Closed-loop Behavior of Nonlinear Model Predictive Control

Model predictive control (MPC) relies on real-time optimization to determine open-loop control profiles and state estimates given process measurements. When the underlying process model is nonlinear, the MPC system exhibits unique behavior not seen in linear MPC. In this article, we highlight some of the characteristics of nonlinear models in the context of closedloop performance. We examine the effects of disturbance models on closed-loop performance and show necessary conditions for how and where steady states of the closed-loop system may be found. We demonstrate these conditions on a simple example to show that the input disturbance model can lead to failure of the control system, and that linear MPC is inadequate for controlling this class of systems. Additionally, due to nonconvexity, the optimization problems solved in nonlinear MPC may have local optima. These local minima may lead to undesirable performance, particularly in the state estimator. We study the existence of these optima in the regulator and estimator and examine their potential effects on the performance of the closed-loop system. To avoid unwanted local minima, we advocate the use of constraints in the estimator and regulator formulations and show how a shorter prediction horizon in the regulator leads to better control profiles for some nonlinear models.