FSE-RBFNN-based LPF-AILC of finite time complete tracking for a class of time-varying NPNL systems with initial state errors - Zhang, Chunli; Yan, Lei; Gao, Yangjie; Yao, Junliang; Qian, Fucai (Frontiers in Physics, 2024)
The paper proposed a low pass filter adaptive iterative learning control (LPF-AILC) strategy for the unmatched uncertain time-varying non-parameterized nonlinear systems (NPNL-systems). Addressing the difficulty of nonlinear parameterization terms in system models, a new function approximator (FSE-RBFNN) which is combined by radial basis function neural network (RBFNN) and Fourier series expansion (FSE) is introduced to model each time-varying nonlinear parameterizatied function. Using adaptive backstepping method to design control laws and parameter adaptive laws. In the process of controller design, we may encounter the problem of too many derivatives, which can cause parameter explosions after derivatives. Therefore, we introduce a first-order low-pass filter to solve this problem and simplify the structure of the controller. As the number of iterations increases, the maximum tracking error gradually decreases until it converges to the nearby region, approaching zero within the entire given interval [0, T ], according to the Lyapunov-like synthesis. To mitigate the impact of initial state errors, a dynamically changing boundary layer is introduced. Introducing a series to 1 * is the corresponding author.