Distributed extremum-seeking control with nonlinear gain for a class of optimization problems

We propose a distributed extremum seeking controller with a nonlinear gain to solve a class of real-time optimization problems. Each dynamic agent in the network has unknown dynamics, and it is assumed that each agent only knows its own local cost measurement. The nonlinear gain term makes the practical implementation of the controller more feasible. It ensures that the gain is large enough to achieve convergence to the optimum and eliminates the issue of tuning the controller gain. The proposed method is illustrated using a simulation example.