| The design of a feedback control such that the output of the closed-loop system is not at all affected by unknown disturbances is called the problem of disturbance decoupling. Generally, disturbance decoupling requires the controlled system should satisfy some certain geometric conditions, which are too restricted for many practical systems. When such conditions fail, it is natural to address the problem of almost disturbance decoupling, that is the design of a feedback control which attenuates the influence of the disturbance on the output up to an arbitrary degree. Although much progress has been made in the research on almost disturbance decoupling, to the best of our knowledge, there has been no report about the problem of almost disturbance decoupling of nonlinear systems with unmodeled dynamics. On the other hand, many methods have been presented to handle the unmodeled dynamics. It has been proved that a modified dynamic signal is a useful tool in handling of unmodeled dynamics.In this paper, a novel definition of robust almost disturbance decoupling is first introduced for the tracking control problem of a class of single-input/single-output nonlinear systems with unmodeled dynamics and bounded time-varying disturbances. Based on the definition, a dynamic signal is used to dominate the unmodeled dynamics, and adaptive nonlinear damping terms are presented to counteract the effects of the unknown parameters and nonlinear uncertainties. The control law isobtained by the transformation of coordinates and the construction of Lyapunov function. It is shown that under certain assumptions, the proposed control law guarantees the realization of the nonlinear tracking in the presence of unmodeled dynamics and bounded time-varying disturbances. Furthermore, the tracking error can be made arbitrarily small by choosing the design constants appropriately. Simulation examples demonstrate that the proposed definition and control scheme are very effective.
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