Distributed Synthesis of State-Dependent Switching Control

Adrien Le Coënt (1) , Laurent Fribourg (2) , Nicolas Markey (2) , Florian de Vuyst (1) , Ludovic Chamoin (3, 4)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 LSV - Laboratoire Spécification et Vérification [Cachan]
3 MATHERIALS - MATHematics for MatERIALS
4 LMT - Laboratoire de Mécanique et Technologie

We present a correct-by-design method of state-dependent control synthesis for linear discrete-time switching systems. Given an objective region R of the state space, the method builds a capture set S and a control which steers any element of S into R. The method works by iterated backward reachability from R. More precisely, S is given as a parametric extension of R, and the maximum value of the parameter is solved by linear programming. The method can also be used to synthesize a stability control which maintains indefinitely within R all the states starting at R. We explain how the synthesis method can be performed in a distributed manner. The method has been implemented and successfully applied to the synthesis of a distributed control of a concrete floor heating system with 11 rooms and 2^11 = 2048 switching modes.

Mots clés: control synthesis; distributed control; compositional synthesis; state-dependent control; reachability

Domaines: Systèmes et contrôle [cs.SY]

Adrien Le Coënt, Laurent Fribourg, Nicolas Markey, Florian de Vuyst, Ludovic Chamoin. Distributed Synthesis of State-Dependent Switching Control. Lecture Notes in Computer Science, 2016, Reachability Problems (RP 2016), 9899, pp.119-133. ⟨10.1007/978-3-319-45994-3_9⟩. ⟨hal-01295738⟩