Least squares dynamics in Newton-Krylov Model Predictive Control

Newton-Krylov methods for nonlinear Model Predictive Control are pioneered by Ohtsuka under the name "C/GMRES". Ohtsuka eliminates a system state over the horizon from Karush-Kuhn-Tucker stationarity conditions of a Lagrangian using equations of system dynamics. We propose instead using least squares to fit the state to the dynamics and some constraints on the state, if they are inconsistent. Correspondingly modified Newton-Krylov methods are described. Numerical tests demonstrate workability of our modification.