A multi-parametric bi-level optimization strategy for hierarchical model predictive control

Hierarchical control structures consist of a hierarchy of control levels. In the case of hierarchical model predictive control (MPC) structures, each control level involves an optimization problem, with the resulting formulation typically corresponding to a multi-level programming problem. The solution of this type of problems is very challenging, even when considering only two linear optimization levels, and typically require the use of global optimization techniques. In this work, we propose the use of a novel algorithm capable of providing the exact, global and multi-parametric solution of bi-level programming problems for the solution of hierarchical control problems. The derivation of hierarchical multi-parametric/explicit MPC controllers through the proposed algorithm, allows the controller to only do simple function evaluations at every control step, instead of solving the full bi-level optimization problem. We are illustrating the proposed methodology through an example of a two level hierarchical mp-MPC of a continuous stirred tank reactor (CSTR) system.