Bridging learning control and repetitive control using basis functions

Learning control aims at improving the tracking accuracy of a repetitive operation where the system is designed to return to the same initial condition before beginning the next repetition. Repetitive control, in contrast, deals with system executing a periodic command continuously without initial condition resetting. It appears that this distinction causes considerable difference between how learning control and repetitive control are treated in the literature. However, it has been observed in actual experiments that the distinction is not as pronounced as it seems mathematically. In this paper, we show how the repetitive control problem can be turned into a learning control problem through the use of basis functions. Repetitive disturbances may be present and unknown. We also examine the issue of observation and control spillover and show that by working in the basis function space, observation spillover is automatically eliminated. When matched basis functions are used, control spillover is also eliminated. The matched basis functions also eliminate the need to know a model of the system before hand. Instead, they are obtained experimentally. With wavelets, the process of extracting the matched basis functions experimentally becomes extremely efficient. Numerical examples are used to illustrate the key findings.