A fast, robust numerical method for solving optimal control problems

Generalized Lagrange Multiplier, combined with Quasi-Newton´s method, is proposed for fast solving terminal constrained optimal control problems. The control variables are discretized and the optimal control problem is converted into Nonlinear Programming (NLP) with 4th Admas predict-modification scheme as integrating procedure. Generalized Lagrange Multiplier (GLM) is introduced to eliminate constraints in NLP, and the obtained unconstrained NLP is solved with Quasi-Newton´s method. Numerical experiments on a simple nonlinear optimal control problem and the complicated lunar soft landing problem demonstrate efficiency, robustness and good accuracy of this method.