Stabilization of the Controlled Inverted Pendulum by a Control with Delay
作者： Leonid Shaikhet
DOI: 10.1007/978-3-319-00101-2_8
关键词:
摘要: Chapter 8 devotes to the classical problem of stabilization controlled inverted pendulum. The for mathematical model pendulum during many years is very popular among researchers. Unlike way in which stabilized control a linear combination state and velocity here another proposed. It supposed that only trajectory can be observed depends on whole Linear nonlinear models by stochastic perturbations are considered, particular, under influence Markovian perturbations. Via general method construction Lyapunov functionals sufficient conditions zero solution obtained, nonzero steady-state solutions investigated. 38 figures show behavior case stable unstable equilibrium.
springer.com
sci-hub.st 参考文章(15)
Leonid Shaikhet, Lyapunov Functionals and Stability of Stochastic Difference Equations ,(2011)
Richard Sharp, Yen-Hsi Tsai, Björn Engquist, Multiple Time Scale Numerical Methods for the Inverted Pendulum Problem Springer, Berlin, Heidelberg. pp. 241- 261 ,(2005) , 10.1007/3-540-26444-2_13
Multiscale Methods in Science and Engineering Springer. ,(2005) , 10.1007/B137594
Mark Levi, Stability of the Inverted Pendulum—A Topological Explanation SIAM Review. ,vol. 30, pp. 639- 644 ,(1988) , 10.1137/1030140
J. M. SANZ-SERNA, STABILIZING WITH A HAMMER Stochastics and Dynamics. ,vol. 08, pp. 47- 57 ,(2008) , 10.1142/S0219493708002263
Leonid Shaikhet, , Improved condition for stabilization of controlled invertedpendulum under stochastic perturbations Discrete and Continuous Dynamical Systems. ,vol. 24, pp. 1335- 1343 ,(2009) , 10.3934/DCDS.2009.24.1335
R. Mitchell, Stability of the inverted pendulum subjected to almost periodic and stochastic base motion—An application of the method of averaging International Journal of Non-Linear Mechanics. ,vol. 7, pp. 101- 123 ,(1972) , 10.1016/0020-7462(72)90025-X
L. Shaikhet, STABILITY OF DIFFERENCE ANALOGUE OF LINEAR MATHEMATICAL INVERTED PENDULUM Discrete Dynamics in Nature and Society. ,vol. 2005, pp. 215- 226 ,(2005) , 10.1155/DDNS.2005.215
A.I. Ovseyevich, The stability of an inverted pendulum when there are rapid random oscillations of the suspension point Journal of Applied Mathematics and Mechanics. ,vol. 70, pp. 762- 768 ,(2006) , 10.1016/J.JAPPMATHMECH.2006.11.010
Gustavo J Mata, E Pestana, Effective Hamiltonian and dynamic stability of the inverted pendulum European Journal of Physics. ,vol. 25, pp. 717- 721 ,(2004) , 10.1088/0143-0807/25/6/003