Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input. Issue 1 (31st December 2023)

• Record Type: Journal Article
• Authors: Xu, Jing; Zhu, Qiuguo; Wu, Jun; Xiong, Rong
• Is Part Of: Applied mathematics in science and engineering. Volume 31:Issue 1(2023)
• Publication Date: 2023-12-31
• Subjects: Dynamical system -- discontinuous input -- nonlinear ordinary differential equation -- initial value problem -- existence and uniqueness -- maximal interval of existence; 34A12 -- 34A34 -- 34A36; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2022.2151595
• Languages: English
• ISSNs: 2769-0911

Abstract

Abstract : 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.