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No doubt: Mathematics has become a technology in its own right, maybe even a key technology. Technology may be defined as the application of science to the problems of commerce and industry. And science? Science maybe defined as developing, testing and improving models for the prediction of system behavior; the language used to describe these models is mathematics and mathematics provides methods to evaluate these models. Here we are! Why has mathematics become a technology only recently? Since it got a tool, a tool to evaluate complex, "near to reality" models: Computer! The model may be quite old - Navier-Stokes equations describe flow behavior rather well, but to solve these equations for realistic geometry and higher Reynolds numbers with sufficient precision is even for powerful parallel computing a real challenge. Make the models as simple as possible, as complex as necessary - and then evaluate them with the help of efficient and reliable algorithms: These are genuine mathematical tasks.
Optimal control methods for the calculation of invariant excitation signals for multibody systems
(2010)
Input signals are needed for the numerical simulation of vehicle multibody systems. With these input data, the equations of motion can be integrated numerically and some output quantities can be calculated from the simulation results. In this work we consider the corresponding inverse problem: We assume that some reference output signals are available, typically gained by measurement and focus on the task to derive the input signals that produce the desired reference output in a suitable sense. If the input data is invariant, i.e., independent of the specific system, it can be transferred and used to excite other system variants. This problem can be formulated as optimal control problem. We discuss solution approaches from optimal control theory, their applicability to this special problem class and give some simulation results.