New Optimal Observer Design Based on State Prediction for a Class of Non-linear Systems Through Approximation

This paper deals with the optimal state observer of non-linear systems based on a new strategy. Despite the development of state prediction in linear systems, state prediction for non-linear systems is still challenging. In this paper, to obtain a future estimation of the system states, initially Taylor series expansion of states in their receding horizons was achieved to any specified order and then an analytic solution was developed for the prediction error problem, which resulted in a closed-form for non-linear optimal observer. In the proposed observer, the observer gain was optimally chosen among gains obtained from the analytic solution of the prediction error problem and satisfied the stability condition. Finally, the qualitative simulation results showed the effectiveness of the proposed method in the state observation.