Abstract
The problem of maximizing the horizontal coordinate of a point moving in a vertical plane under the action of gravity forces, viscous friction, and the interrelated Brachistochrone problem are investigated. It is assumed that inequality-type constraints are imposed on the trajectory inclination angle. The optimal control problem with state constraints is reduced to the problem with control constraints. As a result, the sequence and the number of the reaching the phase constraints for the original problem are determined and the synthesis of the optimal control is designed.
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