Robust Optimization for MPC

Abstract

This chapter aims to give a concise overview of numerical methods and algorithms for implementing robust model predictive control (MPC). We introduce the mathematical problem formulation and discuss convex approximations of linear robust MPC as well as numerical methods for nonlinear robust MPC. In particular, we review and compare generic approaches based on min-max dynamic programming and scenario-trees as well as Tube MPC based on set-propagation methods. As this chapter has a strong focus on numerical methods and their practical implementation, we also review a number of existing software packages for set computations, which can be used as building blocks for the implementation of robust MPC solvers.