Abstract
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.
Highlights
Algorithmic reactive synthesis has recently emerged as a robust methodology to design correct-by-construction controllers for specifications given in temporal logics
The major concern in the application of reactive synthesis to large problems is the poor scalability of game solving algorithms with increasing size of the game graph. We address this challenge by extending the scope of reactive synthesis for control by (i) introducing local game graphs over hierarchies as a new decomposed model, (ii) formalizing hierarchical reactive games over such models, and (iii) proposing a sound reactive controller synthesis algorithm for such games
Dynamical controller synthesis Given the hierarchical reactive games described above, we propose a reactive controller synthesis algorithm to solve such games that allows for dynamic specification changes at each step of the play
Summary
Algorithmic reactive synthesis has recently emerged as a robust methodology to design correct-by-construction controllers for specifications given in temporal logics (see, e.g., Girard and Pappas 2009; Tabuada 2009; Kloetzer and Belta 2008; Wolff et al 2013; Wong et al 2013). We address this challenge by extending the scope of reactive synthesis for control by (i) introducing local game graphs over hierarchies as a new decomposed model, (ii) formalizing hierarchical reactive games over such models, and (iii) proposing a sound reactive controller synthesis algorithm for such games This algorithm allows for dynamic specification changes and uses the construction of assume-admissible winning strategies (Brenguier et al 2015) to explicitly model and use environment assumptions. The dynamic nature of our controller is similar to the receding horizon strategies proposed by Wongpiromsarn et al (2012) and Vasile and Belta (2014) that translate long term goals into current local reachability specifications This approach allows for a particular two-layer hierarchy and uses time horizons to decompose the synthesis problem locally. We show that increasing the number of such predicates causes the monolithic solution to run out of memory very quickly while the computation time of the hierarchical synthesis is hardly affected
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