Adaptive cooperative output regulation: A data-driven distributed internal model approach via value iteration

The existing value-iteration method for solving the cooperative output regulation problem of unknown linear multi-agent systems has employed both the distributed internal model and the distributed observer. By constructing a novel virtual exosystem, this paper shows that the usage of the distributed observer is unnecessary and proposes a purely distributed internal model based approach. The new approach has three advantages. First, without using the distributed observer, the new approach significantly reduces the computational cost and weakens the solvability conditions. Second, the existing algorithm has to delay the data collection until the estimation error of the distributed observer becomes sufficiently small while the new approach can start the algorithm at any time. Third, we further reveal that the existing algorithm only applies to the case where the minimal polynomial of the system matrix of the exosystem is the same as the characteristic polynomial of the exosystem. In contrast, due to the use of the virtue exosystem, the new algorithm applies to any exosystem.