Nicolas Markey

Résumé

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 211 = 2048 switching modes.

@inproceedings{rp2016-LFMDC,
  author =              {Le{~}Co{\"e}nt, Adrien and Fribourg, Laurent and
                         Markey, Nicolas and De{~}Vuyst, Florian and Chamoin,
                         Ludovic},
  title =               {Distributed Synthesis of State-Dependent Switching
                         Control},
  editor =              {Larsen, Kim Guldstrand and Srba, Ji{\v r}{\'\i}},
  booktitle =           {{P}roceedings of the 10th {W}orkshop on
                         {R}eachability {P}roblems in {C}omputational
                         {M}odels ({RP}'16)},
  acronym =             {{RP}'16},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {9899},
  pages =               {119-133},
  year =                {2016},
  month =               sep,
  doi =                 {10.1007/978-3-319-45994-3_9},
  abstract =            {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.},
}