Inexact Newton based Lifted Implicit Integrators for fast Nonlinear MPC

Nonlinear Model Predictive Control (NMPC) requires the online solution of an Optimal Control Problem (OCT) at every sampling instant. In the context of multiple shooting, a numerical integration is needed to discretize the continuous time dynamics. For stiff, implicitly defined or differential-algebraic systems, implicit schemes are preferred to carry out the integration. The NeWton-type optimization method and the implicit integrator then form a nested Newton scheme, solving the optimization and integration problem on two different levels. In recent research, an exact lifting technic-pie was proposed to improve the computational efficiency of the latter framework. Inspired by that work, this paper presents a novel class of lifted implicit integrators, using an inexact Newton method. An additional iterative scheme for computing; the SeILShi VitleS is proposed, which provides similar properties as the exact lifted integrator at considerably reduced computational costs. Using the example of an industrial robot, computational speedups of up to factor 8 are reported. The proposed methods Itave been implemented in the open-source M-2,,ADO code generation software.