OPTIMAL REJECTION OF PERSISTENT AND BOUNDED DISTURBANCES - CONTINUITY PROPERTIES AND ADAPTATION

Continuity properties of the problem of optimal rejection of bounded persistent disturbances, otherwise known as l1-optimal control, are furnished for discrete-time, single-input, single-output systems. It is shown that for any plant with no zeros on the unit circle, the l1-optimal design is continuous as a map from the plant to the optimal closed-loop solution if the plant has a unique optimal solution. In the case of nonuniqueness, a super optimal criterion is proposed that will always lead to a unique solution; however, it still falls short of supplying continuity. A characterization of a general class of adaptive controllers in the presence of bounded disturbances is given. Using this characterization, an adaptive/robust scheme based on the l1 design methodology is proposed, and is shown to be globally convergent. This scheme is expected to improve the performance of the closed-loop system in the presence of disturbances. © 1990 IEEE