Novel fixed-time zeroing neural network models for solving time-varying minimal rank outer inverse problem

There are already several methods to calculate the time-varying minimal rank outer inverse (TV-MROI), but few scholars have employed fixed-time methods to obtain TV-MROI. To obtain TV-MROI within a fixed time frame, this paper introduces four novel fixed-time zeroing neural network (ZNN) models specifically designed to solve the TV-MROI problem. Compared with existing ZNN models, the proposed fixed-time ZNN model can attain TV-MROI before a fixed time, irrespective of the starting initial value. Initially, a new fixed-time stability criterion is established, utilizing a specialized Lyapunov function to ensure stability within a fixed period. Furthermore, a tighter upper bound for the convergence time is derived. An analysis of how various parameters affect this upper bound is undertaken, providing valuable insights into optimal parameter selection. Subsequently, the paper addresses both TV-MROI with specified range and kernel. To tackle these challenges, four innovative fixed-time zeroing neural network models are proposed, along with their respective fixed-time stability theorems. Finally, simulation results demonstrate the efficacy of our proposed methods.