Optimization of Surrogate function using Extremum Seeking Control

Real-time robust optimization of unknown expensive functions has been a challenging problem for data-driven based control applications. Most of the model-free control applications use function approximation technique based on measurements which makes it independent of the mathematical model. In surrogate optimization, the function is approximated using Gaussian Process Regression (GPR) which is a non-parametric approach. GPR based surrogate function makes the system robust by incorporating variance around the mean value, making the system tolerant against disturbances and noise. To make the optimization problem completely model-free, a zeroth-order gradient estimator is used to optimize the objective function. Extremum Seeking Control (ESC) is gradient-free technique that estimates the gradient by incorporating perturbation signals that drive the optimizer towards the optimal value. Using extremum seeking control, this paper provides a model-free, real-time, and robust optimization technique for optimising the surrogate function.