Мақаланы E-mail арқылы жіберу Global Stability of a Second-Order Affine Switching System
- Авторлар: Pesterev A.1
-
Мекемелер:
- Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
- Шығарылым: № 9 (2023)
- Беттер: 95-105
- Бөлім: Articles
- URL: https://journals.rcsi.science/0005-2310/article/view/142072
- DOI: https://doi.org/10.31857/S0005231023090052
- EDN: https://elibrary.ru/JSXFFD
- ID: 142072
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
Stability of an affine switching system is studied. The system comes to existence when stabilizing a chain of two integrators by means of a feedback in the form of nested saturators. The use of such a feedback allows one to easily take into account boundedness of the control resource, to constrain the maximum velocity of approaching the equilibrium state, which is especially important in the case of large initial deviations, and to ensure desired characteristics of the transient process, such as a given exponential rate of the deviation decrease near the equilibrium state. It is proved that the closed-loop system is globally stable.
Авторлар туралы
A. Pesterev
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Хат алмасуға жауапты Автор.
Email: alexanderpesterev.ap@gmail.com
Moscow, Russia
Әдебиет тізімі
- Goebel R., Sanfelice R.G., Teel A.R. Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, 2012.
- Liberzon D. Switching in Systems and Control. Boston: Birkhauser, 1973.
- Lin H., Antsaklis P.J. Stability and stabilizability of switched linear systems: A survey of recent results // IEEE Trans. Automat. Control. 2009. V. 54. P. 308-322.
- Pyatnitskiy E., Rapoport L. Criteria of asymptotic stability of di erential inclusions and periodic motions of time-varying nonlinear control systems // IEEE Trans. Circuits Systems I: Fundamental Theory and Applications. 1996. V. 43. No. 3. P. 219-229.
- Teel A.R. Global stabilization and restricted tracking for multiple integrators with bounded controls // Sys. & Cont. Lett. 1992. V. 18. No. 3. P. 165-171.
- Teel A.R. A nonlinear small gain theorem for the analysis of control systems with saturation // Trans. Autom. Contr., IEEE, 1996. V. 41. No. 9. P. 1256-1270.
- Kurzhanski A.B., Varaiya P. Solution Examples on Ellipsoidal Methods: Computation in High Dimensions. Cham, Switzerland: Springer, 2014.
- Olfati-Saber R. Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles, Ph.D. dissertation, Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science, 2001.
- Hua M.-D., Samson C. Time sub-optimal nonlinear pi and pid controllers applied to longitudinal headway car control // Int. J. Control. 2011. V. 84. P. 1717-1728.
- Pesterev A.V., Morozov Yu.V., Matrosov I.V. On Optimal Selection of Coe cients of a Controller in the Point Stabilization Problem for a Robot-wheel // Communicat. Comput. Inform. Sci. (CCIS). 2020. V. 1340. P. 236-249.
- Pesterev A.V., Morozov Yu.V. Optimizing coe cients of a controller in the point stabilization problem for a robot-wheel // Lect. Notes Comput. Sci. V. 13078. Cham, Switzerland: Springer, 2021. P. 191-202.
- Pesterev A.V., Morozov Yu.V. The Best Ellipsoidal Estimates of Invariant Sets for a Third-Order Switched A ne System // Lect. Notes Comput. Sci. V. 13781 Cham, Switzerland: Springer, 2022. P. 66-78.
- Pesterev A.V., Morozov Yu.V. Global Stability of a Switched A ne System // Proc. of the 16th Int. Conf. on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference). 2022. P. 1-4.
- Пестерев А.В., Морозов Ю.В. Стабилизация тележки с обратным маятником // АиТ. 2022. № 1. С. 95-112.
- Andronov A.A., Leontovich E., Gordon I.I., Maier A. Qualitative Theory of Second-order Dynamic Systems. Wiley, 1973.
- Boyd S., Ghaoui L.E., Feron E., Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
- Пестерев А.В. Построение наилучшей эллипсоидальной аппроксимации области притяжения в задаче стабилизации движения колесного робота // АиТ. 2011. № 3. С. 51-68.
