FSE-RBFNN-Based AILC of Finite Time Complete Tracking for a Class of Time-Varying NPNL Systems with Initial State Errors

The paper proposed an adaptive iterative learning control (AILC) strategy for the unmatched uncertain time-varying nonparameterized nonlinear systems (NPNL systems). Addressing the difficulty of nonlinear parameterization terms in system models, a new function approximator (FSE-RBFNN) which is combined with radial basis function neural network (RBFNN) and Fourier series expansion (FSE) is introduced to model each time-varying nonlinear parameterization function. Using adaptive backstepping method to design control laws and parameter adaptive laws. As the number of iterations increases, the maximum tracking error gradually decreases until it converges to zero on the entire given interval 0,T according to the Lyapunov-like synthesis. A updated time-varying boundary layer is introduced to eliminating the impact of initial state errors. Introducing a series to deal with the unknown error upper bounds. Finally, two simulation examples demonstrate the correctness of the proposed control method.