Distributed Least Mean Square Volterra Model for the Identification of Nonlinear Systems Using WSNs

Abstract

Many practical systems that we encounter involve some extent of nonlinearity in their behavior. Identification and control design of nonlinear systems is achieving increasing attention in practical applications. Mathematical models play a significant role in the development identification and control techniques for such nonlinear systems. In this work, Volterra model is considered for modeling nonlinear systems because of its simple structure and significant modeling capability. The simple and computationally efficient LMS based approach is considered for adaptive estimation of model parameters. The challenging problems involved with the stability and convergence rate of traditional least mean square based approach are demonstrated individually. The leaky-LMS and modified leaky-LMS based estimation of Volterra model parameters are employed to address the weight-drifting and slow convergence issues respectively. The effectiveness of above solutions is demonstrated with the help of appropriate simulation example and results. To incorporate the benefits of cooperation network of wireless sensor nodes is considered for deployment across the system under consideration. To model the behavior of nonlinear dynamical systems using wireless sensor networks (WSNs), the development of computation and energy efficient distributed modeling techniques is of crucial importance. In this work, for real-time estimation of the Volterra model parameters, a simple distributed Volterra LMS algorithm is designed using ADMM. The pertinent cost function is expressed as an unconstrained minimization problem using a decomposable augmented Lagrangian form. To facilitate the distributed convex optimization, the augmented Lagrangian form is minimized using alternating direction method of multipliers. The communication and computational complexities involved in the proposed methodology are provided to show its effectiveness in the real-time applications over centralized and non-cooperative solutions. Simulation results obtained under the noisy environment are plotted to demonstrate the effective performance of the distributed algorithm.