# High-dimensionality

## Regulatory theoretical aspects of nonlinear, high-dimensional systems

For the control of complex, nonlinear systems, suboptimal control trajectories are to be found in the high-dimensional state space. High dimensionality prohibits a gradient-based search for optimal control-based trajectories for reasons of exponential growth of the calculation time. Nonlinearity therefore forbids an analytical solution. Various approaches are being explored. One idea is to be able to reduce the order of the system. Established methods for reducing high-dimensional, nonlinear systems require a selection of state points. Most of the time, however, it is not known which ones are interesting. In addition, they only partially cover the condition space, which limits the model quality in an unforeseen state. In the procedure examined, the entire state space is to be mapped.