Nonlinear Output Regulation

A classical problem in control theory is to impose, via feedback, a prescribed steady-state response to every external command in a given family. This may include, for instance, the problem of having the output of a controlled plant asymptotically track any prescribed reference signal in a certain class of functions of time, as well as the problem of having this output asymptotically reject any undesired disturbance in a certain class of disturbances. In both cases, the issue is to force a suitably defined tracking error to zero, as time tends to infinity, for every reference output and every undesired disturbance ranging over prescribed families of functions of time. Generally speaking, the problem can be cast as follows. Consider a finite-dimensional, time-invariant, nonlinear system modeled by equations of the form