Application of homotopy methods to nonlinear control problems

The purpose of this article is to give a concise introduction to the use of homotopy methods for treating nonlinear control problems. The theoretical foundations are briefly sketched, especially some important topics concerning linearisation along trajectories. The main contribution is that for a certain control the deviation of the actual state from the target state is decaying exponentially with time. The proof of this statement contains an explicit design instruction for the required control. This design instruction is discussed in some detail and explicitly carried out for an example system. We conclude with a short comparison of two usual nonlinear control methods with the proposed method by means of the example system.