Implicit solutions to constrained nonlinear output regulation using MPC

In this paper, we show that a simple model predictive control (MPC) scheme can solve the constrained nonlinear output regulation problem without explicitly solving the classical regulator (Francis-Byrnes-Isidori) equations. We first study the general problem of stabilizing a set with MPC using a positive semidefinite (input/output) cost function under suitable stabilizability and detectability assumptions, similar to Grimm et al. (2005) [1]. We show that in the output regulation setting, these conditions hold, if the nonlinear constrained regulation problem is (strictly) feasible, the plant is detectable (i-IOSS) and the control input can be uniquely reconstructed from the plant/reference output. Given these structural assumptions, by simply penalizing the predicted output error in the MPC stage cost, the closed loop implicitly stabilizes a state trajectory that solves the regulator equations, if a sufficiently large prediction horizon is used.