Reduced-Order Observer-Based Event-Triggered Adaptive Fuzzy Backstepping Control of Uncertain Fractional-Order Strict Feedback Nonlinear Systems

In this paper, a reduced-order observer-based event-triggered adaptive fuzzy backstepping control method is proposed for addressing the tracking control of uncertain fractional order nonlinear systems with unmeasurable states. The design incorporates the utilization of fuzzy logic systems to estimate unknown functions within the backstepping scheme, while also addressing the issue of complexity explosion by introducing a fractional-order command filter. Furthermore, an effective error compensation mechanism is developed to reduce filter errors. In particular, a reduced-order observer is reconstructed to estimate unmeasurable states, avoiding redundant estimation of known output states, thus achieving better estimation performance under the same input. The controller design guarantees the convergence of the tracking error to a small neighborhood around the origin, while also ensuring that all signals are semiglobal uniformly ultimately bounded, and it effectively prevents Zeno behavior. To validate the effectiveness and accuracy of the proposed approach, numerical comparison simulations are conducted.