Explicit (Offline) Optimization for MPC

In this chapter, we present the fundamentals of multi-parametric programming and its application to explicit model predictive control (MPC), i.e. the offline solution of MPC problems for both continuous and hybrid systems. In particular, we first show how MPC problems can be reformulated as multi-parametric programming problems, then we show how explicit/multi-parametric solutions are derived and the key underlying theoretical properties. Finally, we present solution procedures for these type of problems and discuss applicability issues and potential future research directions.