Learning control for trajectory tracking using basis functions

This paper proposes an iterative learning method that makes the output of a general linear time-varying system with unknown coefficients track a finite-time reference trajectory. The system learns by repeated trials, each starting from the same initial conditions. Data from multiple trials can used to identify a model of the system during the finite time interval of interest. A learning controller is then designed from the identified model. If the identification is perfect, the necessary control can be computed directly from the identified model, and there is no need for learning. If the identification is not perfect, the remaining error can be corrected by learning control. By the use of input basis functions, this formulation shows that one need to perform the identification only in a portion of the system dynamics relevant to the specific trajectory to be tracked for successful learning.