A counter-motion method for the solution of a control problem for a final state (Q1914127)

A nonlinear control system is considered, assuming that the admissible controls are piecewise constant functions satisfying some geometrical constraints. The problem consists in synthesizing a control that transfers the system from an initial state to a specified final state. An approach for obtaining a quasioptimal solution to this problem is proposed. This approach consists in establishing a suitable step-wise motion of the system from the initial and final states in opposite directions (at each step, the control vectors are taken to be constant). The corresponding numerical results for solving the example of leading of an aircraft are presented.