Analysis of linear programming in model predictive control

The linear programming formulations of model predictive control are known to exhibit degenerate solution behavior. In this work, a multi-parametric linear programming technique is utilized to analyze the control laws that are generated from various linear programming based MPC routines. These various routines explore a number of factors, including objective function selection and constraint handling on the control laws generated from LP based MPC. A single input single output system is used to demonstrate that the use of input velocity penalties, input blocking, and ∞∞-norm objective functions can limit or eliminate this undesirable behavior. Finally, a paper machine cross directional control problem is used to demonstrate the control laws generated from LP based MPC for a multivariable example.