termed analog computer (Manherz et al., 1968)) for matrix inversion is re-visited by examining different activation functions and various implementation errors. A general neural system for matrix inversion is thus presented which can be constructed by using monotonically-increasing odd activation functions. For superior convergence and robustness of such a system, the power-sigmoid activation function is preferred to be in use if the hardware permits. In addition to investigating the singular case, this paper also presents an application example on inverse-kinematic control of redundant manipulators via online pseudoinverse solution