An exterior/interior-point approach to infeasibility in model predictive control

In this paper we address the issue of infeasibility in model predictive control. One popular way of dealing with infeasibility is to categorise constraints as being either hard or soft and include a penalty for soft constraint violations in the cost function. This penalty term can be made exact in the sense that all constraints will be satisfied if indeed possible. The exact penalty property is typically ensured by further including a linear term in the cost. If this term is not large enough, then the exact penalty property may be lost. We illustrate, by way of example, that choosing this term to be large may be detrimental to system dynamics. We propose a two stage process where feasibility is detected and then a model predictive control problem is solved using this new information. Our development is based on the classical exterior/interior-point framework which allows for an intuitive tuning procedure.