Stability analysis of proportional delayed projection neural network for quadratic programming problem

Abstract

At present, projection neural network (PNN) with bounded time delay has been widely used for solving convex quadratic programming problem (QPP). However, there is little research concerning PNN with unbounded time delay. In this paper, we propose the proportional delayed PNN to solve QPP with equality constraints. By utilizing homeomorphism mapping principle, we prove the proportional delayed PNN exists with unique equilibrium point which is the optimal solution of QPP. Simultaneously, delay-dependent criteria about global exponential stability (GES) and global polynomial stability (GPS) are also acquired by applying the method of variation of constants and inequality techniques. On the other hand, when proportional delay factor [Formula: see text] is equal to 1, the proportional delayed PNN becomes the one without time delay which still can be utilized for solving QPP. But in most situations, [Formula: see text] is not equal to 1, and time delay is unpredictable and may be unbounded in the actual neural network, which causes instability of system. Therefore, it is necessary to consider proportional delayed PNN. A numerical example demonstrates that, compared with the proportional delayed Lagrange neural network, the proportional delayed PNN is faster in terms of convergence rate. The possible reason is that appropriate parameters make the model converge to the equilibrium point along the direction of gradient descent.