Problem of Stabilizing a Switching System Using a Piecewise-Linear Control System
- Authors: Atanesyan A.A.1, Tochilin P.A.1
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Affiliations:
- Department of Computational Mathematics and Cybernetics
- Issue: Vol 43, No 4 (2019)
- Pages: 166-176
- Section: Article
- URL: https://journals.rcsi.science/0278-6419/article/view/176324
- DOI: https://doi.org/10.3103/S0278641919040046
- ID: 176324
Cite item
Abstract
The problem of stabilizing a mathematical hybrid system with switchings between the operating modes is solved. Each of these modes is associated with nonlinear differential equations that have control parameters. The switching instances (conditions) are control components. A stabilizer must be designed in positional form that allows the trajectory of the entire nonlinear system to reach the target set in the phase space for a (prescribed) finite time. To solve the problem, k]an apparatus of continuous piecewise-linear Lyapunov functions is used along with the corresponding piecewise-linear control functions. A theorem concerning the sufficient conditions for the stabilizability of a hybrid system in the considered class of controls is proved. An algorithm for constructing the Lyapunov functions and the stabilizer is given.
About the authors
A. A. Atanesyan
Department of Computational Mathematics and Cybernetics
Author for correspondence.
Email: at-an-ar@yandex.ru
Russian Federation, Moscow, 119991
P. A. Tochilin
Department of Computational Mathematics and Cybernetics
Author for correspondence.
Email: tochilin@cs.msu.su
Russian Federation, Moscow, 119991