Structure of the algorithm for modeling optimal movement of a compound dynamic system

The work is devoted to the development of the structure of the algorithm for modeling the optimal movement of complex dynamic systems (SDS) along a branched trajectory. Complex systems are called systems consisting of separate subsystems, the flight trajectories of which differ and are called branched. Branched trajectories should consist of trajectory segments, the first of which will be common to the entire SDS, and the other trajectory branches will be different, as each subsystem moves to its goal along its own trajectory segment. The proposed algorithm makes it possible to optimize such trajectories in real time and to carry out operational correction of SDS trajectories in the event of the occurrence of unpredictable influencing factors. It is known that the effectiveness of the SDS functioning between structural transformations depends on the coordinates of the mutual location and speed of each subsystem and the choice of optimal moments of time for structural transformations. The efficiency of determining these parameters during the flight is fundamentally important. The necessary conditions for the optimality of the trajectory of the SDS movement are found, which are universal for problems with any finite number of trajectory branches. The implementation of the proposed conditions will allow to reduce the number of computational procedures in the control calculations in conditions of uncertainty of the initial conditions. These conditions are the methodological basis for the development of computational algorithms for modeling the optimal trajectories of the SDS movement. The necessary optimality conditions have a clear physical meaning and are technological and user-friendly. The results of the research presented in the article are important and relevant for the construction of the laws of trajectory control of existing and prospective SDS.