Discrete dynamic feedback for a class of hybrid systems on a lattice

We address the problem of designing a dynamic output feedback control for a hybrid system in order to satisfy system specifications, once the continuous variables are measured. In absence of a structure on the discrete variable space, the design of such a controller requires a number of computations at least proportional to the size of the discrete variable set and to the size of the control set. In this paper, we propose to exploit a partial order structure on the set of discrete variables and inputs. The control input is thus computed as a function of two discrete variable values that are updated at each step. This algorithm is applied to a multi-robot game involving two teams competing against each other in a “capture the flag”-like game.