# ISIS project: Model Predictive Control for Systems Including Binary
Variables

## Background

Model Predictive Control (MPC) has
proved to be a strong method to control large MIMO systems and has
gained substantial interest in the industry, especially within the
process and petrochemical fields. The main benefit is the
possibility to handle constraints on various variables in the
plant.
An extension to ordinary MPC is also to include the ability to use
binary variables as control signals and as internal variables in
the model description.

The central idea in MPC is to state the control problem as an
optimization problem, and solve this optimization problem on-line
repeatedly. When binary variables are used in MPC, the
optimization problem to solve is changed from a Quadratic Program
(QP) to a Mixed Integer Quadratic Program (MIQP), where the latter
is known in general to be NP-hard.

The research is performed in collaboration with ABB Corporate Research.

As an example of linear MPC, let us consider a linear system

A standard MPC controller is typically defined as

The optimization problem can be solved with quadratic programming if
the control and state-constraints are linear. This is most often the
case since amplitude and rate-constraints are the most common
constraints in reality.
## Research Area

As mentioned above, when binary signals are
used in the MPC problem, an NP-hard problem has to be solved in each time
instant. Our research is aiming at finding and exploring the structure
in MIQP problems originating from MPC. The objective with this
research is to speed up the solution of these optimization problems.
## Publications