Generalized Trackability Analysis of Learning Control Systems: A Frequency-Domain Method

For learning control systems operating repetitively over a fixed time interval, the iterative methods are effective in accomplishing the perfect tracking task of a specified trajectory, resulting in the methodology of iterative learning control (ILC). In the classic ILC framework, three key steps are often involved: 1) making necessary hypotheses over ILC systems, 2) designing the ILC algorithms, and 3) establishing convergence conditions. However, a basic trackability problem is neglected: whether there exist some inputs that drive the ILC system such that the output is identical to the specified trajectory from beginning to end. This article is targeted at addressing the trackability problem and the related ILC design and analysis issues for continuous-time linear systems subject to vector relative degrees. The frequency-domain criteria are developed to determine the trackability of the given trajectory. In addition, the ILC design and analysis are proposed by utilizing a frequency-domain method, which establishes a close connection between the achievement of the perfect tracking tasks in ILC and the trackability of the given trajectory. Two examples are utilized to confirm the effectiveness of our trackability-based ILC results.