A ZNN-Based Solver With Adaptive Input Range Fuzzy Logic System for Time-Varying Algebraic Riccati Equation

Time-varying algebraic Riccati equations (TAREs) indeed play a crucial role in science and engineering with widespread applications. This research combines the advantages of zeroing neural network (ZNN) in handling time-varying problems with the flexibility of fuzzy logic system (FLS), proposing a ZNN-based solver for solving the TARE. One of the innovations of this paper is the presentation of an adaptive input range fuzzy logic system (AFLS) with portability and adaptability, offering a novel approach for determining the input range of the FLS. The method effectively resolves the current dilemma of relying on a specific problem and model for determining the FLS input range. Additionally, to enhance convergence speed and achieve predefined-time convergence of the fuzzy predefined-time robust zeroing neural network (FPRZNN) model, we introduce a novel segmental predefined-time robust activation function (SPRAF). Furthermore, three key theorems are proposed to prove the stability, convergence, and robustness of the FPRZNN model. Finally, the numerical simulations showcase the superior convergence and robustness of the FPRZNN model compared to other existing ZNN models.