Finally, new paper!
Actually, I was working on this for almost three months (in the background). As a result, the summary of application the parameter continuation methods to control and parameter identification is presented. At this point I finish the work on algorithmic methods. I will continue to search for applications where it can be successfully used. Also important to consider with category theory the more abstract issues of control problems with linearization and parameter continuation.
You can also download Simulink models for this article.