Parameter Identification Of Time-Delay Systems: A Flatness Based Approach?

Abstract: The use of mathematical models is widely established in various fields of application. To name but a few of their major applications, mathematical models can improve the controller design of complex technical systems or are able to facilitate the understanding of highly complex biochemical systems. No matter what mathematical models are used for, however, they fail to perform the intended task if they are badly parameterized. In general, during the process of parameterization one tries to make differences between simulation results and measurement data as small as possible. Under the assumption of a suitable model candidate this is done by choosing optimal model parameters. Unfortunately, the majority of used models cannot be solved analytically. For example, many dynamical processes are described by systems of ordinary differential equations (ODEs). Usually, analytical solutions do not exist. Although quite efficient numerical routines are available they usually slow down the parameterization process dramatically. The situation is even more demanding if one has to deal with processes that are described by delay differential equations (DDEs). Commonly, standard DDE solvers show a lack of efficiency as well as of robustness, i.e., they are likely to fail to solve the underlying DDE system