On hybrid output regulation for nonlinear systems with periodic jumps: alternative formulations of the solution and a receding horizon approach

The hybrid output regulation problem in the presence of periodic jumps is approached in this paper for a class of nonlinear hybrid systems satisfying rather mild assumptions. We provide sufficient conditions that characterize steady-state trajectories achieving output regulation that are defined, mimicking the linear case, in terms of two equations: the first one describes the solution of a flow-only output regulation problem, while the second is associated to an auxiliary output regulation problem concerning the monodromy equivalent system of the flow zero-dynamics. Such conditions are then revisited and a receding-horizon solution to the (hybrid) output regulation problem is suggested, based on the solution of a sequence of two-point boundary value problems.