Stabilization of first integrals in optimal control problem

The paper considers methods for solving the variational problem of implementing control that stabilizes the optimal movement of the rocket in gravitational fields, finding the most accurate trajectories, and applying the results to solve various practical problems of flight dynamics. The relevance of the study of these problems is due to the fact that space guidance and tracking of the object's trajectory during the entire flight is the most important basis for a successful space maneuver of ships, satellites, and missiles. Building and implementing in practice the laws of Autonomous guidance in application to modern types of propulsion technology is an acute unsolved problem today, which depends on the ability of aircraft engines to produce the necessary thrust for flight. It takes into account the fact that in reality the object does not fly along the specified trajectory, but has a certain deviation due to inaccuracies in the parameters of the flight model and the propulsion system. Therefore, it is necessary to set the stabilization problem in order to find optimal control conditions. The problems of stabilization and traffic control are important both from a theoretical point of view and because of numerous technical applications. From a theoretical point of view, these problems are important primarily because they relate to complex problems of mechanics, and each time they require new approaches and methods for their solution. In this case, the nature of the problem of motion stabilization depends significantly on the additional conditions that are imposed on the dynamic system. © Published under licence by IOP Publishing Ltd.