Path following problem of a UAV carrying a pendulum

The linearized dynamics of a UAV was considered along with a pendulum hanging from it. The state trajectories of the center of mass of the UAV are given. Given the trajectory of the center of mass of the UAV and the state trajectory of its yaw angle, we have to find the control actions and conditions, under which the UAV would follow the path, while holding the pendulum stable around its lower equilibrium point. The problem is solved using the method for solving inverse problem of dynamics. All the state trajectories of the system and all the control actions are calculated. The condition is obtained, under which a solution to the path following problem exists. A specified simple trajectory is chosen as an example to visualize the results.