Vectorized Trigonometric Regularization for Singular Control Problems with Multiple State Path Constraints.

Optimal control problems (OCPs) with a control-affine Hamiltonian may lead to extremal solutions with singular control arcs. The presence of singular control arcs along with multiple nonlinear state path inequality constraints introduces numerical complications during the solution process. Leveraging the primer vector theory of Lawden, we propose an alternative derivation of extremal control expressions for solving OCPs with mixed regular and singular control arcs and in the presence of multiple state path inequality constraints. As an application, we consider the classical Goddard rocket vertical ascent problem with bounded thrust control and two state path inequality constraints on the magnitude of the dynamic pressure and velocity. In addition, an analysis of the switching function time history for OCPs with singular control arcs and state path constraints is presented. The results demonstrate that the proposed method offers noticeable implementation simplicity and provides more accurate solutions with respect to approximating singular control arcs and in capturing the switch instants between different control arcs when compared against a direct optimization method. [ABSTRACT FROM AUTHOR]