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ADMM Based Distributed Volterra Modeling of Nonlinear Dynamical Systems Using Ad-Hoc WSNs

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, Volterra model is considered for the modeling of nonlinear systems because of its significant modeling capability and generalized nonlinear structure. For real-time estimation of the Volterra model parameters, a simple distributed algorithm is designed for a particular framework of WSNs having predefined bridge sensor nodes. 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. The convergence analysis is provided to guarantee the mean stability of the proposed algorithm. Simulation results obtained under the noisy environment are plotted to demonstrate the effective performance of the proposed algorithm.