Distributed Endogenous Internal Model for Modal Consensus and Formation Control

In this paper, the problems of (modal) consensus and formation control are tackled for a group of heterogeneous agents described by linear dynamics and communicating over a network with fixed topology. The classic approach to these problems prescribes that each agent is provided with its own complete internal model of the desired dynamics (which can be viewed as an exosystem). In this paper, the novel concept of Distributed Endogenous Internal Model is introduced and discussed. Such internal model is characterized by two features: i) it is actually distributed over the network, i.e. no single agent is provided with a complete internal model; ii) it is endogenous, namely it is generated by exploiting the dynamics already available to the overall group of agents, through the local cooperation between each agent and its neighbors. As a consequence, each agent is capable of generating the desired steady-state distributed static control input by only exchanging information with its neighbors, without the need for additional dynamics anywhere in the network.