A sampled-data iterative learning control using fuzzy network design

In this paper, a sampled-data iterative learning controller using fuzzy network design is proposed for a class of non-linear uncertain systems. In the first part of the paper, sufficient condition for feedforward learning gain is derived to guarantee convergence and robustness of the learning system. The sup-norm rather than traditional lambda-norm is adopted to develop a new technique for performance analysis. It is shown that tracking error is bounded at each sampling instant for a small sampling period and asymptotically converges to a small residual set. In order to implement the learning gain, we need the information of input-output coupling matrix of the non-linear system. In the second part of this paper, a fuzzy network is proposed to solve the implementation problem. The fuzzy rule base is designed based on if-then rules of Takagi and Sugeno's type so that the fuzzy network can provide the information of input-output coupling matrix. The premise and consequent parameters are tuned by gradient descent and least squares estimate respectively. An off-line training procedure is applied to estimate the non-linear plant by using only input-output data. This will give an initial setting of the sampled-data iterative learning controller. During the control interval, the fuzzy network can also be tuned after each iteration in order to improve the approximation accuracy and increase the tracking speed.