Second order analysis for the optimal selection of time delays

TL;DR

This paper investigates the second-order derivatives of solutions to delay differential equations to optimize delay selection, employing adjoint calculus for efficient sensitivity analysis.

Contribution

It introduces a second-order sensitivity analysis framework for delay differential equations, utilizing adjoint calculus to improve delay optimization methods.

Findings

Second-order derivatives of solutions are characterized.

An adjoint calculus approach simplifies sensitivity computations.

Application to delay optimization demonstrates effectiveness.

Abstract

For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated optimization problem for the time delay. A first- and second-order sensitivity analysis is performed including an adjoint calculus that avoids the second derivative of the state with respect to the delay.