Dynamic Hierarchical Reactive Controller Synthesis
For researchers in formal methods and control synthesis, this work provides a method to scale synthesis to larger systems with hierarchical structure, though it is incremental over existing hierarchical synthesis approaches.
The paper addresses the scalability issue of reactive controller synthesis by exploiting hierarchical structure in game graphs. It introduces local games on hierarchical graphs and a dynamic controller that computes assume-admissible winning strategies, demonstrating soundness through a robot navigation example.
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. 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. In this paper, we propose a modeling formalism and a synthesis algorithm that exploits this hierarchical structure for more scalable synthesis. We define 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. While local games have the potential to reduce the state space for controller synthesis, they lead to more complex synthesis problems where strategies computed for one local game can impose additional requirements on lower-level local games. Our second contribution is a procedure to construct a dynamic controller for local game graphs over hierarchies. The controller computes assume-admissible winning strategies that satisfy local specifications in the presence of environment assumptions, and dynamically updates specifications and strategies due to interactions between games at different abstraction layers at each step of the play. We show that our synthesis procedure is sound: the controller constructs a play which satisfies all local specifications. We illustrate our results through an example controlling an autonomous robot in a known, multistory building.