Data-Efficient Static Cost Optimization via Extremum-Seeking Control with Kernel-Based Function Approximation

We present a novel type of sampled-data extremum-seeking control (ESC) aimed at speeding up convergence to the optimum and reducing the number of costly performance measurements in practical applications. The approach uses collected output measurements to construct online an approximation of the system's steady-state performance function using kernel-based function approximation. In regions where this approximation is detected to be sufficiently accurate, the proposed approach utilizes it to determine the search direction and compute a suitable optimizer gain for the update step. In regions where the approximation is not yet accurate, additional data is collected and employed in a ‘standard’ ESC update step, while also using it to refine the approximation of the performance function. By using the approximation of the performance function to determine the search direction and optimizer gain when possible, the number of required performance measurements and parameter update steps can be significantly reduced, e.g., with respectively 75% and 45 % in our simulation study involving a static cost function.