Discrete-time distributed extremum-seeking control over networks with unstable dynamics

In this paper, we propose a discrete-time version of extremum-seeking control (ESC) which can be implemented by several agents communicating over a network. We consider the problem where several agents each measure a local cost and must cooperate to minimize the total cost which is the sum of the local costs. To solve this problem, we combine a dynamic average consensus algorithm with a proportional integral ESC technique in discrete-time. The consensus algorithm provides each agent with an estimate of the total cost and this estimate is used by the ESC to minimize the total cost. The main contribution of this paper is to show that the distributed agents are able to minimize the total cost despite none of the agents directly measuring it. We provide a proof of the convergence of this algorithm and a simulation example to demonstrate its effectiveness.