Sliding Mode Control Techniques in E-Learning Systems

Mathematical Model Of Learning Dynamics

The fundamental idea of control in learning is to reach the highest level of effectiveness in undertaking a task, which happens when individual’s ability level is congruent with the level of challenge. We associate the degree of challenge with control and denote it as u(t), and denote the individual’s ability as d. When the task challenge is equal (matched) to the individual’s ability the most efficient learning can be achieved. In the case when u>d, stress or anxiety occurs and efficiency of learning is decreased. In the case when d<u, students become bored, and efficiency of learning is decreased too. Because it is practically impossible to design a course ideally matching individual’s ability (not only for technical reasons, but also because this ability is not known a-priori but identified in the process of learning) the adjustment of challenge can only be done in a discontinuous manner by alternating some more and some less challenging tasks. The way they are alternated, or the ratio between more challenging and less challenging tasks, is determined on the basis of feedback received through evaluation of the tasks.