In-Network Distributed Identification of Wiener and Volterra-Laguerre Models for Nonlinear Systems

Abstract

Distributed estimation over wireless sensor networks (WSNs) has been used to obtain the parameters of interest with reduced resource consumption, hence gained importance in system modeling and control applications. Unlike least-squares and fusion-center based approaches, distributed signal processing is competent in real-time applications. In this article, VolterraLaguerre model and Wiener model are identified in a distributed manner through WSNs for modeling of nonlinear systems. A block-structured Wiener model has been widely used as it is characterized by a small number of parameters, but can only model specific nonlinearities. A generalized Volterra model over Wiener model can approximate any nonlinear system to a desired precision but has increased parameter complexity. By expanding nonlinear Volterra kernels with orthogonal Laguerre functions, the parameter complexity is reduced significantly. A distributed recursive algorithm for the identification of abovementioned nonlinear models is designed by minimizing the quadratic prediction error. The algorithm reformulates model identification framework into multiple constrained separable subtasks. These subtasks are optimized using a powerful method called alternating direction method of multipliers. Simulation results for an infinite-order and a 2 nd-order nonlinear systems are obtained under the influence of process noise and are compared with the results of non-cooperative estimation showing the superiority of the proposed algorithm.