State Estimation for Nonlinear Complex Dynamical Networks With Random Coupling Strengths: A Decode-and-Forward Relay-Based Strategy

This article is concerned with the finite-horizon $H_{\infty}$ state estimation problem for a specific class of nonlinear complex dynamical networks (CDNs) which are subject to random couplings and packet dropouts. The random coupling strengths among network nodes are characterized by a set of random variables with known statistical information. Three sequences of Bernoulli distributed random variables are utilized to model the packet dropouts over different communication channels. A decode-and-forward relay-based strategy is implemented to enhance the quality of communication by controlling the signal transmission in each sensor-to-estimator channel. The primary goal of this investigation is to create an appropriate state estimator for each node of the CDN, enabling the fulfillment of a specific $H_{\infty}$ performance requirement for the estimation error dynamics over a finite horizon. Through the use of stochastic analysis techniques and matrix operations, a preliminary sufficient condition is given to meet the finite-horizon $H_{\infty}$ performance requirement. The expected estimator gains are subsequently determined, which are defined in terms of the solutions to a series of recursive matrix inequalities. The effectiveness of the proposed relay-based estimation scheme is ultimately demonstrated through a numerical example.