A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises

Jianfeng Li, Linxi Qu, Zhan Li (), Bolin Liao, Shuai Li, Yang Rong, Zheyu Liu, Zhijie Liu and Kunhuang Lin
Additional contact information
Jianfeng Li: College of Computer Science and Engineering, Jishou University, Jishou 416000, China
Linxi Qu: College of Computer Science and Engineering, Jishou University, Jishou 416000, China
Zhan Li: Department of Computer Science, Swansea University, Swansea SA1 8EN, UK
Bolin Liao: College of Computer Science and Engineering, Jishou University, Jishou 416000, China
Shuai Li: Department of Mechanical Engineering, Swansea University, Swansea SA1 8EN, UK
Yang Rong: College of Computer Science and Engineering, Jishou University, Jishou 416000, China
Zheyu Liu: College of Mathematics and Statistics, Jishou University, Jishou 416000, China
Zhijie Liu: College of Computer Science and Engineering, Jishou University, Jishou 416000, China
Kunhuang Lin: College of Computer Science and Engineering, Jishou University, Jishou 416000, China

Mathematics, 2023, vol. 11, issue 2, 1-13

Abstract: The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation problem under linear noise, a new error-processing design formula is proposed, and a resultant novel zeroing neural network model is developed. The new design formula incorporates a second-order error-processing manner, and the double-integration-enhanced zeroing neural network (DIEZNN) model is further proposed for solving time-varying quadratic matrix equations subject to linear noises. Compared with the original zeroing neural network (OZNN) model, finite-time zeroing neural network (FTZNN) model and integration-enhanced zeroing neural network (IEZNN) model, the DIEZNN model shows the superiority of its solution under linear noise; that is, when solving the problem of a time-varying quadratic matrix equation in the environment of linear noise, the residual error of the existing model will maintain a large level due to the influence of linear noise, which will eventually lead to the solution’s failure. The newly proposed DIEZNN model can guarantee a normal solution to the time-varying quadratic matrix equation task no matter how much linear noise there is. In addition, the theoretical analysis proves that the neural state of the DIEZNN model can converge to the theoretical solution even under linear noise. The computer simulation results further substantiate the superiority of the DIEZNN model in solving time-varying quadratic matrix equations under linear noise.

Keywords: time-varying quadratic matrix equation; double-integration-enhanced zeroing neural network; linear noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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