Research On Iterative Learning Control Based On Two-dimensional Uncertain Discrete Systems

Two-dimensional(2-D) discrete systems has aroused great attention and widely applied to industrial fields owing to its profound background of Engineering Physics in recent decades. Meanwhile, theoretical research of 2-D discrete systems are constantly abundant laying the foundation for further research. In addition, uncertainty or disturbance will probably affect the systems performance and bring about control difficulties. So the control research of 2-D uncertain discrete systems are greatly provided with theoretical significance and application value.Since Japanese scholars Arimoto, etc clearly stated it, Iterative Learning Control (ILC) has become an important part of intelligent control after in twenty years of research, gradually becoming a new research direction in control theory. Due to the iterative learning process is carried out simultaneously along two independent directions(time and cycle),ILC is essentially a 2-D system, which using its theory analyze and solve the problems of ILC.The main idea in this paper is:firstly, the closed-loop system on the effect of ILC is transformed into a 2-D system; afterward, the stability issue of the original close-loop system is converted correspondingly. Therefore, based on 2-D system model and Lyapunov stability theory and combing ILC technique, we consider the issue of stability analysis and controller design with regarding to a series of specific discrete systems with uncertainty. The obtained results are formulated in terms of the linear matrix inequalities (LMIs).The detailed contents of this paper are as follows:(1) The problem of stabilization is addressed for the discrete systems with uncertainty by designing fuzzy closed-loop iterative learning controller. A sufficient criterion is obtained to ensure the closed-loop system to have the characteristics of asymptotic stability establishing positive piecewise Lyapunov functions based on Lyapunov stability theory. Finally, a numerical simulation example is provided to ensure the effectiveness of the results.(2) The problem of stabilization is discussed for the discrete systems with uncertainty and state delay. According to Lyapunov stability theory, a 2-D iterative learning controller with state feedback is designed to guarantee the systems to be asymptotically stable on basis of positive Lyapunov-Krasovskii functions. The results are shown, via a numerical example, to be applicable at last.(3) The problem of robust stabilization is considered for the uncertain discrete systems with iteration-varying disturbances. Based on Lyapunov stability theory, a feedback-feedforward ILC scheme is proposed, which to guarantee the systems to be robust mean-square asymptotically stable. The results obtained is demonstrated to be valid via a numerical simulation example.