Maintaining Strong Structural Controllability for Multi-Agent Systems with Varying Number of Agents

This paper investigates strong structural controllability for multi-agent systems (MAS) with dynamically joining and leaving agents. Changing sets of agents can compromise controllability if only a subset of agents is equipped with control inputs. Based on the graph-theoretical concept of zero forcing, conditions are derived under which MAS with joining and leaving agents can maintain strong structural controllability without needing to reconfigure the leader set. Two methods are proposed: The first, employs so-called zero forcing chains, to provide definitive statements on maintaining SSC. The second is based on forcing agents and offers a quick assessment of feasibility for joining or leaving, but confirms SSC only in specific cases.