Data-efficient extremum-seeking control using kernel-based function approximation

Existing extremum-seeking control (ESC) approaches typically rely on repeatedly perturbing input parameters and measuring the corresponding performance output. The required separation between the different timescales in the ESC loop makes performing these measurements a time-consuming task. Moreover, performing measurements can be costly in practice, e.g., due to the use of resources. With these challenges in mind, it is desirable to reduce the number of measurements needed to optimize performance. Therefore, in this work, we present a sampled-data ESC approach aimed at achieving such a reduction. In the proposed approach, we use input–output data obtained during regular operation of the extremum-seeking controller to construct online a kernel-based approximation of the system’s underlying cost function. By using this approximation to perform parameter updates when a decrease in the cost can be guaranteed, instead of performing additional measurements to perform this update, we make more efficient use of data collected during regular operation of the extremum-seeking controller. As a result, we indeed obtain a reduction in the number of measurements required to achieve optimization. We provide a stability analysis of the novel sampled-data ESC approach, and demonstrate the benefits of the synergy between kernel-based function approximation and standard ESC in simulation on a multi-input dynamical system.