A fuzzy adaptive zeroing neural network with superior finite-time convergence for solving time-variant linear matrix equations

摘要

Zeroing neural network (ZNN) has a wide application in various fields, which is a very important and novel type of recurrent neural network (RNN). To deepen and expand the design mechanism of the traditional zeroing neural network (TZNN), this paper proposes a new type of the ZNN model with a fuzzy adaptive parameter to settle the time-variant linear matrix equation (TVLME) problem. Due to its adaptability, this new model is thus called the fuzzy adaptive ZNN (FAZNN) model. In comparison to the TZNN model, the FAZNN model has a very obvious feature that the fuzzy adaptive parameter is produced by a fuzzy logic system based on the calculation error, which makes the FAZNN model have the characteristics of adaptability and accelerated convergence. Theoretical analysis and proofs are given for the convergence of the FAZNN model with four classical activation functions involved. More importantly, theoretical proofs show that when the modified Li activation function or Li activation function is used, the FAZNN model can make its state solution converge to the theoretical solution within a shorter finite-time. Moreover, in order to compare the influence of the types of membership functions, two different membership functions are involved in fuzzy logic systems. Theoretical proofs, simulative experiments and a mobile manipulator control application prove that the FAZNN model with the fuzzy adaptive parameter has a significant effect on settling the TVLME problem.