Residual-Based Parameter Estimation for Higher-Order Uncertain Differential Equations

Uncertain differential equations have been expanded in many directions as an important modeling tool. As a class of differential equations including higher-order derivatives of uncertain processes, higher-order uncertain differential equations are widely used in the modeling of dynamic systems in uncertain environments. The equations usually involve unknown parameters to be estimated, and parameter estimation methods based on the difference format do not work when the time intervals between observations are not short enough. In this paper, residual-based moment estimation is applied to higher-order uncertain differential equations, some examples are given to illustrate the parameter estimation methods, and uncertain hypothesis test is used to verify whether the higher-order uncertain differential equations fit the observations.