Parameter estimation in uncertain delay differential equations via the method of moments

Abstract

Uncertain delay differential equations model time-delayed automatic control systems in which noises are described by Liu process. Parameter estimation plays a pivotal part in the applications of uncertain delay differential equations. In this paper, we first obtain a difference equation of uncertain delay differential equations by the forward Euler’s method. A function of the parameter is given by the difference equation, which is verified to obey the standard normal uncertainty distribution. By using the method of moments, we employ the observed data to obtain the empirical moments that equal the moments given by the standard normal uncertainty distribution, the estimated value of parameters are derived. Moreover, some examples are investigated to demonstrate that the method of moments is effective. Finally, we provide an uncertain delay logistic model to describe the population dynamics of American by using the method of parameter estimation proposed in this paper.