Solving Quadratic Programming By Neural Networks And Stability Analysis

Artificial neural network as a new subject, which has the very strong nonlinearmapping capability, parallel information processing, optimization calculation andassociative memory. So it plays a very important role in nonlinear science. Due to timedelay exists, it is necessary that we bring the time delay into system in order to ensure thesystem maintaining stability. Paper from quadratic programming with linear constraints,considering the constraint conditions of the interval and existence of the time delay, twokinds of solving quadratic programming problems neural network with linear constraintsare proposed. From the fuzzy rules, the interference factors and the effect of the mixeddelay, the fuzzy neural network with mixed time-varying delays is proposed. Main work isas follows:Firstly, an approach of solving interval quadratic programming problems with linearconstraints is considered. Based on Saddle point theorem, the equilibrium point of theneural network is proved to be equivalent to the optimal solution of the interval quadraticprogramming problems. The global exponential stability of the proposed neural network isanalyzed in terms of a Lyapunov approach. Two illustrative examples are provided toillustrate the usefulness and the efficiency of the theoretical results.Secondly, a class of neural networks with time varying delays is proposed to solvequadratic programming problems with linear constraints. Based on Lyapunov stable theoryand linear matrix inequality, two criteria for exponential of the Lagrange network areestablished.Thirdly, we analyze a class of global robust asymptotic stability for fuzzyCohen-Grossberg neural networks with mixed time-varying delays. By constructing aLyapunov function, using the linear matrix inequality and theory T-S fuzzy model will beexpanded to Cohen-Grossberg neural networks with mixed time-varying delays and givesthe sufficient condition of the global robust asymptotic stability of the system. Finally,through the simulation example shows the effectiveness of the conclusion.