About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps
The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pendulum. Linear and nonlinear models of the controlled inve...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/1/29 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832589139730497536 |
|---|---|
| author | Leonid Shaikhet |
| author_facet | Leonid Shaikhet |
| author_sort | Leonid Shaikhet |
| collection | DOAJ |
| description | The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pendulum. Linear and nonlinear models of the controlled inverted pendulum are considered, and the stability of the zero and nonzero equilibria is studied. The obtained results are illustrated by examples with numerical simulation of solutions of the equations under consideration. |
| format | Article |
| id | doaj-art-b260eff0685a4b3ab1ddb10ca857fd74 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-b260eff0685a4b3ab1ddb10ca857fd742025-01-24T13:22:12ZengMDPI AGAxioms2075-16802024-12-011412910.3390/axioms14010029About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s JumpsLeonid Shaikhet0Department of Mathematics, Ariel University, Ariel 40700, IsraelThe classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pendulum. Linear and nonlinear models of the controlled inverted pendulum are considered, and the stability of the zero and nonzero equilibria is studied. The obtained results are illustrated by examples with numerical simulation of solutions of the equations under consideration.https://www.mdpi.com/2075-1680/14/1/29controlled inverted pendulumstochastic perturbationsPoisson’s jumpszero and nonzero equilibriaasymptotic mean square stabilitystability in probability |
| spellingShingle | Leonid Shaikhet About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps Axioms controlled inverted pendulum stochastic perturbations Poisson’s jumps zero and nonzero equilibria asymptotic mean square stability stability in probability |
| title | About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps |
| title_full | About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps |
| title_fullStr | About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps |
| title_full_unstemmed | About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps |
| title_short | About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps |
| title_sort | about stabilization of the controlled inverted pendulum under stochastic perturbations of the type of poisson s jumps |
| topic | controlled inverted pendulum stochastic perturbations Poisson’s jumps zero and nonzero equilibria asymptotic mean square stability stability in probability |
| url | https://www.mdpi.com/2075-1680/14/1/29 |
| work_keys_str_mv | AT leonidshaikhet aboutstabilizationofthecontrolledinvertedpendulumunderstochasticperturbationsofthetypeofpoissonsjumps |