Zeroing-Type Recurrent Neural Network for Solving Time-Dependent Lyapunov Equation with Noise Rejection

It is well known that many engineering communities are confronted with the problem of Lyapunov equation (LE) solving, and a mass of methods are proposed to solve the problem under the circumstance of no-noise. Whereas, noise is inevitable during actual experiments due to all kinds of factors, and models with resistance to noises are needed. To fill this lacuna, this paper proposes a zeroing-type recurrent neural network (ZTRNN) model for the task of solving the time-dependent LE. Additionally, the original zeroing neural network (OZNN) model is described for the purpose of comparison. Rigorous theoretical analyses concerning the convergence and the resistance to noises of the ZTRNN model are presented. Further, a numerical example of the time-dependent LE is solved by using the ZTRNN model and the OZNN model separately. Computer simulations are carried out perfectly and the results verify the feasibility and resistance to noises of the ZTRNN model, reflecting that the ZTRNN model outperforms the OZNN model in terms of resistance to noises.