Constrained Order Observer Design for Disturbance Decoupled Output Estimation

Abstract

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Optimal Observer Design of State Delay Systems

“…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.…”

“…Step (HTGA method execution [47]). By integrating (19), (21), and (22), the HTGA method is utilized to search for the optimal observer gain matrix , where a penalty on the fitness value is given for the chromosome violating the LMI-based constraint in (13).…”