Variational principles in optimal control and their applications

In this paper, the classical variational principles and generalized variational principles in optimal control are established, and the compatible model, hybrid model, mixed compatible model and mixed hybrid model are provided. As an example, using mixed compatible model, algorithm and modeling results are presented. These classical variational principles and generalized variational principles cannot only be valid for holonomic control systems but also be valid for nonholonomic control systems.