Orbital Decompositions of Control Systems and TrajectoryPlanning

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 system decomposition in which the problem is transformed into two coupled Cauchy problems. One of these problems has boundary conditions at the initial time, and the second, at the final time. The case is considered when the boundary conditions of the problem are imposed only on part of the state variables. To transform the system into a decomposable form, invertible transformations of the most general type—orbital equivalences—are used. We give a nontrivial example demonstrating the possibility of implementing this approach.