Incremental synthesis of control policies for heterogeneous multi-agent systems with linear temporal logic specifications

We consider automatic synthesis of control policies for non-independent, heterogeneous multi-agent systems with the objective of maximizing the probability of satisfying a given specification. The specification is expressed as a formula in linear temporal logic. The agents are modeled by Markov decision processes with a common set of actions. These actions, however, may or may not affect the behaviors of all the agents. To alleviate the well-known state explosion problem, an incremental approach is proposed where only a small subset of agents is incorporated in the synthesis procedure initially and more agents are successively added until the limitations on computational resources are reached. The proposed algorithm runs in an anytime fashion, where the probability of satisfying the specification increases as the algorithm progresses.