Direct Adaptive Cooperative Output Regulation of Unknown Multiagent Systems via Distributed Internal Model

The existing result on the cooperative output regulation problem for unknown linear multi-agent systems using the data-driven distributed internal model approach is limited to the case where each follower is a single-input and single-output system and the communication network among all agents is an acyclic static digraph. In this paper, we further address the same problem for unknown linear multi-agent systems with multi-input and multi-output followers over a general static and connected digraph by a value iteration approach. Further we make two main improvements over the existing result. First, compared with the existing approach, we reduce the number of the unknown variables governed by a sequence of linear algebraic equations. Second, we show that the sequence of linear algebraic equations can be further decoupled to two sequences of lower-dimensional linear algebraic equations. As a result, our approach not only drastically reduces the computational cost, but also significantly weakens the solvability conditions. A numerical example is used to illustrate the effectiveness of our approach.