Explicit Calculation of Reachable Sets to Illustrate Concepts in Optimal Control

This paper, which grew out of an ongoing project geared towards improvements in control education, provides an example of an autonomous two-dimensional control system which is simple enough to be completely analyzed analytically, but rich enough to exhibit interesting features. This example can be readily used in a course on optimal control to illustrate und visualize relevant control-theoretical concepts. We tried to present the material in a comprehensible and illustrative way which can be easily adapted for classroom use.