### International Journal of Intelligent Systems and Applications(IJISA)

*ISSN: *2074-904X (Print), *ISSN: *2074-9058 (Online)

*Published By: *MECS Press

*IJISA Vol.8, No.3, Mar. 2016*

#### System with Distributed Lag: Adaptive Identification and Prediction

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#### Abstract

Adaptive algorithms of parametric identifica-tion of discrete systems with lag variables are proposed. Adaptive algorithms (AA) in the presence of lag input variables are developed. The convergence of the AA and the boundedness of the trajectories the adaptive system is proved. Convergence domain АА depends on operating disturbance. Models with multiplicative parameters (MPM) for the decrease of a number estimated parameters are offered. The process for selection of the vector of base parameters MPM was developed. The performance of adaptive system identification for this case is proved. It is shown that parameters of system estimation at the application of multiplicative identification must be chosen from a condition of minimization of the criterion of the prediction error. Transformation of interdependence be-tween the lagged variables is offered, allowing eliminating their effect on system work. In the second part of work, the method of synthesis АА identification of the systems containing lagged output variables is offered. We consider a case of linear correlation between an output of the system and operating disturbance. For a solution of a problem, we suggest fulfilling an estimation of operating disturbance. Corresponding procedures are described and proved their efficiency. Simulation results are presented that confirm the efficiency of the adaptive methods.

#### Cite This Paper

Nikolay Karabutov,"System with Distributed Lag: Adaptive Identification and Prediction", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.3, pp.1-13, 2016. DOI: 10.5815/ijisa.2016.03.01

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