A Proximal Method for the Numerical Solution of Singular Optimal Control Problems Using a Modified Radau Collocation Method

摘要

A proximal method is developed for solving optimal control problems whose solutions contain a singular arc. The method employs a regularization technique previously established in literature using a modified Legendre-Gauss-Radau (LGR) orthogonal direct collocation method. The cost functional of a singular optimal control problem is modified by the addition of an integral term and then transcribed into a nonlinear programming (NLP) problem using a modified LGR collocation scheme. This modification to the optimal control problem transcribes the original singular NLP into a nonsingular NLP that is now solved iterativcly until an approximation of the original singular solution is achieved within some error tolerance. Finally, the accuracy and effectiveness of this proposed method is demonstrated on an optimal control problem with a known solution whose structure is bang-singular.