In this paper, we investigate team optimal control of a population of heterogeneous LQ (Linear Quadratic) agents. The population consists of finite distinct sub-populations so that agents in each sub-population are homogeneous. For each agent, the state evolves linearly (i.e. linear dynamics) and the cost is quadratic in state and action. The agents are coupled in both dynamics and cost through the empirical mean (also called mean-field) of states and actions of agents. Each agent observes its local state and the mean-field. This information structure is called mean-field sharing information structure and it is a non-classical decentralized information structure. The objective of agents is to team up with each other to minimize the total cost. We identify the team-optimal solution and show that it is unique and linear. The optimal gains are computed by the solution of appropriate Riccati equations. One of the key salient features of our approach is that the computational complexity of our solution does not depend on the number of agents, yet it depends on the number of sub-populations. This implies that the optimal strategy can be computed without any knowledge on the number of agents. We generalize our results to tracking problem, infinite horizon, and infinite population.
Published November 2015 , 21 pages