Recurrent neural networks for solving linear inequalities and equations

Abstract

This paper presents two types of recurrent neural networks, continuous-time and discrete-time ones, for solving linear inequality and equality systems. In addition to the basic continuous-time and discrete-time neural-network models, two improved discrete-time neural networks with faster convergence rate are proposed by use of scaling techniques. The proposed neural networks can solve a linear inequality and equality system, can solve a linear program and its dual simultaneously, and thus extend and modify existing neural networks for solving linear equations or inequalities. Rigorous proofs on the global convergence of the proposed neural networks are given. Digital realization of the proposed recurrent neural networks are also discussed. Index Terms-Linear equalities and equations, recurrent neural networks.Youshen Xia received the B.S. and M.S. degrees in computational mathematics from Nanjing University, China, in 1982 and 1989, respectively. . His primary research interests are in applicationdriven algorithms and architectures, reconfigurable computing, and design of high-performance digital/computing systems for applications in areas such as image/signal processing, pattern classification, real-time control, optimization, and computational intelligence.Dr. Hung is a member of Eta Kappa Nu.

A new variant of the Zhang neural network for solving online time-varying linear inequalities

“…In recent years, the online solution of LMVIs (viewed as a special case of LMIs) has been considered to be an important problem encountered in the science and engineering fields (Xia et al 1999;Zhang & Wang 2004;Zhang 2006) (e.g. online solution of time-varying inequality constraint for obstacle avoidance of redundant robot manipulators).…”

“…In recent years, online solution of linear inequalities (LIs) has been considered to be an important problem encountered in numerous fields of science and engineering applications (Yang et al 1992;Xia 1996;Cichocki & Bargiela 1997;Labonte 1997;Xia et al 1999;Lin et al 2000;Zhang 2006). For example, an inequality-based criterion/constraint has been recently proposed, introduced and investigated by Zhang et al for obstacle avoidance of redundant robot manipulators (Zhang & Wang 2004), which is used to generate escape velocities of variable magnitude, and then drive the affected links away from obstacles.…”

“…linear programmes), which are then solved by using classical methods, e.g. the simplex method and the penalty method (Xia et al 1999;Lin et al 2000).…”

“…Because of the parallel distributed nature and the suitability for hardware realization, neural networks have been proposed, developed and studied for scientific research and engineering applications (Ramasamy et al 1995;Cichocki & Bargiela 1997;Labonte 1997;Xia et al 1999;Lin et al 2000;Liao et al 2002;Zhang et al 2002;Novo et al 2005;Zhang & Ge 2005;Chetwynd et al 2006;Yu et al 2007;Liu 2009;Zhang & Li 2009;Li & Zhang 2010;Guo et al 2011;Kaslik & Sivasundaram 2011), drawing extensive interest and investigation by researchers. Recently, owing to in-depth research on neural networks, the artificial neural-dynamic approach based on recurrent neural networks has been viewed as a powerful alternative to online solution of LMIs as well as LMVIs.…”

A Review on Neural Dynamics for Robot Autonomy

“…[1][2][3][4][5] Neural networks usually possess the characteristics of adaptivity, nonlinearity, parallelism and distributed storage, which can be used to solve the complicated problems that can not be solved by other approaches. [6][7][8][9] Specifically, the applications of neural networks including (but not limited to) the pattern classification, [10,11] deep learning, [12,13] approximation and prediction, [14,15] image processing, [16,17] machine learning, [18,19] optimization and computation, [20,21] complex system control [22][23][24] (including the robot system control). [25,26] Due to the extensive and significant applications of neu-ral networks, the development and investigation of neural networks have become common and heated topics for the researchers in biology, mathematics, physics, and computer science.…”