Tachynina O. Methods for the synthesis of optimal control of deterministic compound dynamical systems with branching trajectories of motion

The thesis is dedicated to the development of methods for the optimal control of discontinuous systems with respect to their application for solving the problems of operative synthesis of necessary, sufficient, necessary and sufficient conditions for optimality of branching trajectories and control of modern and perspective compound dynamic systems. The scientific problem of optimality conditions development describing the set of operations and rules of their alternation is investigated and solved, which are the basis for the operational synthesis of optimal control of compound dynamical systems that move along branching trajectories. The necessary, sufficient, necessary and sufficient conditions for the optimality of the control of a deterministic compound dynamical system moving along a branching trajectory with an arbitrary branching scheme are formulated and proved in the form of basic theorems. From the main theorems, we deduce the consequences for the most typical practical cases of branching trajectories of compound dynamical systems. The consequences are presented in the form of the most computational algorithms for developing on their basis.