Hybrid power control on a wireless networked control system*

We use a discrete-time stochastic hybrid system (dtSHS) to model a networked control system where measures and control signals are exchanged via a single-hop wireless communication channel affected by slow fading. We apply an abstraction algorithm to approximate the infinite dimensional dtSHS as a finite dimensional Markov Decision Process (MDP), and combine standard optimization methods over MDPs and stochastic model checking algorithms to perform power control in order to minimize the energy consumption while satisfying probabilistic safety constraints. We use error bounds on the approximation error induced by the abstraction to validate the effectiveness of the control policy designed over the MDP, when applied to the original dtSHS model.