In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.
This paper is concerned with the problem of passivity analysis and passification for a class of stochastic impulsive memristor-based piecewise linear (PWL) systems with mixed delays and nonlinearity disturbances. Based on the PWL memristor, a PWL system is set up. And some novel sufficient conditions are derived to ensure the passivity/passification performance, such that, for all admissible stochastic disturbances and nonlinearity, the closed-loop stochastic impulsive memristor-based PWL system is passive in the sense of expectation. Copyright (c) 2013 John Wiley & Sons, Ltd.