Partial controllability of continuous-time multi-agent systems with multiple leaders

Abstract

The complete controllability of multi-agent systems are mainly focused on the whole system referring to transferring the remaining agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of agents under exchanged information between each other, which makes the system reflect the effect of a whole. However, in practice, it may not be necessary to ensure all nodes be controllable. This paper mainly investigates the partial controllability of multi-agent systems under undirected fixed topology. The concept of partial controllability is proposed and some sufficient and necessary conditions are proposed for the partial controllability of continuous-time multi-agent systems with multiple leaders. Numerical example and simulations are presented to illustrate the theoretical results.