Global Stability of a Second-Order Affine Switching System

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Acesso é pago ou somente para assinantes

Resumo

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.

Sobre autores

A. Pesterev

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences

Autor responsável pela correspondência
Email: alexanderpesterev.ap@gmail.com
Moscow, Russia

Bibliografia

  1. Goebel R., Sanfelice R.G., Teel A.R. Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, 2012.
  2. Liberzon D. Switching in Systems and Control. Boston: Birkhauser, 1973.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Kurzhanski A.B., Varaiya P. Solution Examples on Ellipsoidal Methods: Computation in High Dimensions. Cham, Switzerland: Springer, 2014.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Пестерев А.В., Морозов Ю.В. Стабилизация тележки с обратным маятником // АиТ. 2022. № 1. С. 95-112.
  15. Andronov A.A., Leontovich E., Gordon I.I., Maier A. Qualitative Theory of Second-order Dynamic Systems. Wiley, 1973.
  16. Boyd S., Ghaoui L.E., Feron E., Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
  17. Пестерев А.В. Построение наилучшей эллипсоидальной аппроксимации области притяжения в задаче стабилизации движения колесного робота // АиТ. 2011. № 3. С. 51-68.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar

Declaração de direitos autorais © The Russian Academy of Sciences, 2023