Fast Model Predictive Control with soft constraints

This paper describes a fast optimization algorithm for Model Predictive Control (MPC) with soft constraints. The method relies on the Kreisselmeier-Steinhauser function to provide a smooth approximation of the penalty function for a soft constraint. This is analogous to the approximation of a hard constraint by a smooth logarithmic barrier function. By introducing this approximation directly into the objective of an interior point optimization, there is no need for additional slack variables to capture constraint violation. Simulation results show significant speed-up compared to using slack variables.