Adaptive Deep Neural Control for Fractional-Order Nonlinear Systems
摘要
In this article, a dynamic-memory event-triggered mechanism based on deep neural networks (DNNs) is proposed for fractional-order nonlinear systems. Fractional-order calculus provides a superior framework for modeling systems with memory effects and non-local behaviors. First, a DNN, with its complex multi-layer nested architecture and exceptional function approximation capabilities, is employed to approximate the unknown system dynamic. The weight update law is designed based on the first-order Taylor expansion to reduce mathematical complexity. Furthermore, the influence of historical information from internal dynamic variables on trigger conditions is considered in the dynamic-memory event-triggered mechanism, which more effectively reduces the consumption of system communication resources. Using the proposed controller, it can be demonstrated that the follower successfully tracks the specific trajectory established by the leader. Finally, the effectiveness of the proposed algorithm is verified through both stability analysis and simulation results.