Generalized moment estimation of multi-dimensional uncertain differential equations

Article type: Research Article

Authors: Yao, Linjie | Zhang, Guidong | Sheng, Yuhong^{; *}

Affiliations: College of Mathematical and System Sciences, Xinjiang University, Urumqi, China

Correspondence: [*] Corresponding author. Yuhong Sheng, College of Mathematical and System Sciences, Xinjiang University, Urumqi 830046, China. Tel.: +86 18167978160; E-mail: shengyh@xju.edu.cn.

Abstract: Multi-dimensional uncertain differential equations (MUDEs) are often used to describe complex systems that vary with time. In this paper, the generalized moment estimation method is employed to estimate the MUDEs’ unknown parameters. A method to optimize parameters with multiple estimation results is proposed. The hypothesis test and α-path are proposed to verify the feasibility of the parameter results. Several examples of parameter estimation for MUDEs are given, as well as two numerical examples to verify the feasibility of the method.

Keywords: Uncertainty theory, multi-dimensional uncertain differential equation, generalized moment estimation, parameter estimation

DOI: 10.3233/JIFS-213503

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 2, pp. 2427-2439, 2023