Direct optimization methods applied to a nonlinear optimal control problem

The paper compares the direct collocation with nonlinear programming method and the quadrature rule scheme in the category of direct optimization methods. It is pointed out that the original quadrature rule scheme produces control discontinuities as the result of discrete computation of the state variables. The paper proposes a modified quadrature rule scheme that combines the original quadrature rule scheme with the idea of control smoothing that characterizes the direct collocation with nonlinear programming method. These direct optimization methods are applied to the problem of dynamic soaring of a glider, formulated as a nonlinear optimal control problem. The solutions by the direct methods excluding the original quadrature rule scheme are consistent, and it is demonstrated that a glider is capable of making an energy balanced flight of dynamic soaring.