Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input
We consider an initial value problem for a second-order nonlinear dynamical system that allows discontinuous inputs. In this problem, one state variable is restricted in a closed and bounded interval while the other state variable is unlimited. The existence and uniqueness of the solution to this pr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | http://dx.doi.org/10.1080/27690911.2022.2151595 |
| _version_ | 1797640999539834880 |
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| author | Jing Xu Qiuguo Zhu Jun Wu Rong Xiong |
| author_facet | Jing Xu Qiuguo Zhu Jun Wu Rong Xiong |
| author_sort | Jing Xu |
| collection | DOAJ |
| description | We consider an initial value problem for a second-order nonlinear dynamical system that allows discontinuous inputs. In this problem, one state variable is restricted in a closed and bounded interval while the other state variable is unlimited. The existence and uniqueness of the solution to this problem is studied in a time interval determined by two adjacent instants at which the input may be discontinuous. Some results are obtained on the maximal interval of existence of the unique solution in this time interval. The results are then extended to the entire time domain. A robot example is given to verify our results. |
| first_indexed | 2024-03-11T13:39:16Z |
| format | Article |
| id | doaj.art-4d5ad5f046df408ca2041ca9d0134e67 |
| institution | Directory Open Access Journal |
| issn | 2769-0911 |
| language | English |
| last_indexed | 2024-03-11T13:39:16Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj.art-4d5ad5f046df408ca2041ca9d0134e672023-11-02T13:48:31ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112023-12-0131110.1080/27690911.2022.21515952151595Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous inputJing Xu0Qiuguo Zhu1Jun Wu2Rong Xiong3Zhejiang UniversityZhejiang UniversityZhejiang UniversityZhejiang UniversityWe consider an initial value problem for a second-order nonlinear dynamical system that allows discontinuous inputs. In this problem, one state variable is restricted in a closed and bounded interval while the other state variable is unlimited. The existence and uniqueness of the solution to this problem is studied in a time interval determined by two adjacent instants at which the input may be discontinuous. Some results are obtained on the maximal interval of existence of the unique solution in this time interval. The results are then extended to the entire time domain. A robot example is given to verify our results.http://dx.doi.org/10.1080/27690911.2022.2151595dynamical systemdiscontinuous inputnonlinear ordinary differential equationinitial value problemexistence and uniquenessmaximal interval of existence |
| spellingShingle | Jing Xu Qiuguo Zhu Jun Wu Rong Xiong Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input Applied Mathematics in Science and Engineering dynamical system discontinuous input nonlinear ordinary differential equation initial value problem existence and uniqueness maximal interval of existence |
| title | Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input |
| title_full | Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input |
| title_fullStr | Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input |
| title_full_unstemmed | Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input |
| title_short | Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input |
| title_sort | existence and uniqueness of the solution to a second order nonlinear dynamical system model with an unbounded variable and a discontinuous input |
| topic | dynamical system discontinuous input nonlinear ordinary differential equation initial value problem existence and uniqueness maximal interval of existence |
| url | http://dx.doi.org/10.1080/27690911.2022.2151595 |
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