A low-pass filtered FSE–FLS adaptive iterative learning control strategy for mismatched uncertain time-varying non-parameterized nonlinear systems with inconsistent initial state

A low-pass filtering-adaptive iterative learning control approach is developed to address mismatched, uncertain, and time-varying non-parameterized nonlinear systems, aiming to achieve precise tracking over a finite time span. To overcome challenges in parameterized nonlinear terms within the system model, an innovative function approximator integrating fuzzy logic systems (FLS) with Fourier series expansion (FSE), termed FSE–FLS, is introduced to represent various time-varying nonlinear parameterized functions. Following Lyapunov theory, the controller design and parameter adaptation rules are established. In the course of controller design, excessive derivatives may trigger parameter explosion after differentiation. To counter this, a first-order low-pass filter is applied to reduce such issues and streamline the controller’s structure. According to Lyapunov synthesis, as the iteration count grows, the peak tracking error progressively diminishes, approaching zero across the entire interval [0, T]. To reduce the impact of mismatched initial states, a time-varying boundary function is adopted to manage the unknown upper bound of the error. Finally, the validity and performance of the proposed control framework are confirmed through two simulation studies.