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Dynamic hierarchical reactive controller synthesis. (English) Zbl 1379.93048

Summary: 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 that 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 that satisfies all local specifications. We illustrate our results through an example controlling an autonomous robot in a building with known floor plan and provide simulation results using an implementation of our algorithm on top of LTLMoP.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93A15 Large-scale systems
93A13 Hierarchical systems
93B50 Synthesis problems
91A65 Hierarchical games (including Stackelberg games)
93C85 Automated systems (robots, etc.) in control theory
94C15 Applications of graph theory to circuits and networks
03B44 Temporal logic

Software:

PESSOA; LTLMoP; TuLiP
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References:

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