Abstract
In this chapter, by defining three different ZFs, three different ZD models are proposed, generalized, developed, and investigated to solve the time-varying linear matrix-vector inequality. Theoretical results are given as well to show the excellent convergence performance of such ZD models. Computer simulation results are presented to further substantiate the efficacy of the proposed ZD models for time-varying linear matrix-vector inequality solving.
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References
Marashdeh Q, Warsito W, Fan L, Teixeira F (2006) A nonlinear image reconstruction technique for ECT using a combined neural network approach. Meas Sci Technol 17:2097–2103
Cichocki A, Bargiela A (1997) Neural network for solving linear inequality systems. Parallel Comput 22:1455–1475
Labonte G (1997) On solving systems of linear inequalities with artificial neural network. IEEE Trans Neural Netw 8:590–600
Lin C, Lai C, Huang T (2000) A neural network for linear matrix inequality problems. IEEE Trans Neural Netw 11:1078–1092
Yang K, Murty KG, Mangasarian OL (1992) New iterative methods for linear inequalities. J Optim Theory Appl 72:163–185
Guo D, Zhang Y (2012) A new variant of the Zhang neural network for solving online time-varying linear inequalities. Proc R Soc A 468(2144):2255–2271
Zhang Y (2006) A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network. Neurocomputing 70:513–524
Zhang Y (2002) Analysis and design of recurrent neural networks and their applications to control and robotic systems. Ph.D. dissertation, Chinese University of Hong Kong, Hong Kong
Zhang Y, Wang J (2004) Obstacle avoidance for kinematically redundant manipulators using a dual neural network. IEEE Trans Syst Man Cybern Part B 34:752–759
Guo D, Zhang Y (2012) A new inequality-based obstacle-avoidance MVN scheme and its application to redundant robot manipulators. IEEE Trans Syst Man Cybern Part C 42(6):1326–1340
Xia Y (1996) A new neural network for solving linear programming problems and its application. IEEE Trans Neural Netw 7:525–529
Xia Y, Wang J, Hung DL (1999) Recurrent neural networks for solving linear inequalities and equations. IEEE Trans Circuits Syst I Fundam Theory Appl 46:452–462
Xiao L, Zhang Y (2011) Zhang neural network versus gradient neural network for solving time-varying linear inequalities. IEEE Trans Neural Netw 22(10):1676–1684
Mathews JH, Fink KD (2004) Numerical methods using MATLAB. Prentice Hall, New Jersey
Xiao L, Zhang Y (2013) Different Zhang functions resulting in different ZNN models demonstrated via time-varying linear matrix-vector inequalities solving. Neurocomputing 121:140–149
Cichocki A, Bargiela A (1997) Neural network for solving linear inequality systems. Parallel Comput 22:1455–1475
Guo D, Zhang Y (2014) Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion. IEEE Trans Neural Netw Learn Syst 25(2):370–382
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Zhang, Y., Guo, D. (2015). Time-Varying Linear Matrix-Vector Inequality. In: Zhang Functions and Various Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47334-4_6
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DOI: https://doi.org/10.1007/978-3-662-47334-4_6
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