Implicit solutions to constrained nonlinear output regulation using MPC

Johannes Köhler, Matthias A. Müller, Frank Allgöwer

Abstract: 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). 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.