Distributed Leader-Following Optimal Control for Linear Multi-Agent Systems with Nonzero Leader's Control Input

This paper studies the distributed leader-following optimal control problem for multi-agent systems (MASs). In particular, a class of linear MASs with leader's bounded unknown control input is considered. We propose a dynamical sliding mode control protocol to address the presence of nonzero control input of leader. Meanwhile, we design a distributed optimal nominal control protocol to achieve leader-following consensus control of MASs. Under the nominal control protocol, the energy cost performance of the MASs can be optimized by solving the algebraic Riccati equation (ARE). Finally, a numerical simulation of multi spacecraft consensus tracking control example is provided to verify the effectiveness of the proposed algorithm.