Control-based observer for discrete-time nonlinear systems

Abstract

Observer-based controllers are well-known techniques and have been used to generate state feedback control strategies for incomplete state measured systems. However, the reverse process, namely control-based observers, has never been introduced as a tool to design observers for either linear or nonlinear systems. The main objective of this paper is to introduce such a technique as a tool to design observers for nonlinear discrete-time systems. The proposed approach, besides leading to very satisfactory estimation results for nonlinear systems, is unlike other widely used estimation techniques in the literature. More specifically, it has no limitations and/or restrictions, needs no state transformation, the overshoots at the start of the estimation process are either zero or very small, and last but not least the estimation errors converge to the zero steady states within a very short transient period. The stability of the proposed estimator is rigorously analyzed. Finally, the state estimation of the Permanent Magnet Synchronous Motor and a Hyperchaotic system are presented to illustrate the applicability and the efficiency of the developed approach.