Orbital Decompositions of Control Systems and Trajectory Planning

The paper studies the problem of transferring a nonlinear dynamic control system from a given initial state to a given final state. An approach is developed based on constructing such a decomposition of the system, in which the specified problem is transformed into two coupled Cauchy problems. One of these problems has boundary conditions at the initial moment, and the second — at the final moment. The case is considered when the boundary conditions of the problem are imposed only on a part of the state variables. To transform the system into a decomposable form, invertible transformations of the most general type are used — orbital equivalences. The given nontrivial example demonstrates the possibility of implementing the specified approach.