Finite-time time-varying output formation-tracking of heterogeneous linear multi-agent systems

In this paper, the finite-time time-varying output formation-tracking (FT-TV-OFT) problem of heterogeneous linear multi-agent systems (HL-MASs) is investigated. First, we propose an adaptive finite-time observer for each follower, aiming to estimate not only the leader's state but also the leader's system matrix. Compared with conventional observers, the dependence of the observer parameters on any global information is completely removed. Moreover, exact estimate can be achieved in a finite time. Then, an adaptive algorithm is used to calculate the regulation equations, such that control gains can be obtained. Next, an adaptive distributed controller is constructed to solve the FT-TV-OFT problem. Moreover, we also extend above results to the case of the directed communication topology. Finally, examples are given to demonstrate the effectiveness of the results.