Adaptive learning control with spatially-periodic and unknown random disturbances

This paper presents a design scheme of adaptive learning controller for the simple second-order dynamic systems with spatially-periodic disturbance as well as random unknown disturbance. The paper develops a robust adaptive learning controller in the presence of random disturbance on a spatial domain; then it provides a new design strategy for a continuously forward moving of the system. Mainly, the paper attempts to find a point along a spatial domain where the boundary of the speed error is specified. It will be shown that there always exists the point where the speed error is reduced within the specified value. Through a numerical test, the validity of the proposed schemes is evaluated.