Adaptive ILC Design for Nonlinear Discrete-time Systems With Randomly Varying Trail Lengths and Uncertain Control Directions

In this paper, an adaptive iterative learning control (ILC) design method is proposed for a class of non-linear discrete-time systems with nonaffine structure, randomly varying trail length, and uncertain control direction. In order to achieve repetitive tracking control of the nonaffine structure systems with uncertain control direction, randomly varying trail length, and other uncertainties, we apply a high-order neural network to approximate the expected system input. Then, a novel adaptation law is designed for the neural network weight vector. The main feature of the method proposed in this paper is that the weight vector norm instead of the weight vector itself is updated iteratively to realize the successive approximation of the expected system input, the custom-designed identification mechanism is not necessary to deal with the uncertain control direction, and the analysis of randomly varying trail lengths problem is strictly established. The convergence of the proposed adaptive ILC is set up by a composite energy function. The effectiveness of the proposed adaptive ILC design is validated by two simulation examples.