# Identification Problem for Determining the Parameters of a Discrete Dynamic System

• F. A. Aliev
• N. S. Hajieva
• A. A. Namazov
• N. A. Safarova
Article

An identification problem is considered. It allows determining the parameters of a dynamic system in the discrete case. First, the nonlinear discrete equation is linearized by the method of quasi-linearization. Then, the quadratic functional and its gradient are derived using statistical data. A calculation algorithm is proposed to solve the problem. It is shown by way of an example that the statistical value of the coefficient of hydraulic resistance differs from the calculated value by 10–4. This is indicative of the adequacy of the mathematical model.

## Keywords

dynamic system nonlinear discrete equation method of quasi-linearization gradient of functional identification statistical data coefficient of hydraulic resistance

## References

1. 1.
S. D. Akbarov, “Forced vibration of the hydro-viscoelastic and elastic systems consisting of the viscoelastic or elastic plate, compressible viscous fluid and rigid wall: A review,” Appl. Comp. Math., 17, No. 3, 221–245 (2018).
2. 2.
F. A. Aliev, N. A. Aliev, N. A. Safarova, K. G. Gasimova, and N. I. Velieva, “Solution of linear fractional-derivative ordinary differential equations with constant matrix coefficients,” Appl. Comp. Math., 17, No. 3, 317–322 (2018).
3. 3.
F. A. Aliev, N. A. Ismailov, H. Haciyev, and M. F. Guliev, “A method of determine the coefficient of hydraulic resistance in different area of pump-compressor pipes,” TWMS J. Pure Appl. Math., 7, No. 2, 211–217 (2016).
4. 4.
F. A. Aliev, N. A. Ismailov, E. V. Mamedova, N. S. Mukhtarova, “Computational algorithm for solving problem of optimal boundary-control with nonseparated boundary conditions,” J. Comp. Syst. Sci. Int., 55, No. 5, 700–711 (2016).
5. 5.
F. A. Aliev, N. A. Ismayilov, Y. S. Gasimov, and A. A. Namazov, “On an identification problem on the definition of the parameters of the dynamic system,” Proc. IAM, 3, No. 2, 139–151 (2014).
6. 6.
F. A. Aliev, M. Kh. Ilyasov, and N. B. Nuriev, “Problems of modeling and optimal stabilization of the gas-lift process,” Int. Appl. Mech., 46, No. 6, 709–717 (2010).
7. 7.
T. A. Aliev, N. F. Musaeva, N. E. Rzaeva, and U. E. Sattarova, “Algorithms for forming correlation matrices equivalent to matrices of useful signals of multidimensional stochastic objects,” Appl. Comp. Math., 17, No. 2, 205–216 (2018).
8. 8.
D. M. Altshul, Hydraulic Resistance [in Russian], Nedra, Moscow (1970).Google Scholar
9. 9.
P. E. Bellman and P.E. Kalaba, Quasilinearization and Nonlinear Boundary Problems [Russian translation], Mir, Moscow (1968).
10. 10.
A. Brayson and X. Yu-Shi, Applied Theory of Optimal Control, Mir, Moscow (1972).Google Scholar
11. 11.
N. S. Hajieva, N. A, Safarova, and N. A. Ismailov, “Algorithm defining the hydraulic resistance coefficient by lines method in gas-lift process,” Miskolc Math. Notes, 18, No. 2, 771–777 (2017).Google Scholar
12. 12.
N. A. Ismailov and N. S. Mukhtarova, “Method for solution of the problem of discrete optimization with boundary control,” Proc. IAM, 2, No. 1, 20–27 (2013).Google Scholar
13. 13.
M. A. Jamalbayov and N. A. Veliyev, “The technique of early determination of reservoir drive of gas condensate and velotail oil deposits on the basis of new diagnosis indicators,” TWMS J. Pure Appl. Math., 8, No. 2, 237–250 (2017).
14. 14.
L. Ljung, System Identification, Wiley Encyclopedia of Electrical and Electronics Engineering (1999), pp. 263–282.Google Scholar
15. 15.
A. Kh. Mirzadjanzadeh, I. M. Akhmetov, A. M. Khasaev, and V. I. Gusev, Technology and Technique of Oil Production [in Russian], Nedra, Moscow (1986).Google Scholar
16. 16.
N. S. Mukhtarova, “Algorithm to solution the identification problem for finding the coefficient of hydraulic resistance in gas-lift processes,” Proc. IAM, 4, No. 2, 206–213 (2015).
17. 17.
N. S. Mukhtarova and N. A. Ismailov, “Algorithm to solution of the optimization problem with periodic condition and boundary control,” TWMS J. Pure Appl. Math., 5, No. 1, 130–137 (2014).
18. 18.
H. Triki T. Ak, and A. Biswas, “New types of solution-like solutions for a second order wave equation of Korteweg-de Vries type,” Appl. Comp. Math., 14, No. 2, 168–176 (2017).

## Authors and Affiliations

• F. A. Aliev
• 1
• 2
Email author
• N. S. Hajieva
• 1
• A. A. Namazov
• 1
• N. A. Safarova
• 1
1. 1.Institute of Applied MathematicsBaku State UniversityBakuAzerbaijan
2. 2.Institute of Information Technology of NAS AzerbaijanBakuAzerbaijan