A gain-adjustment neural network based time-varying underdetermined linear equation solving method

Abstract

To solve the time-varying underdetermined linear equation (TVULE), a gain-adjustment neural network (GANN) is proposed, designed and analyzed. First, based on the exploited error monitoring function and neural dynamic method, a GANN based linear equation solving method with gain-adjustment parameter is obtained. Second, the global convergence theorem is proved and shows that the state output of the GANN will converge to the solution of TVULE super-exponentially. Furthermore, the strong robustness of the GANN can be ensured theoretically. Third, compared with some traditional neural networks like the gradient neural network and the zeroing neural network, the computer simulations illustrate that the GANN has the fastest speed, the best accuracy and the best anti-noise capability when considering external disturbances. Meanwhile, a practical application to solve a motion planning scheme of redundant robot manipulators further verifies the flexibility and superiority of the GANN.