An Improved Finite Time Convergence Recurrent Neural Network with Application to Time-Varying Linear Complex Matrix Equation Solution

Abstract

Linear matrix equation (LME) is a kind of very important mathematical equation, and many practical problems in scientific and engineering fields can be described by LMEs in mathematics. In this paper, an improved finite time convergence zeroing neural network (FTCZNN) for online solving time-varying linear complex matrix equation (TVLCME) is realized. Different from the exponential convergence conventional zeroing neural network (CZNN), the new FTCZNN adopts a novel design formula for its error matrix converging to zero. Theoretical analysis and proof of the new FTCZNN converges to the theoretical solution of the TVLCME in finite time are provided. For comparison purpose, the CZNN is also developed for solving the same TVLCME. Compared with the exponentially converging CZNN, the new FTCZNN has great improvement in convergence performance, and the simulation results demonstrate that the new FTCZNN is a more effective and superior candidate for online solving TVLCME.