New Optimal Observer Design Based on State Prediction for Linear Systems

In this study, a new optimal observer design is presented for linear systems. First, the system states are predicted in their receding horizon, and then, based on the error of state prediction, a quadratic cost function is defined such that its minimization results in an optimal gain for the proposed observer. Since the present analytic approach uses off-line optimization, it can overcome the related difficulties that may arise in non-convex optimization problems. In addition, the condition ensuring the asymptotic stability of the proposed optimal observer is developed, thus guaranteeing the asymptotic convergence of the state estimation error to zero. The estimation of the optimal state based on the prediction of system states, achieved through the asymptotic stability of the estimation error, is among the main features of the proposed method. Furthermore, the proposed observer design is independent of the type of system controller. Finally, three examples are provided to demonstrate the effectiveness of the proposed method in state estimation.