Please advise literature or articles on nonlinear geometric control (for beginners). Preferably with computational examples. I want to study this topic, but I do not know where to start.
Remark:
Thanks to everyone who advised the book. I have not studied all the questions, but the initial presentation in my head has taken shape. Some of the "white spots" in these books for me remain: 1. Computational aspects. The object is represented in a similar way to the classical form in the state space as А * x + B * u, which is easy to model in Simulink. How are computations organized in the framework of group theory? 2. Optimum. How is a system created in the framework of geometrical control, the transient processes in which are characterized by given parameters: overshoot and the end time of the transition process? 3. Control of non-linear objects with features: are there any advantages of geometric control of non-linear objects, for example, with friction?
I hope my questions are relevant and correctly posed.
Try Geometric Optimal Control by Schättler-Ledzewicz. They do a lot of applications. I also liked Sussman's Introduction to the coordinate-free Maximum Principle for a more philosophical take. There is also one by Russian authors, Control Theory from Geometric Viewpoint by Agrachev-Sachkov, but I am not sure about "for beginners". A very different type of geometric approach, based not on Pontryagin's maximum principle but rather geometric feedback approach, is in Singular Optimal Control in Mathematical Economics by Zelikin-Borisov. They are pretty elementary and do many examples.