A Modified Brachistochrone Problem with State Constraints and Thrust

Abstract

The problem of maximizing the horizontal coordinate of a mass point moving in a vertical plane driven by gravity, viscous drag, curve reaction force, and thrust is considered. It is assumed that inequality-type constraints are imposed on the angle of inclination of the trajectory. The system of equations belongs to a certain type that allows us to reduce the optimal control problem with constraints on the state variable to the optimal control problem with control constraints. The sequence and the number of switchings of the state constraints along the optimal trajectory are determined, and a scheme for optimal control is designed.