2. Algebraic Graph Theory and Cooperative Control Consensus

Cooperative control studies the dynamics of multi-agent dynamical systems linked to each other by a communication graph. The graph represents the allowed information flow between the agents. The objective of cooperative control is to devise control protocols for the individual agents that guarantee synchronized behavior of the states of all the agents in some prescribed sense. In cooperative systems, any control protocol must be distributed in the sense that it respects the prescribed graph topology. That is, the control protocol for each agent is allowed to depend only on information about that agent and its neighbors in the graph. The communication restrictions imposed by graph topologies can severely limit what can be accomplished by local distributed control protocols at each agent. In fact, the graph topological properties complicate the design of synchronization controllers and result in intriguing behaviors of multi-agent systems on graphs that do not occur in single-agent, centralized, or decentralized feedback control systems.