On the numerical approximation of some inverse problems governed by nonlinear delay differential equation
Mourad Nachaoui, Abdeljalil Nachaoui, Tamaz Tadumadze
Abstract
The paper deals with the approximate solving of an inverse problem for the nonlinear delay differential equation, which consists of finding the initial moment and delay parameter based on some observed data. The inverse problem is considered as a nonlinear optimal control problem for which the necessary conditions of optimality are formulated and proved. The obtained optimal control problem is solved by a method based on an improved parallel evolutionary algorithm. The efficiency of the proposed approach is demonstrated through various numerical experiments.
Topics & Concepts
MathematicsNonlinear systemInverse problemOptimal controlMoment (physics)InverseDelay differential equationApplied mathematicsDifferential equationMathematical optimizationMathematical analysisClassical mechanicsPhysicsGeometryQuantum mechanicsNumerical methods in inverse problemsTopology Optimization in EngineeringIterative Methods for Nonlinear Equations