In-Network Distributed Least Mean Square Identification of Nonlinear Systems using Volterra-Laguerre Model

It is of great importance to model the behavior of nonlinear systems in a distributed fashion using wireless sensor networks (WSNs) because of its computation and energy-efficient data processing. However, least squares methods have been previously employed to estimate the parameters of Volterra model for modeling nonlinear systems. Still, it is more convenient and advantageous to use in-network distributed identification strategy for real-time modeling and control. In this context, a black-box model with generalized structure and remarkable modeling ability called Volterra-Laguerre model is considered in which distributed signal processing is employed to identify the nonlinear systems in a distributed manner. The model cost function is expressed as a separable constrained minimization problem which is decomposed into augmented Lagrangian form to facilitate the distributed optimization. Then, alternating direction method of multipliers is employed to estimate the optimal parameters of the model. Convergence of the algorithm is guaranteed by providing its mean stability analysis. Simulation results for a nonlinear system are obtained under the noisy environment. These results are plotted against the results of noncooperative and centralized methods, demonstrating the effectiveness and superior performance of the proposed algorithm.