RADIOELECTRONIC AND COMPUTER SYSTEMS

The subject of the article is a variant of an efficient algorithm for synthesizing a dual discrete model and controller for tracking a given trajectory of a dynamic nonlinear, nonstationary black box object, using standard procedures for diagonalizing the state matrix, which makes it possible to simplify obtaining control values in numerical form and reduce the number of calculations. The current article presents one the possible solutions to the problem of regulator synthesis to ensure stable development of a given trajectory of motion of a nonlinear, non-stationary object of "black box" type using the concept of dual control. The task was set to simplify the previously proposed synthesis algorithm for the adaptive control of dynamic nonlinear, non-stationary objects using the example of first-order object of the "black box" type, using standard procedures for the diagonalization of the state matrix. An extended state matrix is the basis for obtaining a control model and predicting the behavior of a nonlinear non-stationary object, which in turn makes it possible to effectively use the concept of dual control. Methods used in the work are based on concept of dual control, nonlinear dynamic models, matrix theory, difference equations. Obtained results of this work consist of the development of a version of a dual nonparametric controller of nonstationary nonlinear processes, which has adaptive properties, does not require knowledge of the physics of functioning of the control object, is presented in the form of a simple algebraic formula that does not contain coefficients that require adjustment. Conclusion. Scientific novelty lies in the application of each interval matrix operator control for the diagonalization of the state submatrix. This operator is used for subsequent calculation of the control action. This approach enables the use of a standard diagonalization procedure using mathematical applications. The results are presented in the form of a final formula that does not require use of matrix operations during control, which makes it possible to simplify the synthesis of the controller using standard mathematical procedures.

“black box”; dual control; extended state matrix; diagonalization; local model; global model; deterministic chaos

Kulik, A., Dergachov, K., Pasichnik, S., Yashyn, S. Motions models of a two-wheeled experimental sample. Radioelectronic and Computer Systems, 2021, no. 1, pp. 40-49. DOI: 10.32620/reks.2021.1.03.

Ashby, W. Ross. An Introduction to Cybernetics. London, Chapman & Hall Publ., 1957. 295 p.

Fel'dbaum, A. A. Teoriya dual'nogo upravleniya I, II [Dual control theory I, II]. Avtomatika i Telemekhanika – Automation and telemechanics, 1960, no. 21 (9, 11), pp. 1240-1249, 1453-1464.

Fel'dbaum, A. A. Teoriya dual'nogo upravleniya III, IV [Dual control theory III, IV]. Avtomatika i Telemekhanika – Automation and telemechanics, 1961, no. 22 (1, 2), pp. 3-16, 129-142.

Jafarov, S. M., Aliyeva, A. S Synthesis of intelligent control system with coordinate and parametric feedback. Procedia Computer Science, 2017, vol. 120, pp. 554-560. DOI: 10.1016/j.procs.2017.11.278.

Iantovics, L. B. Black-Box-Based Mathematical Modelling of Machine Intelligence Measuring. Mathematics, 2021, vol. 9(6), article no. 681. DOI: 10.3390/math9060681.

Medvedev, A. V. Teoriya neparametricheskikh sistem. Obshchii podkhod [Theory of nonparametric systems. General approach]. Vestn. CibGAU im. ak. M. F. Reshetneva – Bullet. of SibGAU them. ac. M. F. Reshetnev, Krasnoyarsk, 2008, vol. 3(20), pp. 65-69.

Medvedev, A. V. Identification and control for linear dynamic system of unknown order. Optimization Techniques IFIP Technical Conference, Berlin – New York, Springer-Verlag Publ., 1975, pp. 48–56.

Matthew, C., Bogdanski, K. Extending the Kalman filter for structured identification of linear and nonlinear systems. J. Modelling, Identification and Control, 2017, vol. 2(27), pp. 114-124. DOI: 10.1504/IJMIC.2017.082952.

Shoukat, H., Tahir, H., Ali, K. Approximate GP Inference for Nonlinear Dynamical System Identification Using Data-Driven Basis Set. IEEE Access, 2020, vol. 8, pp. 90665-90675, DOI: 10.1109/ACCESS.2020.2994089.

Zhosan, A. A. The method of synthesizing a nonparametric discrete model of a black box - type dynamic object with the scalar input and output. Visnyk Kryvoriz'koho natsional'noho universytetu – Bulletin of Kryvyi Rih National University, 2020, vol. 50, pp. 118-121. DOI: 10.31721/2306-5451-2020-1-50-118-122.

Efroimovich, S. Yu. Nonparametric curve estimation. Methods, theory and application, Berlin – New-York, Springer-Verlag Publ., 1999. 134 p.

Bayard, D., Schumitzky, A. Implicit dual control based on particle filtering and forward dynamic programming. J. Adapt Control Signal Process, 2010, vol. 3(24), pp. 155-177. DOI: 10.1002/acs.1094.

Zhang, Z., Ren, J. Locally Weighted Non-Parametric Modeling of Ship Maneuvering Motion Based on Sparse Gaussian Process. Journal of Marine Science and Engineering, 2021, vol. 9(6), article no. 606. DOI: 10.3390/jmse9060606.

Medvedev, A. V., Raskina, A. V. The dual control algorithm of nonlinear dynamic processes in the conditions of incomplete a priori information. IOP Conf. Series: Materials Science and Engineering, 2020, vol. 865, article no. 012006, pp. 1-7. DOI: 10.1088/1757-899X/865/1/012006.

Wittenmark, B., Elevitch, C. An adaptive control algorithm with dual features. 7th IFAC/IFORS Symp. on Identification and Systems Parameter Estimation, York, U.K., 1985, pp. 587-592.

Zhosan, A. A., Fedorenko, O. L. Dualne upravlinnya perevernutim mayatnikom yak «chornim yaschikom» [Dual control of the inverted pendulum as a "black box"]. Visnyk Kryvoriz'koho natsional'noho universytetu – Bulletin of Kryvyi Rih National University, 2017, vol. 44, pp. 24-29.

Zhosan, A., Lipanchikov, S. Numerical modeling of disintegration process dual control. Metallurgical and Mining Industry, 2015, no. 3, pp. 74-77.

Medvedeva, N. A. Nonparametrically Estimation of Statistical Characteristics in Problem of Modelling. Proceedings of the International Conference «Computer Data Analysis and Modeling». Minsk, BSU, 1995, pp. 89-93.

Lindof, B., Holst, J. Suboptimal dual control of stochastic systems with time-varying parameters. Technical report TFMS-3152, Department of Mathematical Statistics, Lund Institute of Technology, Lund, Sweden, 1997. 25 p.