Title:
Computational methods for distributed delay differential equations based on kernel approximations

Abstract:
In this presentation, we will discuss computational methods for delay differential equations (DDEs) with distributed (or continuous) time delays. The key innovation is that we approximate the involved kernels (or memory functions) by the probability density function of a mixed Erlang distribution. We will discuss the validity of this approximation as well as potential alternatives. Next, we will present methods for numerical simulation and identification of the kernel based on the approximations and the linear chain trick (LCT). Finally, we will briefly look at future research topics, including 1) methods for control based on linearization of the kernel, 2) derivation of DDEs with distributed time delays for basic phenomena, e.g., flow in a pipe, 3) PID control algorithms with forgetting factors, and 4) the effective memory of conventional PID controllers.