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The paper proposes a low-pass filter adaptive iterative learning control (LPF-AILC) strategy for unmatched, uncertain, time-varying, non-parameterized nonlinear systems (NPNL systems). To address the difficulty of nonlinear parameterization terms in system models, a new function approximator (FSE-RBFNN), which combines the radial basis function neural network (RBFNN) and Fourier series expansion (FSE), is introduced to model each time-varying nonlinear parameterized function. The adaptive backstepping method is used 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, along with a series to deal with the unknown error upper bounds. Finally, two simulation examples prove the correctness of the proposed control method.

A new adaptive iterative learning control (AILC) scheme is proposed to solve the finite-time hybrid function projective synchronization (HFPS) problem of chaotic systems with unknown periodic time-varying parameters. Fourier series expansion (FSE) is introduced to deal with the problem of uncertain time-varying parameters. The bound of the expanded remaining items is unknown. A typical convergent series is used to deal with the unknown bound in the design process of the controller. The adaptive iterative learning synchronization controller and parameter update laws are designed. Two different chaotic systems are synchronized asymptotically according to different proportional functions on a finite time interval by Lyapunov stability analysis. The simulation example proves the feasibility and effectiveness of the proposed method.

Based on a neural network, this paper presents a new adaptive iterative learning control method for the finite-time tracking control problem of an uncertain aircraft track angle system, which can control the aircraft track inclination through the designed control input rudder deflection angle, so that it can track the preset trajectory in a finite time interval. First, the flight path angle system of the aircraft is abstractly modeled by variable substitution to obtain a triangular model in the form of strict feedback. Second, radial basis function neural network approximation is used to model the uncertain part of the system, aiming at the abstract strict feedback model, and two virtual quantities are designed through the three-layer inversion design method, and then, Lyapunov functions are designed for each subsystem to derive virtual control laws, the actual control law, and the neural network weight adaptive laws. Through Lyapunov stability analysis, it can be seen that the designed controller and adaptive laws can make the whole closed-loop system tend to be stable and realize the tracking of a target trajectory in a finite time interval. Finally, the feasibility and effectiveness of the theory are verified by a simulation example.