DESIGNS OF LEARNING CONTROLLERS BASED ON AUTOREGRESSIVE REPRESENTATION OF A LINEAR-SYSTEM

Learning controllers that improve tracking performance through repeate d trials are derived. The design is based on an autoregressive represe ntation of a linear system. This input-output model can be interpreted in terms of an observer in state-space form. The control input is mod ified at every repetition as the system learns to produce a desired re sponse, even in the presence of unknown repetitive disturbances. The c oefficients of a nominal autoregressive model are first identified fro m input-output data. Using the identified coefficients, simple linear feedback learning controllers are designed that can correct for the er rors that remain. An optimal learning gain matrix is also derived give n the identified model. Numerical examples are provided to illustrate the proposed learning approach.