Dynamic Hierarchical Reactive Controller Synthesis

In the formal approach to reactive controller synthesis, a symbolic controller for a possibly hybrid system is obtained by algorithmically computing a winning strategy in a two-player game graph. Such game-solving algorithms scale poorly as the size of the game graph increases. However, in many applications, the game graph has a natural hierarchical structure which has, so far, not been exploited. In this paper, we propose local games on hierarchical graphs as a modeling formalism which decomposes a large-scale reactive synthesis problem in two dimensions. First, the construction of a hierarchical game graph introduces abstraction layers, where each layer is again a two-player game graph. Second, every such layer is decomposed into multiple local game graphs, each corresponding to a node in the higher level game graph. We propose a technique to calculate winning strategies for such sets of local game graphs over hierarchies that allows for dynamic specification changes and revisions at each step of the play. We show that this synthesis is sound under natural assumptions. We illustrate our results through an example controlling an autonomous robot in a known, multistory building with adversarial environment.