Iterative Learning Sliding Mode Control of Continuous-Time Systems via 2D System Approach

In this paper, the iterative learning sliding mode control problem of one-dimensional (1D) continuous-time systems is addressed based on two-dimensional (2D) system approach. Firstly, the iterative learning process of 1D continuous-time systems is described by 2D continuous-discrete Roesser model and the corresponding 2D error system (including state error and output error) is obtained. Combining the characteristics of continuous and discrete-time systems, a novel reaching law is proposed, which is related to the derivative of the sliding function along the time direction and the difference of the sliding function along the iteration direction. Accordingly, the iterative learning sliding mode controller is provided, which not only reflect the influence of signals in both time and iteration but also guarantee the reachability of sliding domain. Based on 2D system theory, the desirable learning gain is designed to achieve the satisfactory system performance. Finally, a numerical example is presented to illustrate the effectiveness of the proposed control scheme.