5. Cooperative Globally Optimal Control for Multi-Agent Systems on Directed Graph Topologies

In Chaps. 3 and 4, we showed that locally optimal design in terms of Riccati equations can guarantee synchronization for cooperative multi-agents on graphs. In this chapter, we examine the design of distributed control protocols that solve global optimal problems for all the agents in the graph. In cooperative control systems on graphs, it turns out that local optimality for each agent and global optimality for all the agents are not the same. This chapter brings together stability and optimality theory to design distributed cooperative control protocols that guarantee synchronization and are also optimal with respect to a positive semidefinite global performance criterion. A common problem in optimal decentralized control is that global optimization problems generally require global information from all the agents, which is not available to distributed controllers. In cooperative control of multi-agent systems on graphs, each agent is only allowed to use distributed information that respects the graph topology, that is, information about itself and its neighbors. Global optimal control for multi-agent systems is complicated by the fact that the communication graph topology interplays with agent system dynamics.