A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations

This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications.

[1]  Fation Sevrani,et al.  On the Synthesis of Brain-State-in-a-Box Neural Models with Application to Associative Memory , 2000, Neural Computation.

[2]  Malur K. Sundareshan,et al.  Exponential stability and a systematic synthesis of a neural network for quadratic minimization , 1991, Neural Networks.

[3]  Jun Wang,et al.  A recurrent neural network for solving linear projection equations , 2000, Neural Networks.

[4]  Jun Wang,et al.  A dual neural network for kinematic control of redundant robot manipulators , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[5]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[6]  吉川 恒夫,et al.  Foundations of robotics : analysis and control , 1990 .

[7]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[8]  Zhang Yi,et al.  Estimate of exponential convergence rate and exponential stability for neural networks , 1999, IEEE Trans. Neural Networks.

[9]  N. Kalouptsidis Signal Processing Systems: Theory and Design , 1997 .

[10]  Jun Wang,et al.  A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits , 2003, IEEE Trans. Neural Networks.

[11]  Fan-Tien Cheng,et al.  Resolving manipulator redundancy under inequality constraints , 1994, IEEE Trans. Robotics Autom..

[12]  J. Pang,et al.  On a Generalization of a Normal Map and Equation , 1995 .

[13]  Richard M. Golden,et al.  Mathematical Methods for Neural Network Analysis and Design , 1996 .

[14]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[15]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[16]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.