Adaptive control using reduced-order observers

In many practical situations uncertain plants are such that the unknown parameters do not affect the entire state of the system, but only some of the state variables. A question that arises in this context is the following: can a reduced-order adaptive observer be designed based only on the part of the dynamics affected by the uncertainty, such that, when the corresponding parameter estimates are used in the control law, the closed-loop stability is guaranteed? The related objective is to design the adaptive observer that has the number of adjustable parameters equal to the number of uncertain paramaters, and whose order coincides with the lowest-order subsystem affected by the uncertainty. In this paper a new systematic procedure is developed for the design of stable adaptive controllers using local reducedorder adaptive observers. It is shown that, for the class of plants considered in the paper, even when the unknown parameters are estimated using such lower-order observers, the resulting closed-loop system will be stable, and the asymptotic convergence of the tracking error to zero is guaranteed.