Probability-Guaranteed Filtering for 2-D Nonlinear Systems Over Full-Duplex Relay Network With Energy Harvesting Constraint
针对二维非线性时变系统，研究在全双工中继网络和能量收集约束下的概率保证滤波问题，设计滤波器以概率椭球约束估计误差，并通过递归线性矩阵不等式给出存在条件和优化算法。
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.