Fractional Sliding-Mode Control for Microgyroscope Based on Multilayer Recurrent Fuzzy Neural Network

In this article, an approximation-based adaptive fractional sliding-mode control (SMC) scheme is proposed for a microgyroscope, where a double-loop recurrent fuzzy neural network (DLRFNN) is employed to approximate system uncertainties and disturbance. A fractional-order term is incorporated into the sliding surface that could add an extra degree of freedom and combine the advantages of fractional calculus and SMC. A new four-layer fuzzy neural network (FNN) is studied, which has two feedback loops (internal feedback loop and external feedback loop) to capture the weights and output signal calculated in the previous step and use it as a feedback signal for the next step. On the one hand, the proposed DLRFNN structure combines a fuzzy system to process uncertain information with a neural network to learn from the process. On the other hand, both the internal state information and the output signal are acquired and stored so that better approximation performance is obtained compared with a regular FNN system. Furthermore, the adaptive laws of DLRFNN parameters are derived, which can automatically update free parameters with a bound. Finally, the effectiveness of the proposed adaptive fractional SMC using the DLRFNN strategy is identified by the simulations' analysis with different fractional orders, whereby tracking errors are uniformly ultimately bounded. The proposed adaptive fractional SMC using the DLRFNN strategy can achieve remarkably superior tracking performance in terms of high precision and fast response by comprehensive comparisons.