Avoidance of Poorly Observable Trajectories: A Predictive Control Perspective

Abstract

Nonlinear systems can be poorly or non-observable along specific state and output trajectories or in certain regions of the state space. Operating the system along such trajectories or in such regions can lead to poor state estimates being provided by an observer. Such trajectories should be avoided if used for state-feedback control or monitoring purposes. In this paper, we outline two possible approaches to avoid weakly observable trajectories in the frame of nonlinear predictive control. The first approach is based on the use of a term in the cost functional that penalizes weakly observable trajectories and thus leads to avoidance of weakly or non-observable regions of operation. In the second approach, the observer error dynamics are directly considered in the prediction. Large state estimation errors lead to a large penalization in the cost functional and are thus avoided. The approaches are exemplified by considering an example system.