Output-feedback nonlinear model predictive control using high-gain observers in original coordinates

In the recent years various nonlinear model predictive control (NMPC) schemes have been derived that achieve guaranteed stability of the closed loop. However, most of these schemes are based on the assumption that the full state information is available. Since in general not all states can be directly measured, it is of paramount importance how one can estimate the not directly measurable states without jeopardizing the stability of the closed-loop. To overcome this problem it has been shown in recent works, that combining sampled-data NMPC for continuous time systems with high-gain observers can lead to semi-global practical stability. However, the resulting output feedback controller uses a high-gain observer which is formulated in observability normal form. Thus explicit knowledge of the inverse of the observability map is required. In this paper we show that one can also use high-gain observers in original coordinates, thus allowing to circumvent the explicit knowledge of the inverse of the observability map. The resulting output feedback schemes is applied to the control of a mixed culture bioreactor.