Containment control of directed networks with time-varying nonlinear multi-agents using minimum number of leaders

In this paper, the problem of containment control with minimum number of leaders in arbitrary directed networks consisting of time-varying nonlinear multi-agents is investigated. Unlike the existing containment control problem with redundant leaders in special networks, we consider the problem with minimum number of leaders in arbitrary directed networks. We show that the problem of finding the minimum number of leaders can be converted into a minimum spanning tree problem by introducing a toll station connecting with each agent. By employing the developed Edmonds' algorithm, the minimum number of leaders is located at the roots of each tree in the obtained spanning forest. This situation allows us to achieve containment control in a distributed manner. On the basis of this situation, a distributed protocol is developed to address the containment control of multi-agent systems with time-varying nonlinear dynamics. Simulation results are provided to illustrate the efficiency of the proposed methodology. Our work makes it possible for studying and extending application of containment control problems in various complex networks. (C) 2019 Published by Elsevier B.V.