A new DMOC-based approach to solve Goddard rocket problem

A new methodology - DMOC (Discrete Mechanics and Optimal Control) is presented to solve the classic Goddard rocket problem. This method firstly discretizes the Lagrange-d´Alembert principle for the rocket system, the resulting forced discrete Euler-Lagrange equations then serve as constraints for the optimization of a given cost functional. Therefore the optimal control problem is converted into a nonlinear programming (NLP) problem, which is modelled in AMPL (Advanced Mathematical Programming Language) and solved in a solver named as IPOPT (Interior Point Optimizer). Finally, the DMOC-based approach successfully solves the Goddard rocket problem, which is a terminal free, singular optimal control problem with path constrain; the results are proved reliable and effective by comparison with the results of conventional solution and statistical analysis.