OPTIMAL REJECTION OF PERSISTENT BOUNDED DISTURBANCES

The problem of optimal disturbance rejection is formulated in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary. The objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance. Mathematically, this corresponds to requiring uniformly good disturbance rejection over all time. Since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used, the theory presented can also be used to design optimal controllers that achieve uniformly good tracking over all time. Complete solutions to the problem are given in several important cases, including those where the plant is minimum phase or when it has only a single unstable zero. In other cases, procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers.