Stabilization of a chain of three integrators by a feedback in the form of nested saturators

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Аннотация

The problem of stabilizing a chain of three integrators subject to a phase constraint by a continuous constrained control is considered. The application of a feedback in the form of nested saturators results in study of a switching system. Necessary conditions of local stability are established. A Lyapunov function is constructed by means of which it is proved that the necessary conditions are sufficient for global stability of the closed-loop system. The discussion is illustrated by numerical examples.

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Авторлар туралы

Yu. Morozov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Хат алмасуға жауапты Автор.
Email: tot1983@inbox.ru
Ресей, Moscow

A. Pesterev

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Email: alexanderpesterev.ap@gmail.com
Ресей, Moscow

Әдебиет тізімі

  1. Kurzhanski A.B., Varaiya P. Solution Examples on Ellipsoidal Methods: Computation inHigh Dimensions. Cham, Switzerland: Springer, 2014.
  2. Teel A.R. Global Stabilization and Restricted Tracking for Multiple Integrators with Bounded Controls // Sys. & Cont. Lett. 1992. V. 18. № 3. P. 165–171.
  3. Teel A.R. A Nonlinear Small Gain Theorem for the Analysis of Control Systems with Saturation // Trans. Autom. Contr. IEEE. 1996. V. 41. № 9. P. 1256–1270.
  4. Li Y., Lin Z. Stability and Performance of Control Systems with Actuator Saturation. Basel: Birkhauser, 2018.
  5. 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.
  6. Hua M.D., Samson C. Time Sub-optimal Nonlinear Pi and Pid Controllers applied to Longitudinal Headway Car Control // Intern. J. Control. 2011. V. 84. P. 1717–1728.
  7. Pesterev A.V., Morozov Yu.V., Matrosov I.V. On Optimal Selection of Coefficients of a Controller in the Point Stabilization Problem for a Robot-wheel // Communicat. Comput. Inform. Sci. (CCIS). 2020. V. 1340. P. 236–249.
  8. Pesterev A.V., Morozov Yu.V. Optimizing Coefficients of a Controller in the Point Stabilization Problem for a Robot-wheel // Lect. Notes Comput. Sci. 2021. V. 13078. P. 191–202.
  9. Pesterev A.V., Morozov Yu.V. The Best Ellipsoidal Estimates of Invariant Sets for a Third-Order Switched Affine System // Lect. Notes Comput. Sci. 2022. V. 13781. P. 66–78.
  10. Pesterev A.V., Morozov Yu.V. Optimizing a Feedback in the Form of Nested Saturators to Stabilize the Chain of Three Integrators // Lect. NotesComput. Sci. 2023. V. 14395. P. 88–88.
  11. Морозов Ю.В., Пестерев А.В. Глобальная устойчивость гибридной аффинной системы 4-го порядка // Изв. РАН. ТиСУ. 2023. № 5. С. 3–15.
  12. Пестерев А.В., Morozov Yu.V. Глобальная стабилизация интегратора второго порядка обратной связью в виде вложенных сатураторов // АиТ. 2024. № 4. C. 55–60.
  13. Поляк Б.Т., Щербаков П.С. Робастная устойчивость и управление. М.: Наука, 2002.
  14. Барбашин Е.А. Введение в теорию устойчивости. Сер.: Физико-математическая библиотека инженера. М.: Наука, 1967.
  15. Кузнецов Н.В. Теория скрытых колебаний и устойчивость систем управления // Изв. РАН. ТиСУ. 2020. № 5. C. 5–27.
  16. Лурье А.И., Постников В.Н. К теории устойчивости регулируемых систем // ПММ. 1944. № 3. C. 246–248.
  17. Рапопорт Л.Б. Оценка области притяжения в задаче управления колесным роботом // АиТ. 2006. № 9. С. 69–89.
  18. Generalov A., Rapoport L., Shavin M. Attraction Domains in the Control Problem of a Wheeled Robot Following a Curvilinear Path over an Uneven Surface // Lect. NotesComput. Sci. 2021. V. 13078. P. 176–190.

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Әрекет
1. JATS XML
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2. Formula 4.1

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3. Formula 4.2

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4. Formula 4.3

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5. Formula 4.4

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6. Fig. 1. Partition of the phase plane into sets D1, D2, D3

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7. Fig. 2. Level surface of the Lyapunov function (4.1)

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8. Fig. 3. Intersection of invariant regions and Π

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9. Fig. 4. Intersection of invariant regions and Π

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10. Fig. 5. Graphs of the time dependences of the deviation x1(t) (1), speed x2(t) (2), acceleration x3(t) (3) and control U(t) (4)

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