A new fractional‐order L1L₁ adaptive feedback control of dynamical systems: Design, stability analysis, and application

This study focuses on the development of a new fractional‐order adaptive feedback control strategy of dynamical systems. Specifically, the original adaptive controller is revisited based on the consideration of fractional‐order filters using the Oustaloup recursive approximation. To show the effectiveness and superiority of the proposed fractional‐order filter, a comparative study is conducted against classical integer‐order filters based on both time analysis using performance metrics such as the integral of absolute error (IAE) and energy consumption, and frequency analysis, including Nyquist criterion and stability margins. The proposed control scheme is validated, on an electro‐hydraulic system (EHS), through several numerical simulation scenarios to show enhanced performance and robustness. Results indicate up to 86% improvement in tracking performance compared to the original controller.