Extremum-seeking control of distributed systems using consensus estimation

A method for solving constrained optimization problems in real-time using a distributed control system is presented in this work. The actions of a controller is based on measurements of a part of the total cost function. The algorithm is classified as an extremum-seeking control approach because the design requires no knowledge of the cost function. The controllers coordinate movements by solving a consensus estimation problem in parallel with the optimization. A proof for the algorithm's convergence is presented. Two simulation examples are used to study the behaviour of the proposed system.