Control of Parametrically Perturbed Objects with a Full Information
https://doi.org/10.17587/mau.22.3-11
Abstract
The objective of this paper was to justify the new synthesis method of stabilizing controller for parametrically perturbed systems,which often appear in mobile robots, aircrafts, engineering objects with non-stationary parameters, intellectual control systems with aself-learning etc. Due to the high complexity and uncertainty of these systems, the classical PID controllers are not applicable and soa full information about the object state vector is used. Controllers obtained in this way allow to minimize the integral quality criterionof the system with the worst case parameter perturbation. For this purpose, the methods of differential games and switching systemstheories were applied. Control laws are calculated by using the value function of the corresponding differential game, which can beobtained by solving the Hamilton-Jacobi-Bellman-Isaacs equations. A special set of basic functions was developed to approximate thevalue function and satisfy the boundary conditions. Finally, controller synthesis for a specific object with a nonstationary parameteris given. It significantly exceeds both the linear and fuzzy controllers in terms of quality. In the task of analyzing system qualitativecharacteristics under the worst parametric perturbation, our results are compared to the modern direct collocation methods of optimalcontrol. With the same accuracy, proposed method is two times faster for low order systems. To verify that developed controllers canbe employed in real time applications, we present computational time and memory usage in the end of the article.
Keywords
differential games,
Hamilton-Jacobi-Bellman-Isaacs equations,
value function,
switching systems,
absolute stability,
Lyapunov functions,
implicit Euler scheme,
fuzzy controllers
Supporting agencies: This work was supported by the Russian Science Foundation, according to research project No 16-19-00052. Also, authors would like to thank Natalia Sadivova for translation assistance throughout all aspects of this paper.
About the Authors
V. P. Berdnikov
MIREA — Russian Technological University
Russian Federation
Russian Federation
Postgraduate Student
Moscow, 119454
V. M. Lokhin
MIREA — Russian Technological University
Russian Federation
Russian Federation
D. Sc, Professor
Moscow, 119454
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Review
For citations:
Berdnikov V.P., Lokhin V.M. Control of Parametrically Perturbed Objects with a Full Information. Mekhatronika, Avtomatizatsiya, Upravlenie. 2021;22(1):3-11. https://doi.org/10.17587/mau.22.3-11
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