Controllability of Networks with Multivariable Agents

We study the controllability problem of multiagent networks in which each agent has multiple state variables. In many applications such as robot swarms and smart grids, a nontrivial number of variables is needed to fully describe the status of an agent, making analysis of the whole network difficult. Due to limitations of communication bandwidth, computing power, and energy consumption, it is desirable to secure controllability of a network using the minimum number of drivers. For systems with single-variable agents, this problem can be solved efficiently by finding the minimum number of externally controlled state variables. For systems with multivariable agents, a driver is an externally controlled agent with possibly multiple state variables, and such a method does not guarantee finding the minimum number of drivers. To our best knowledge, there has not been a general efficient method to determine the minimum (agent-) drivers for networks with multivariable agents. In this paper, we introduce a method to solve this problem by transforming it into a standard 0-1 linear programming problem. A systematic derivation and proof of the transformation is presented. Accuracy of the proposed method is numerically validated against the solution from a brute-force method.