Chemical Technology, Control and Management


Algorithms for the formation of a procedure for the stable estimation of parameters matrices and covariances of perturbation vectors in indefinite dynamic systems based on the concepts of matrix pseudo-inversion are given. For stable pseudo-inversion, the matrix partitioning method is used using simplified regularization. The above algorithms allow for a stable estimation of the matrix of parameters and covariances of the perturbation vectors in dynamic systems and thereby increase the accuracy of adaptive control systems operating in parametric and signal uncertainty conditions.

First Page


Last Page





1. V.N.Afanasyev, “Manage undefined dynamic objects”, Mоscоw: Fizmatlit, 2008, 208 p.

2. V.O.Nikiforov, A.V.Ushakov, “Management in conditions of uncertainty: sensitivity, adaptation, robustness”, SankPeterburg: SankPeterburg HITMO, 2002, 232p.

3. H.Z.Igamberdiev, A.N.Yusupbekov, O.O.Zaripov, “Regular methods of estimating and managing dynamic objects in conditions of uncertainty”, Tashkent: Tashkent State Technical University, 2012, 320 p.

4. A.R.Pankov, K.V.Semenikhin, “Minimax Identification of Uncertainly Stochastic Linear Model”, A and T, no. 11, pp. 158171, 1998.

5. A.B.Kurzhansky, “Identification Problem: Theory of Guarantee Estimates (Review)”, A and T, no. 4, pp. 326, 1991.

6. M.L.Lidov, B.Ts.Bakhshiyan, A.I.Matasov, “On One Direction in the Problem of Guaranteeing Assessment (Review)”, Space Research, vol. 29, no. 5, pp. 659-684, 1991.

7. A.N.Tikhonov, V.Y.Arsenin, “Methods of solving incorrect problems”, Mоscоw: Nauka, 1986, 288 p.

8. V.A.Morozov, “Methods for solving incorrectly posed problems”, Springer Science & Business Media, 2012.

9. A.S.Householder, “The theory of matrices in numerical analysis”, Courier Corporation, 2013.

10, C.C.MacDuffee, “The theory of matrices”, Courier Corporation, 2004.

11. L.P.Sysoev, “Estimating matrixes of parameters and covariances of perturbation vectors in multidimensional dynamical systems with discrete time with a special structure of unknown covariance matrices”, A and T, no. 2, 2010, pp. 192206, 2010,

12. V.M.Verzhbitsky “Computational linear algebra”, Mоscоw: Higher. school, 2009. 351 p.

13. F.R.Gantmakher, “The theory of matrices”, American Mathematical Soc., 2000, vol. 131.

14. V.V.Vasin, A.L.Ageev, “Invalid problems with a priori information”, Ekaterinburg, Science, 1993.

15. A.I.Zhdanov. “Introduction to methods for solving illposed problems”, Ed. Samara State. Aerospace University, 2006. 87 p.

16. Golub, Gene H., and Charles F. Van Loan. “Matrix computations”, Vol. 3. JHU Press, 2012.

17. A.F.Verlan, V.S.Sizikov, Integral equations: methods, algorithms, programs Naukova Dumka, Kiev. 1986. vol. 543.

18. A.R.Pankov, K.V.Semenikhin, “Methods of parametric identification of multidimensional linear models under conditions of a priori uncertainty”, Avvol. at. and Telemekh, 2000, no. 5, pp. 76-92.

Included in

Engineering Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.