Control-based observer for discrete-time nonlinear systems

Most of the available observer design techniques for nonlinear systems either lead to very large overshoots at the start of the estimation process with short transient period of the estimation error, or vice versa. If it is desired to derive control strategies from the estimated states, large overshoots may lead to harmful effect to the system while long transient periods of the estimation errors delay the achievement of the desired system response. Therefore, it is highly desired to develop an estimation approach to avoid, or at least minimize, the impact of the aforementioned drawbacks on the system performance. Observer-based controllers are well-known techniques and have been used to generate state feedback control strategies for incomplete state measured systems. However, the concept of control-based observers has never been introduced as a tool to design observers using control methodologies for either linear or nonlinear systems. The main objective of this paper is to introduce such a technique as a new observer design approach for nonlinear discrete-time systems. The proposed approach, besides leading to very satisfactory estimation results for nonlinear systems, is completely different from other widely used approaches in the literature. More specifically, it has no limitations and/or restrictions, and 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.