“Sensitivity analysis of systems with delays”

During the lecture the structural approach to sensitivity analysis, both forward and adjoint, will be presented. It is assumed that the system with discrete delay(s) is given in a structural form – as a block diagram. Then, a set of simple rules is used for construction of a sensitivity and/or adjoint system. They can serve for generation of a gradient of a given objective function (in parameter estimation or control optimization problems) in spaces of: parameters of the model, including delay times, and in spaces of initial functions for delay elements. Examples of estimation of parameters and initial functions for different model structures and measurements will be presented. Some remarks on identifiability of such systems will be given as well.