A dynamic neural network approach for solving nonlinear inequalities defined on a graph and its application to distributed, routing-free, range-free localization of WSNs

In this paper, we are concerned with the problem of finding a feasible solution to a class of nonlinear inequalities defined on a graph. A recurrent neural network is proposed to tackle this problem. The convergence of the neural network and the solution feasibility to the defined problem are both theoretically proven. The proposed neural network features a parallel computing mechanism and a distributed topology isomorphic to the corresponding graph. Thus it is suitable for distributed real-time computation. The proposed neural network is applied to range-free localization of wireless sensor networks (WSNs). The analog circuit implementation of the neural network for such an application is also explored. Simulations demonstrate the effectiveness of the proposed method.