  For general nonlinear control systems we present a novel approach to adaptive
control, which employs a certainty equivalence (indirect) control law and an
identifier with event-triggered updates of the plant parameter estimates, where
the triggers are based on the size of the plant's state and the updates are
conducted using a non-recursive least-squares estimation over certain finite
time intervals, with updates employing delayed measurements of the state. With
a suitable non-restrictive parameter-observability assumption, our adaptive
controller guarantees global stability, regulation of the plant state, and our
identifier achieves parameter convergence, in finite time, even in the absence
of persistent excitation, for all initial conditions other than those where the
initial plant state is zero. The robustness of our event-triggered adaptive
control scheme to vanishing and non-vanishing disturbances is verified in
simulations with the assistance of a dead zone-like modification of the update
law. The major distinctions of our approach from supervisory adaptive schemes
is that our approach is indirect and our triggering is related to the control
objective (the regulation error). The major distinction from the classical
indirect Lyapunov adaptive schemes based on tuning related to the regulation
error is that our approach does not involve a complex redesign of the
controller to compensate for the detrimental effects of rapid tuning on the
transients by incorporating the update law into the control law. Instead, our
approach allows for the first time to use a simple certainty equivalence
adaptive controller for general nonlinear systems. All proofs are given in a
companion paper.
