Deterministic Learning-Based Fault Identification for Nonlinear Sampled-Data Systems: Learning Accuracy Analysis

In this article, a sampled-data fault identification (SDFI) scheme for nonlinear uncertain systems is proposed based on the deterministic learning approach, and the learning performance of the SDFI algorithm is analyzed. First, a learning-based estimator is designed, and a sampled-data (SD) linear time-varying (LTV) system is employed to describe the learning systems. Second, by constructing a special time-varying symmetric positive definite matrix, the exponential convergence property of the SD LTV system is derived. Third, explicit formulas for learning accuracy are established, which illuminate the relation between the learning performance, persistent excitation (PE) level of neural networks (NNs), and the parameters of the learning system. The main advantage of the theoretical results given in this article is that the parameters in learning accuracy formulas can be derived from measurable signals, allowing for effective evaluation of the learning performance of the SDFI scheme in practical applications. Simulation studies of a robot manipulator and a compressor system are included to show the effectiveness of the proposed method.