Probability-Guaranteed Filtering for 2-D Nonlinear Systems Over Full-Duplex Relay Network With Energy Harvesting Constraint

This article studies the problem of probability-guaranteed filtering for a class of nonlinear two-dimensional (2-D) shift-varying systems. Motivated by the high-demand for efficient long-distance wireless communication, a full-duplex relay network operating under a decode-and-forward strategy is applied within the 2-D framework. Additionally, an extended energy harvesting scheme is introduced to address the limitations of energy storage and supplement during the signal forwarding process. This article aims to design an appropriate filter for estimating the states of the objective 2-D systems. Unlike previous studies that focus on precise filtering at high-costs, this research incorporates an ellipsoidal constraint in a probabilistic sense to describe the dynamics of the estimation errors, which can better meet more filtering requirements and is more intuitive for practical engineering applications. Based on this, sufficient conditions are established by recursive linear matrix inequalities to ensure the existence of such a filter. Furthermore, an optimized algorithm is proposed to minimize the ellipsoidal bound of the estimation error, and a sequence of optimal filter gains is calculated. Finally, a numerical example is provided to demonstrate the feasibility of the proposed filtering method.