TITLE OF YOUR SUBMISSION
Estimation of absolute and distributed time delays in differential equations based on the linear chain trick

ABSTRACT
Many dynamical processes involve time delays, and they have a significant effect on the stability and dynamics of the process. Therefore, it is important to account for them when designing an advanced process control strategy. However, identifying delays in general nonlinear differential equations is not trivial because the numerical simulation of such systems requires specialized methods. Therefore, in this presentation, we 1) describe how delays (both absolute and distributed delays) can be approximated by a distributed delay with an Erlang probability density function as kernel (also called memory function), 2) use the linear chain trick (LCT) to transform the resulting distributed delay differential equations (DDEs) to ordinary differential equations (ODEs), and 3) formulate the delay identification problem as a least-squares parameter estimation problem. We solve this problem using a single-shooting method and we compute the gradient of the objective function using a forward approach. We implement the method in Matlab, and we solve the involved optimization problem using fmincon. Furthermore, we discuss different regularization strategies for encouraging sparsity in the kernel parameters as well as an either small or large kernel derivative. Finally, we present numerical examples involving joint parameter and delay estimation in the logistic equation and in an exothermic chemical reaction in a continuous stirred tank reactor (CSTR).