Parameter estimation in uncertain differential equations with exponential solutions

Abstract

This paper proposes three methods to estimate the parameters in uncertain differential equations (UDEs) based on discrete observation data. The first method is designed for a class of UDEs in which their solutions have the explicit expressions of uncertainty distribution. The second method is given to solve the estimation problem through the inverse uncertainty distribution. In the third method, the unknown parameters of UDEs are estimated by the solution of the corresponding α-path. These methods are interpreted to be efficient and practical by using a popular UDE with exponential solutions and obtaining the detailed estimators of the parameters.