Аннотация:The problem of maximization of the horizontal coordinate of mass-point
moving in the vertical plane driven by gravity, viscous drag, and thrust is considered.
The slope angle and the thrust are considered as a control variables. The problem is
related to the modified brachistochrone problem. Principle maximum procedure
allows to reduce the optimal control problem to the boundary value problem for a
system of two nonlinear differential equations. The qualitative analysis of the
trajectories of this system is performed, and the robust properties of the optimal
solutions are determined. Optimal controls depending on the state variables are
designed. Characteristic features of the designed controls allow to construct quasioptimal
solutions for the more complex systems, where phase plane method is not
applicable.