  This paper proposes an event-triggered control scheme for multivariable
extremum seeking of static maps. Both static and dynamic triggering conditions
are developed. Integrating Lyapunov and averaging theories for discontinuous
systems, a systematic design procedure and stability analysis are developed.
Both event-based methods enable one to achieve an asymptotic stability result.
Ultimately, the resulting closed-loop dynamics demonstrates the advantages of
combining both approaches, namely, event-triggered control and extremum
seeking. Although we keep the presentation using the classical event-triggered
method, the extension of the results for the periodic event-triggered approach
is also indicated. An illustration of the benefits of the new control method is
presented using consistent simulation results, which compare the static and the
dynamic triggering approaches.
