The problem of the adaptive compensation of a periodical input disturbance

Concerns the problem of linear plant stabilization in the presence of a deterministic unknown periodical external disturbance. The proposed approach is aimed at stabilization of the plant model in the presence of the periodical unknown input disturbance and based on the results obtained in the passivity theory. It ensures the asymptotic stability of the plant model and moreover the restoration of input disturbances. The presented results can have a wide application in the motion control of the multivariable plants along unknown geometric objects, e.g. analytical description of the path to be followed is not a priori given. Such a problem seems realistic and has a greater practical significance. The well known solution to the problem is based on a self-learning strategy that implies training trajectory motions and restoration of unknown functional components. As an illustrative example we consider adaptive control system design for the mobile wheeled robot.