Cooperative tracking problem of unknown discrete-time MIMO multi-agent systems with switching topologies

This paper is concerned with the cooperative output tracking problem of a class of unknown heterogeneous discrete-time multi-input multi-output (MI-MO) linear multi-agent systems (MASs) under switching topologies. A novel design framework is developed based on a distributed observer and a distributed multivariable adaptive control approach. First, a distributed observer is constructed to estimate the leader’s states by using the neighboring relative information under the influences of switching topologies. Then, to handle the unknown parameters of MIMO systems, a distributed multivariable model reference adaptive control approach is designed to follow the estimation states of the leader. It is shown that under the proposed design framework, the boundedness of all signals and variables in the closed-loop system is guaranteed, and the output tracking of the MASs is achieved. Moreover, the proposed design framework does not need the knowledge of global graph information. Finally, an example is provided to illustrate the effectiveness of the proposed approach.