Hessian Approximations in Multi-Level Iterations

Armin Nurkanovic

Siemens AG, University of Freiburg

Thursday, October 04, 2018, 14:30

Room 02-012, Georges-Köhler Allee 102, Freiburg 79110, Germany

In the case of Economic Nonlinear Model Predictive Control (ENMPC) it is still a challenge to solve the nonlinear Optimal Control Problem (OCP) reliably in real-time. In this talk a few methods are presented to tackle this problem. The usage of exact Hessians turns out to be crucial for good ENMPC controller performance. We show the importance of proper use of regularization strategies for indefinite Hessian matrices and compare it to Quasi-Newton methods. We show the influence of inexact derivatives and different regularization strategies on generalized tangential predictors for a tutorial example. In order to achieve very high feedback rates in ENMPC one can use the Multi-Level Iteration (MLI) scheme. A few new variants of the MLI are discussed with a focus on the interplay of exact Hessian and Hessian approximations.

Even though in ENMPC one has to solve a number of neighboring problems, it is a non-trivial task to properly adapt the solution of the previous problem to get a good starting guess for the next problem such that recursive feasibility and optimality can be obtained. We propose several strategies for finding new linearization points and compare them to standard approaches such as shift initialization and warm start. All new methods are demonstrated on non-trivial numerical example.