Uncertain Circuit Equation
Yang Liu
Abstract
Differential equation is a powerful tool for investigating the transient and steady-state solutions of electrical circuit in the time domain. By considering the noise in actual circuit system, this paper first presents an uncertain circuit equation, which is a type of differential equation driven by Liu process. Then the solution of uncertain circuit equation and the inverse uncertainty distribution of solution are derived. Following that, two applications of solution are provided as well. Based on the observations, the method of moments is used to estimate the unknown parameters in uncertain circuit equation. In addition, a paradox for stochastic circuit equation is also given.
Topics & Concepts
Differential equationStochastic differential equationTransient (computer programming)Characteristic equationPartial differential equationFirst-order partial differential equationMathematicsComputer scienceControl theory (sociology)Applied mathematicsMathematical analysisOperating systemArtificial intelligenceControl (management)Fuzzy Systems and OptimizationControl Systems and IdentificationProbabilistic and Robust Engineering Design