Consensus-based iterative learning of heterogeneous agents with application to distributed optimization

This paper deals with the distributed iterative learning control (ILC) problem of leaderless consensus in a network of heterogeneous nonlinear agents. For a general case that the topology graph is dynamically changing with respect to both iteration and time axes, an ILC-based consensus protocol is designed for each agent by utilizing its control input and neighboring information from the last iteration. It is shown that under a basic joint spanning tree condition, the states of all agents can exponentially agree on a common trajectory along the iteration axis. Interestingly, by the appropriate design of the agents’ dynamics, it is found that the consensus trajectory and the network state can approach the unique optimal point of a convex optimization problem as the time evolves. Simulations demonstrate the validity of the proposed algorithms and theoretical analysis.