Design of Optimal Linear Reduced-Order Observers for Suppressing Transient Estimation Error

By exploiting the idea of orthogonal functions and evolutionary optimization, a new approach is proposed in this paper to design a coordinate-change-based linear reduced-order observer such that (i) the eigenvalues of the reduced order observer are specified to satisfy desired convergence performance, and (ii) a quadratic performance measurement of the state estimation error is minimized so as to suppress the transient estimation error. The proposed optimal design method can be used to uniquely determine the observer gain matrix when the number of the output is greater than the number of states to be estimated, whereas existing approaches fail to do so. Two illustrative examples are also given to demonstrate the effectiveness and efficiency of the proposed optimization method for state estimations.