Zhang Neural Networks for Online Solution of Time-Varying Linear Inequalities

In this chapter, a special type of recurrent neural networks termed “Zhang neural network” (ZNN) is presented and studied for online solution of time-varying linear (matrix-vector and matrix) inequalities. Specifically, focusing on solving the timevarying linear matrix-vector inequality (LMVI), we develop and investigate two different ZNN models based on two different Zhang functions (ZFs). Then, being an extension, by defining another two different ZFs, another two ZNN models are developed and investigated to solve the time-varying linear matrix inequality (LMI). For such ZNN models, theoretical results and analyses are presented as well to show their computational performances. Simulation results with two illustrative examples further substantiate the efficacy of the presented ZNN models for time-varying LMVI and LMI solving.

[1]  Carver Mead,et al.  Analog VLSI and neural systems , 1989 .

[2]  K. G. Murty,et al.  New iterative methods for linear inequalities , 1992 .

[3]  A. Cichocki,et al.  Neural Networks for Solving Linear Inequality Systems , 1997, Parallel Comput..

[4]  Euntai Kim,et al.  Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[5]  Jun Wang,et al.  Recurrent neural networks for solving linear inequalities and equations , 1999 .

[6]  Chih-Chin Lai,et al.  A neural network for linear matrix inequality problems , 2000, IEEE Trans. Neural Networks Learn. Syst..

[7]  Jun Wang,et al.  A recurrent neural network for solving Sylvester equation with time-varying coefficients , 2002, IEEE Trans. Neural Networks.

[8]  Shuzhi Sam Ge,et al.  Design and analysis of a general recurrent neural network model for time-varying matrix inversion , 2005, IEEE Transactions on Neural Networks.

[9]  Yunong Zhang,et al.  A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network , 2006, Neurocomputing.

[10]  Shuangzhe Liu,et al.  Hadamard, Khatri-Rao, Kronecker and Other Matrix Products , 2008 .

[11]  Long Cheng,et al.  A Simplified Neural Network for Linear Matrix Inequality Problems , 2009, Neural Processing Letters.

[12]  Yunong Zhang,et al.  Improved Zhang neural network model and its solution of time-varying generalized linear matrix equations , 2010, Expert Syst. Appl..

[13]  Xiaolin Hu,et al.  Dynamic system methods for solving mixed linear matrix inequalities and linear vector inequalities and equalities , 2010, Appl. Math. Comput..

[14]  Yunong Zhang,et al.  Zhang Neural Network Versus Gradient Neural Network for Solving Time-Varying Linear Inequalities , 2011, IEEE Transactions on Neural Networks.

[15]  Bin Jiang,et al.  LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures , 2011, IEEE Transactions on Neural Networks.

[16]  Yunong Zhang,et al.  Zhang Neural Networks and Neural-Dynamic Method , 2011 .

[17]  Xingjian Jing,et al.  Robust adaptive learning of feedforward neural networks via LMI optimizations , 2012, Neural Networks.

[18]  Yunong Zhang,et al.  A new variant of the Zhang neural network for solving online time-varying linear inequalities , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  Dongsheng Guo,et al.  A New Inequality-Based Obstacle-Avoidance MVN Scheme and Its Application to Redundant Robot Manipulators , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[20]  Yunong Zhang,et al.  Different Zhang functions resulting in different ZNN models demonstrated via time-varying linear matrix-vector inequalities solving , 2013, Neurocomputing.

[21]  Dongsheng Guo,et al.  Acceleration-Level Inequality-Based MAN Scheme for Obstacle Avoidance of Redundant Robot Manipulators , 2014, IEEE Transactions on Industrial Electronics.

[22]  Dongsheng Guo,et al.  Zhang Neural Network for Online Solution of Time-Varying Linear Matrix Inequality Aided With an Equality Conversion , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Dongsheng Guo,et al.  ZNN for solving online time-varying linear matrix-vector inequality via equality conversion , 2015, Appl. Math. Comput..