Abstract
The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.
Highlights
For the sake of rationally handling the likelihood that something will happen, uncertainty theory was established by Liu [1] and perfected by Liu [2]
Among the theoretical branches of uncertainty theory, an uncertain differential equation is a type of differential equation driven by Liu process
As the most significant contribution, the Yao–Chen formula was shown by Yao and Chen [10] to associate uncertain differential equation with ordinary differential equations, which greatly promoted the development of uncertain differential equation
Summary
For the sake of rationally handling the likelihood that something will happen, uncertainty theory was established by Liu [1] and perfected by Liu [2]. Among the theoretical branches of uncertainty theory, an uncertain differential equation is a type of differential equation driven by Liu process. Based on the Yao–Chen formula, the numerical method of solving uncertain differential equation was first presented by Yao and Chen [10], which was developed by Yang and Shen [11], Yang and Ralescu [12], Gao [13], etc. In order to model the series RL circuit system more reasonably, this paper first proposes the uncertain RL circuit equation based on multifactor uncertain differential equation by considering the external noise and internal noise.
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