Discrete Stochastic Regulator on a Manifold, Minimizing Dispersion of the Output Macrovariable
https://doi.org/10.17587/mau.20.707-713
Abstract
A theoretical result is presented in the form of a new algorithm for the synthesis of a control system over a non-linear object, whose mathematical model represents a stochastic matrix difference equation having noise with a zero mean and finite dispersion in the righthand part. The new algorithm for synthesizing stochastic control for such an object is based on a three-stage procedure. In the first stage, the structure of the control system is formed in accordance with the classical method of analytical design of aggregated regulators (ADAR) in a fixed-noise assumption. In the second stage, the conditional mathematical expectation of the resulting expression for the first-stage control is determined. In the third stage, the control model is refined by excluding the noise variable from the control formula based on decomposing the initial control system affected by the new control. It is shown that the proposed control strategies minimize the target macro variable dispersion and ensure a stable, on average, achievement of the target manifold. A detailed example of an application of the algorithm for synthesizing control over the motion of an immobile center of mass is given, whose analog is represented by the objects such as by robot-manipulators, is given. The results of numerical modeling are presented, which confirm the operability of the constructed controller. Numerical simulations of the designed control system was performed using the authentic working equipment data.
About the Authors
A. A. Kolesnikov
Institute of Computer Technology and Information Security of SFU University
Russian Federation
Russian Federation
Taganrog, 347922
S. I. Kolesnikovа
SUAI University
Russian Federation
Russian Federation
Kolesnikova Svetlana, D. Sc.
St. Petersburg, 190000
S. A. Tsvetnitskaya
TSU University
Russian Federation
Russian Federation
Tomsk, 634050
References
1. Kolesni kov А. А. Synergetics and problems of control theory: Collected articles, Moscow, Fizmatlit, 2004, 504 p. (In Russian).
2. Khalil H. K. Nonlinear systems, Prentice Hall, 1996, 734 p.
3. Kokotović P., Arcak M. Activation of Nonlinear Feedback Concepts. In: Djaferis T. E., Schick I. C. (eds) System Theory, The Springer International Series in Engineering and Computer Science, 2000, vol. 518. Springer, Boston, MA, pp. 379—389, available at: https://doi.org/10.1007/978-1-4615-5223-9_28.
4. Utkin V. I. Sliding modes in control and optimization, Springer, 2012, 286 p, available at: http://bookre.org/reader?file=1220607.
5. Tyukin I. Yu., Terekhov V. A. Adaptation in nonlinear dynamical systems, SPb, LKI, 2008, 384 p. (in Russian), available at: http://bookre.org/reader?file=760301.
6. Krasovskiy A. A. Problems of Control Physical Theory, Avtomatika i telemehanika, 1990, no. 1, pp. 3—28 (in Russian).
7. Astroem K. J. Introduction to Stochastic Control Theory, New York and London, Academic Press, 1970, 299 p.
8. Astroem K. J., Wittenmark B. Adaptive control, New York, Dover Publications, 2008, 590 p.
9. Matyukhin V. I. Stabilizing manipulator motion along a given surface. Automation and Remote Control, 2011, vol. 72, no. 4, pp. 740—753.
10. Matyukhin V. I. Stability of the manifolds of controlled motions of a manipulator, Automation and Remote Control, 1998, vol. 59, no. 4, pp. 494—501.
11. Pobegailo P. A. The working equipment of a single-bucket hydraulic excavator: on the accuracy of bucket movement, Gornyy informatsionno-analiticheskiy byulleten (nauchno-tekhnicheskiy zhurnal), 2017, no. 11, pp. 113-117 (in Russian).
12. Kolesnikova S. I. A multiple-control system for nonlinear discrete object under uncertainty, Optimization Methods and Software, 2018, vol. 34, no. 3, pp. 578—585, available at: https://doi.org/10.1080/10556788.2018.1472258.
13. Kolesnikov A. A. New nonlinear methods of flight control, Moscow, Fizmatlit, 2013, 193 p. (in Russian).
14. Kolesnikova S. I. Synthesis of a stochastic controller on manifolds for a nonlinear discrete object, Prikladnaya informatika, 2018, no. 6, pp. 18—30 (in Russian), available at: https://www.litres.ru/s-kolesnikova/sintez-stohasticheskogo-regulyatora-dlyavyvodanel-40275083/.
Review
For citations:
Kolesnikov A.A., Kolesnikovа S.I., Tsvetnitskaya S.A. Discrete Stochastic Regulator on a Manifold, Minimizing Dispersion of the Output Macrovariable. Mekhatronika, Avtomatizatsiya, Upravlenie. 2019;20(12):707-713. https://doi.org/10.17587/mau.20.707-713
Views:
717
.png)
Email this article 