Controllability of Multi-Agent Systems over Finite Fields via Semi-Tensor Product Method

This paper proposes a semi-tensor product method for the controllability of multi-agent systems (MASs) over finite fields. The main tool is the algebraic state space representation (ASSR) approach. Firstly, the dynamics of MASs over finite fields is converted into an equivalent algebraic form by using the semi-tensor product of matrices. Secondly, a controllability matrix is constructed by using the algebraic form, based on which, a necessary and sufficient condition is presented for the controllability of MASs over finite fields. Thirdly, an algorithm is given to find the minimal number of leaders which makes MASs over finite fields controllable. Finally, an example is given to show the effectiveness of the obtained new results.