State Estimation in Nonlinear Model Predictive Control, Unscented Kalman Filter Advantages

Abstract

Model predictive control (NMPC) proves to be a suitable technique for controlling nonlinear systems, moreover the simplicity of including constraints in its formulation makes it very attractive for a large class of applications. Due to heavy online computational requirements, NMPC has traditionally been applied mostly to systems with slow dynamics. Recent developments is likely to expand NMPCs applicability to systems with faster dynamics.

Most NMPC formulations are based on the availability of the present state. However, in many applications not all states are directly measurable. Although there is no Separation Theorem which is generally applicable for nonlinear systems, the control and state estimation problems are usually handled separately.

State estimation introduces extra computational load which can be relevant in case of systems with relatively fast dynamics. In this case accurate estimation methods with low computational cost are desired, for example the Extended Kalman Filter (EKF). Clearly, the EKF does not perform well with all nonlinear systems, but its straightforwardness is the main reason of its popularity.

In this work, a type of locally weakly unobservable system is studied. For this type of system, we find that the EKF drifts because the system is unobservable at the desired operation point. The Unscented Kalman Filter (UKF) is described, and similarities with the EKF are discussed. Finally, it is shown how the UKF is used for state estimation in this type of nonlinear systems, and that it provides a stable state estimate, despite the fact that the system is locally unobservable.