A Perturbed Chord (Newton-Kantorovich) Method for Constrained Nonlinear Model Predictive Control

An approach to the computational implementation of Constrained Nonlinear Model Predictive Control (CNMPC) algorithms is described based on exploiting the modified Newton's method originally proposed by Kantorovich for solving nonlinear equations. This method is distinguished by avoiding the need to compute the Jacobian at each iteration while still ensuring convergence. In this paper, new results characterizing the convergence of this method while accounting for perturbations that may result from various approximations are obtained. Examples illustrating the potential of the proposed approach for spacecraft attitude control and diesel engine air path control are reported. They indicate that good tracking performance can be achieved and constraints can be enforced while the computational effort is reduced.