Fuzzy Neural Network-Based Adaptive Sliding-Mode Descriptor Observer

This study examines the state estimation problem for uncertain descriptor systems subject to unknown dynamics. An integration of interval type-2 fuzzy set (IT2-FS) and cerebellar model articulation controller (CMAC) neural network, called the IT2-FCMAC approximator, is introduced to approximate the unknown dynamics and is incorporated into a sliding-mode descriptor observer. Then, its learning problem is cast into a robust control framework subject to discrete-time nonlinear systems, and a robust $\mathcal {H}_{\infty }$ control-based learning algorithm is proposed. Besides, an adaptive compensator is introduced to mitigate the impact of approximation error. An IT2-FCMAC-based adaptive sliding-mode observer is developed and the calculation of observer gain and learning parameters is solved by several linear matrix inequalities (LMIs). The proposed scheme is applied in estimating the state of charge (SOC) of lithium-ion batteries, showcasing its exceptional performance.