Recursive identification of nonlinear nonparametric systems under event-triggered observations

In the paper, recursive identification of the nonlinear nonparametric system is considered, where measurements for identification are subject to an event-triggered scheme and the system itself is of a finite impulse response (FIR) type. First, an adaptive event detector is designed and the measurements for identification are transmitted depending whether the value of the detector is 1 or 0. Second, a recursive identification algorithm is proposed with the help of a kernel-based stochastic approximation algorithm with expanding truncations (SAAWET). Third, under some reasonable assumptions, the estimates are proved to be strongly consistent, i.e., converging almost surely to the values of the unknown function in the system at any fixed points, and the transmission rate of the detector is analyzed as well. Finally, numerical examples are given to justify the theoretical results.