Time-optimal steering of an object moving in a viscous medium to a desired phase state

The two-point problem of the time-optimal attainment of a desired phase state by a multidimensional dynamic object is investigated. The motion occurs in a viscous medium by means of a limited force. The open-loop and/or feedback control laws constructed by numerical-analytical methods for arbitrary initial data. An asymptotically approximate solution of the maximum principle boundary-value problem is presented for short and long time intervals. The singularities of the optimal trajectory are established for the initial and final parts of the motion. The solution obtained of the two-point problem of the optimal control of the motion of a dynamic object in a homogeneous viscous medium by means of a force of bounded modulus is compared with the known solutions in special formulations.