Integral-based event-triggered extremum seeking of general nonlinear static maps under delays and multiplicative noise

This article presents an integral-based event-triggered extremum seeking control for n-dimensional general nonlinear static maps subject to time-varying measurement delay, communication delay and multiplicative measurement noise. Both static and dynamic integral-based event-triggered mechanisms are developed. These mechanisms provide a mathematically well-defined event-triggered implementation under continuous multiplicative measurement noise. They also reduce controller updates relative to the corresponding periodic implementation while excluding Zeno behaviour. An approximation-free representation of the closed-loop system is developed using the time-delay approach to averaging. Based on this representation, sufficient linear matrix inequality conditions are obtained to guarantee mean-square exponential ultimate boundedness of the closed-loop system. To validate the proposed results, a numerical example drawn from the literature is presented.