Adaptive linear control of nonlinear systems

The theory of stable parameter adaptive control has advanced to allow linear time-varying plants. However, a more honest view of such systems is that they are often derived from inexact linearization about a trajectory of a nonlinear system. Then standard adaptive control based on a linear model can be interpreted as one way to realize a nonlinear controller for a nonlinear plant. The implications of this view are studied. Analytically, the stability problem is seen to be equivalent to showing robustness to time-varying parameters and a locally bounded model uncertainty. It is shown that if the trajectory is known to be within a bound, a parameter estimator with projection can ensure boundedness of departures from the trajectory.