Multi-Level Iteration schemes (MLI) are a state-of-the-art numerical method for Nonlinear Model Predictive Control (NMPC), where the dynamical models are described by ordinary differential equations. The method is based on Direct Multiple Shooting for the discretization of the optimal control problems to be solved in each sample. The arising parametric nonlinear problems are solved approximately by setting up a generalized tangential predictor in a preparation phase. This generalized tangential predictor is given by a quadratic program (QP), which implicitly defines a piecewise affine linear feedback law. The feedback law is then evaluated in a feedback phase by solving the QP for the current state estimate as soon as it becomes known to the controller.

The STMLI package is an extension module to MLI for scenario tree robustification approach. STMLI performs the dual decomposition approach with a non-smooth Newton method. The online active set strategy is employed for the decoupled inner QPs. For integration and sensitivity computations methods based on backward difference formulas or Runge-Kutta-Fehlberg formulas are available.Positive definite approximations of the inner QP Hessians by Limited Memory BFGS updates can be used to generate strictly convex QPs that are required for the dual decomposition approach. Another feature is the Control Move Regularization (CMR) to penalize differences in subsequent controls.

[1] Leonard Wirsching: Multi-level iteration schemes with adaptive level choice for nonlinear model predictive control, PhD Thesis, 2018. Online: http://archiv.ub.uni-heidelberg.de/volltextserver/24402/

[2] Conrad Leidereiter: Numerical Methods for Scenario Tree Nonlinear Model Predictive Control. PhD Thesis, Heidelberg University, 2018. Online: http://archiv.ub.uni-heidelberg.de/volltextserver/24124/