Transferring a system with unknown disturbance under optimal control to a state of dynamic balance and to $\epsilon$-vicinity of a final state

The problem of transferring a linear system to a state of dynamic balance under simultaneous action of an unknown disturbance and time-optimal control is considered. Optimal control is calculated along the phase trajectory, and it is periodically updated for discrete phase coordinate values. It is proved that the phase trajectory comes to the dynamic equilibrium point and makes undamped periodic motions (a stable limit cycle). The location of the dynamic equilibrium point and the limit cycle form are considered as functions of different parameters. With the disturbance calculated in the process of control, the accuracy of transferring to the required final state increases. A method for estimating attainable accuracy is presented. Results of simulation and numerical calculations are given.