Multi-layer observer as new structure for state estimation in linear systems

Abstract

Abstract:A new structure to design observers for linear systems is presented in this work. The key step is the construction of two layers where the first consists of multiple observers and the second connects them providing the weighted estimation state. The main difficulty is to find a new feedback which is responsible for control weights. To define observation law, we rely on multi observers from the first layer. The proposed structure significantly improves the transient characteristics of the observation process, which is shown in illustrative examples.

Optimal Observer Design of State Delay Systems

“…By using the asymptotic stability criterion of (8), when the observer gain matrix has been previously given, only the property of asymptotic convergence of the state estimation error vector ( ) can be guaranteed. However, this observer design result is not satisfactory, as a large estimation error may occur during the transient period of observation [19]. Hence, the problem considered here is how to specify the × observer gain matrix in (2a), (2b), and (2c) so that the constraint of the LMI-based condition of the state estimation error vector asymptotically converging to zero in (13) can be satisfied, while the quadratic performance measurement of estimation error in (7) is simultaneously minimized.…”

“…in which 1 = 1 1 1 , 2 = 2 2 2 , and the constant matrices ℎ and denote, respectively, the productintegration-matrix of two OF basis vectors having different time intervals [22]. From (19), (21), and (22), it can be seen that the OFA-based computational approach does not limit the sizes of both ℎ and , where ℎ is the given known constant time delay and is the final time which is given by the control engineer for desiring state estimation error decreased to almost zero.…”

“…First, randomly generate the initial population with the chromosomes of form̃= [ 11 , 12 , ⋅ ⋅ ⋅ , ] for executing the HTGA. Next, compute the solutions of̃1 and̃2 by applying (19) and (21), and compute by using (22) which is defined as the fitness function of the HTGA. Then, the fitness values of the initial population feasible for the LMI-based constraint in (13) are calculated.…”

“…These existing observer design methods guarantee that the state estimation errors can asymptotically converge to zero. Although the existing approaches can be applied to improve the convergence of the estimated states, they may lead to unsatisfactory estimation results, since a large estimation error may occur during the transient period of observation [19].…”

Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

“…[13][14][15] Several previous studies have been devoted to coping with the design issue of reducing the large estimation error occurring during the transient period of observation. [12][13][14][15][16][17] The reduced-order observer reduces the order of the observer by using the sensed outputs. To the authors' best knowledge, to date, only Kung and Yeh 13 as well as Horng and Chou 14,15 have studied the problem of transient estimation performance improvement for "reduced-order observers.…”