MS19.4: Systems with Time Delay

A time-series based approach has been developed to overcome the tedious calculations involved in the center manifold reduction for delay-differential equations. By using a numerical solution at the critical value of the bifurcation parameter, the coefficients of flow on the center manifold are recovered by a least-squares fit. This planar system can then be analyzed by normal form theory.

We study theoretically the mechanisms of square-wave (SW) formation in vertical external-cavity Kerr-Gires-Tournois interferometers in presence of anti-resonant injection. We provide simple analytical approximations for their plateau intensities and for the conditions of their emergence. We demonstrate that SWs may appear via a homoclinic snaking scenario, leading to the formation of complex-shaped multistable SW solutions. The resulting SWs can host localized structures and robust bound-states.

Inverted pendulum systems are classical mechanical systems for studying stability and control algorithms. To identify a delayed PD controller of a cart inverted pendulum, an adjoint sensitivity analysis based algorithm is proposed for the control parameters identification. The result shows that the proposed algorithm is efficient and accurate for parameter identification of retarded systems.

A human-in-the-loop simulation environment is developed to investigate the guided control of a human driver via an automated lead vehicle. The lead vehicle is following a reference velocity, while it also takes into account the velocity of the following human-driven vehicle. The graphical interface displays the automated vehicle ahead and the human operator controls the velocity of the following vehicle with a pedal. Using various control gain combinations of the automated vehicle, nine subjects carried out measurements, which show good agreement with the theoretical stability boundaries.